Corruption, fiscal policy, and growth: a unified approach

Sugata Ghosh; Kyriakos C. Neanidis

doi:10.1515/bejm-2016-0010

Published by De Gruyter June 26, 2017

Corruption, fiscal policy, and growth: a unified approach

Sugata Ghosh and Kyriakos C. Neanidis

From the journal The B.E. Journal of Macroeconomics

https://doi.org/10.1515/bejm-2016-0010

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Abstract

We study the effects of bureaucratic corruption on fiscal policy and economic growth, where corruption (i) reduces the tax revenue raised from households, (ii) inflates the volume of government spending, and (iii) reduces the productivity of “effective” government expenditure. We distinguish between the policies pursued by (a) a non-optimizing, and (b) an optimizing government. For both cases, corruption leads to higher income tax and inflation rates and a lower level of government spending, thus hindering growth. In the circumstances, an activist government could allocate its resources in attempting to reduce the type of corruption that harms growth the most. Finally, the findings from our unified framework could rationalize the sometimes conflicting empirical evidence on the impact of corruption on growth in the literature.

Keywords: corruption; economic growth; non-optimizing and optimizing government; public expenditure and revenue

JEL Classification: D73; E60; O42

Acknowledgements

We would like to thank participants at the 2014 Royal Economic Society Annual Conference in Manchester, where this paper was presented, and an anonymous referee for insightful comments and constructive suggestions. The usual disclaimer applies.

A Appendices

A.1 Appendix

Under the assumptions of dθ = 0 and dτ = 0, the matrix form expression of equations (15) and (16) is

(22)[a11a12a21a22][dγdR]=[a13a14a15a23a24a25][dηdχdλ],

where a₁₁ = 1 > 0, a12=−(1−τ)αbμ∂Δ∂R<0,a₁₃ = 0, a14=(1−τ)αΔμ1+σΔ1+σ∂b∂χ<0,a15=(1−τ)αΔμ1+σΔ1+σ∂b∂λ<0,a21=1b1−ΔΔ>0,a22=−[1−ΔΔ+(γ−R)1Δ2∂Δ∂R]1b<0,a23=−αμτ<0,a24=θε+(γ−R)1Δ1b21−Δ1+σ∂b∂χ, and a25=(γ−R)1Δ1b21−Δ1+σ∂b∂λ<0.

In obtaining the signs of a₁₄, a₁₅, a₂₄, and a₂₅, we have used equation (5) and the expression of b from the output per capita equation (3), from where it can be shown that ∂b/∂χ < 0 and ∂b/∂λ < 0.

Using equation (22), we can derive the inflation and growth effects of a change in corruption related with the collection of tax revenues; that is, of a lower η. These are

(23)dRdη=a11a23−a21a13Det,

(24)dγdη=a13a22−a23a12Det,

where “Det” is the determinant, for which the expression is provided in equation (30) below.

Using equation (22) again, we can derive the inflation and growth effects of a change in corruption related with the procurement of public goods; that is, of a higher χ. These are

(25)dRdχ=a11a24−a21a14Det,

(26)dγdχ=a14a22−a24a12Det,

Finally, using equation (22) we can derive the inflation and growth effects of a change in corruption related with the productivity of public goods; that is, of a higher λ, as

(27)dRdλ=a11a25−a21a15Det,

(28)dγdλ=a15a22−a25a12Det,

In equations (23)–(28) the determinant is given by

Det=a11a22−a21a12=−[1−ΔΔ+(γ−R)1Δ2∂Δ∂R−1−ΔΔ1Δ∂Δ∂Rγ]1b.

Using equation (11), we find

(29)∂Δ∂R=ΔRσ1+σ11+(q1−q)(Rr)σ1+σ>0.

So, the determinant becomes

(30)Det=−1b1Δ11+σ1+σΔγR1+(q1−q)(Rr)σ1+σ<0.

Using equation (30) along with the expressions for a_ij defined above into the pairs of equations (23)–(24), (25)–(26), and (27)–(28), respectively, we obtain that dR/dη > 0, dγ/dη > 0, dR/dχ < 0, dγ/dχ < 0, dR/dλ > 0, and dγ/dλ < 0, which form the basis for Proposition 1.

A.2 Appendix

Under the assumptions of dθ = 0 and dR = 0, the new matrix form expression for the set of equations (15) and (16) now is

(31)[b11b12b21b22][dγdτ]=[b13b14b15b23b24b25][dηdχdλ],

where b_ij = a_ij except for b12=αbμΔ>0 and b22=ηαμ>0.

