Appendix: A Generalization of the Barro (1990) Model as a Benchmark
This appendix develops a simple generalization of the Barro (1990) model, which may constitute a useful benchmark to analyze the relationship between corruption and the composition of government expenditure. It shows that if corruption were to act simply as a proportional tax on income, the ratio of each component of government expenditure to GDP would be the same, no matter how corrupt or unstable the government.
Following Barro (1990), taxes are assumed to be levied as a proportion of income. The production function is assumed to be of the form:
where y is income per worker, A is a technological parameter, k is private capital per worker, and gj is the flow of public services from government expenditure of type i, per worker. This is the simple extension to N types of government expenditure of the production function in Devarajan et al. (1993).
Defining ϕi so that
where g is the total flow of public services from productive government expenditure per worker, the production function in (1) reduces to the Barro (1990) production function if N=1.
Barro (1990) examines two extreme cases: (i) A benevolent government maximizes the lifetime utility of the representative consumer, subject to the constraint that τ = g/y; solving for the optimal τ yields τ**=(g/y)*=α, (ii) A self-interested (infinitely-lived) government obtains consumption equal to Cg=[τ-(g/y)]y; that is, corrupt bureaucrats get to consume the “budget surplus” (τ represents the sum of a proportional tax rate and a proportional bribe rate); the self-interested government maximizes the present value of the future flow of utility derived from Cg, subject to t τ≥g/y.
In order to analyze the role of institutions in determining the composition of public expenditure, it is interesting to analyze the problem of a government that maximizes a weighted average of the lifetime utility of the representative consumer and of the lifetime utility derived from consumption by its self-interested members. The maximization program may be expressed as: choose τ and (g/y), subject to τ ≥ g/y, so as to maximize (1 ψ) U+ ψ Ug, with 0≤ψ≤1, and where U is the lifetime utility of the representative consumer and Ug is the lifetime utility of the self-interested government official.
Following Barro (1990), lifetime utility of the citizen can be assumed to be:
where ρ is the rate of time preference and σ is the inverse of the intertemporal elasticity of substitution. Similarly, lifetime utility of the self-interested government official can be assumed to be:
where θ is the sum of the government official’s rate of time preference and of her probability of death (a metaphor for government collapse, for analytical simplicity).
Cases (i) and (ii) analyzed by Barro (1990) are special cases of the above maximization program, where ψ=0 and ψ=1, respectively. The weight given to the lifetime utility of the self-interested government officials, ψ, may be taken to represent the degree to which the country is “corrupt”.
It can be shown that more corrupt (higher ψ) and the more unstable (higher θ) the government, the higher τ, and therefore the lower private investment and economic growth. This result is consistent with the observation that corruption reduces private investment and growth (Section III.2).
On the other hand, in this model, it can also be shown that the optimal share of government infrastructure services is independent of corruption and political stability; that is, (g/y)*=α, regardless of the weights assigned to the two classes of people and of the discount rate. A proof of this proposition can be obtained by simply taking derivatives of (1-ψ) U+ ψ Ug with respect to τ and g/y. A few pages of algebra yield the result.
The following condition relating to the composition of productive government expenditure maximizes the lifetime utility of both the representative consumer and the self-interested bureaucrat:
As a consequence, any government would choose the composition of expenditure implied by (5), regardless of corruption and political instability. Therefore, under the assumptions of the Barro (1990) model, and most notably that corruption act as a proportional tax on income, the ratio of each component of government expenditure to GDP would be the same, no matter how corrupt or unstable the government.
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Helpful conversations with Andrei Shleifer and Vito Tanzi are gratefully acknowledged. The views expressed here are strictly personal. The author does not necessarily agree with the subjective indices relating to any given country. This paper is forthcoming in the conference volume “Corruption and the World Economy,” edited by Kimberly Ann Elliott, Washington: Institute for International Economics.
An example of the former might be the decision by top ministers to purchase an expensive aircraft fighter in order to be able to obtain large bribes, while an example of the latter could be the request for a petty bribe by a public official in order to speed up the issue of a driver’s license.
Under poorly-organized corruption, the required amount and appropriate recipient of a bribe are not clear, and payment does not guarantee that the favor will be actually obtained. The uncertainty that characterizes poorly-organized corruption systems makes them even more deleterious (Shleifer and Vishny, 1993).
For a discussion of how government activities may bring about corruption see also Tanzi (1994), who