Using equation (31), we can derive the income tax rate and growth effects of a change in corruption related with the collection of tax revenues; that is, of a lower η. These are

(32)dτdη=b11b23−b21b13DET,

(33)dγdη=b13b22−b23b12DET,

where “DET” is the determinant, for which the expression is provided in equation (38) below.

Using equation (31) again, we can derive the income tax rate and growth effects of a change in corruption related with the procurement of public goods; that is, of a higher χ. These are

(34)dτdχ=b11b24−b21b14DET,

(35)dγdχ=b14b22−b24b12DET,

Finally, using equation (31) we can derive the income tax rate and growth effects of a change in corruption related with the productivity of public goods; that is, of a higher λ, as

(36)dτdλ=b11b25−b21b15DET,

(37)dγdλ=b15b22−b25b12DET,

In equations (32)–(37) the determinant is given by^[31]

(38)DET=b11b22−b21b12=b22=η+Δ−1>0.

Using equation (38) along with the expressions for b_ij defined above into the pairs of equations (32)–(33), (34)–(35), and (36)–(37), respectively, we obtain that dτ/dη < 0, dγ/dη > 0, dτ/dχ > 0, dγ/dχ > 0, dτ/dλ > 0, and dγ/dλ < 0, which form the basis for Proposition 2.

A.3 Appendix

Using the restrictions that dτ = 0 and dR = 0, the new matrix form expression for the set of equations (15) and (16) now is

(39)[c11c12c21c22][dγdθ]=[c13c14c15c23c24c25][dηdχdλ],

where c_ij = a_ij except for c12=−(1−τ)αΔμ1+σΔ1+σ∂b∂θ<0 and c22=−[1+χε+(γ−R)1Δ1b21−Δ1+σ∂b∂θ]<0.

Using equation (39), we can derive the effects of a change in corruption associated with the collection of tax revenues (a lower η) on government expenditure and growth. These are

(40)dθdη=c11c23−c21c13Det′,

(41)dγdη=c13c22−c23c12Det′,

where “Det” is the determinant, for which the expression is provided in equation (46) below.

Using equation (39) again, we can derive the effects of a change in corruption associated with the procurement of public goods (a higher χ) on government expenditure and growth. These are

(42)dθdχ=c11c24−c21c14Det′,

(43)dγdχ=c14c22−c24c12Det′,

Finally, using equation (39) we can derive the effects of a change in corruption associated with the productivity of public goods (a higher λ) on government expenditure and growth. These are

(44)dθdλ=c11c25−c21c15Det′,

(45)dγdλ=c15c22−c25c12Det′,

In equations (40)–(45) the determinant is given by

(46)Det′=c11c22−c21c12=R1−ΔΔ1b2∂b∂θ−(1+χε).

Multiplying and dividing through equation (46) by θ, and using equations (3), (6) and that ∂b/∂θ = (1 – β/β)(b/θ), yields

(47)Det′=1θ[R+γσΔ1+σ1b1−ΔΔ1−ββ−gy],

the sign of which is in general ambiguous. The sign depends on the relative size of total spending on public goods and services (as a fraction of GDP). If this ratio is large, then Det′ < 0 and the effects captured by equations (40)–(45) can be assigned the following signs: dθ/dη > 0, dγ/dη > 0, dθ/dχ < 0, dγ/dχ < 0, dθ/dλ < 0, and dγ/dλ < 0. If g/y is relatively small, the opposite effects take shape. These findings form the basis for Corollary 3.1.

B Appendix

B.1 Appendix

The economy is populated by two types of agents, households and bureaucrats, of which bureaucrats are divided into those that oversee the collection of tax revenue and those that deal with the procurement of the public good. In these two classes of bureaucrats, there are in place both honest and corrupt public officials. This description of the structure of our economy shows that there is no such thing as one representative agent. Therefore, when the benevolent government is deriving the welfare criterion, Ω in equation (18), it takes into account the discounted lifetime utility of all agents. Given that utility is solely based on consumption during the second period of the agents’ lives, the appropriate measure of welfare is a function of the total level of consumption in the economy during the agents’ lifetime.

The income of households and the legal income of bureaucrats are saved with the financial intermediaries, while the illegal income of bureaucrats is saved “under the mattress.” This means that only the income saved through banks is subject to an uncertain rate of return conditional on the probability of the agent’s relocation. The illegal income, on the other hand, carries no rate of return. This latter income is represented by the total amount appropriated by corrupt bureaucrats: (1 – μ)[(1 – η)τw_t + χεθy_t]. This illegal income, however, is not included in the government’s social welfare function given that the government knows the proportion of corrupt bureaucrats, and thus the size of their income. In other words, the government considers in its welfare function only consumption that arises from legal income.

From equations (18), (1), and (8), the benevolent government maximizes

(48)Ω≡∑t=0∞ρtUt,

where

(49)Ut=−q[(1−τ)wtit]−σσ−(1−q)[(1−τ)wtIt]−σσ,

subject to the economic growth rate equation (12) and the government budget constraint equation (14), which we re-write both here for convenience

(50)γ=(1−τ)αbμΔ(R,r),

(51)(γ−Rb)[1−Δ(R,r)Δ(R,r)]+ηαμτ=(1+χε)θ+(1−μ)αμ.

Using equations (3), (4), (5), (9), and (10) into equation (49), the latter becomes

Ut=−1σ{q[(1−τ)αμRq[1−Δ(R,r)]]−σ+(1−q)[(1−τ)αμβb1−qΔ(R,r)]−σ}(bkt)−σ,

or,

(52)Ut=−1σ{[(1−τ)αμ]−σY(R,r)}(bkt)−σ,

where^[32]

Y(R,r)≡q1+σ[R[1−Δ(R,r)]]−σ+(1−q)1+σ[βbΔ(R,r)]−σ>0.

Using equation (52) and the growth rate equation (50), some algebra reveals that equation (48) becomes equation (19), or

(53)Ω=−(bk−1)−σσ(γσ−ρ){[(1−τ)αμ]−σY(R,r)}.

Solving for the benevolent government’s optimization problem, which amounts to maximizing equation (53) subject to equations (50) and (51) with respect to the three fiscal policy instruments (τ, θ, and R), the optimality conditions are given, respectively by

(54)Ωσ(11−τ)(2γσ−ργσ−ρ)+λ(αμ)(1−Δ−η)=0,

(55)−Ωσ(1−ββ)(1θ){(1γσ−ρ)[γσ(2+σ(1+Δ)1+σ)−ρ]}−−Ωσ(1−ββ)(1θ){(1Y)(11+σ)[σΔY+(1−q)1+σ(βbΔ)−σ]}++{1+χε−(1−ΔΔ)(1b)(1−ββ)(1θ)(11+σ)(R+γσΔ)}=0,

(56)−Ωσ{(σγσγσ−ρ)(1−Δ)+(1Y)[σ(1−Δ)Y+q1+σ[R(1−Δ)]−σ]}++λ(1b)(1−ΔΔ)(R+γσΔ)=0,

where λ is the Lagrange multiplier associated with the government budget constraint and ∂Δ/∂R and ∂Y/∂R are as defined in the text.^[33]

Next, combining equations (54) and (55), and simplifying, yields

(57)(11−τ)(2γσ−ργσ−ρ){1+χε−(1−ΔΔ)(1b)(1−ββ)(1θ)(11+σ)(R+γσΔ)}=−(αμ)(1−Δ−η)(1−ββ)(1θ){(1γσ−ρ)[γσ(2+σ(1+Δ)1+σ)−ρ]}−−(αμ)(1−Δ−η)(1−ββ)(1θ){(1Y)(11+σ)[σΔY+(1−q)1+σ(βbΔ)−σ]}+,

while combining equations (54) and (56), yields

(58)(11−τ)(2γσ−ργσ−ρ)(1−ΔΔ)(1b)(R+γσΔ)=−(αμ)(1−Δ−η){(σγσγσ−ρ)(1−Δ)+(1Y)[σ(1−Δ)Y+q1+σ[R(1−Δ)]−σ]}.

These two reduced optimality conditions, (57) and (58), which define the two implicit functions J₁(·) and J₂(·) in the text, along with the government budget constraint (14), are used to solve for the three (second-best) optimal fiscal instruments, θ*, τ*, and R*. These expressions, however, are highly non-linear, and as a result explicit solutions for the optimal fiscal instruments, and of the effects of corruption, cannot be obtained. For this reason, we rely on numerical simulations, as discussed in the text.

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Published Online: 2017-6-26

Corruption, fiscal policy, and growth: a unified approach

Abstract

Acknowledgements

A Appendices

A.1 Appendix

A.2 Appendix

A.3 Appendix

B Appendix

B.1 Appendix

References

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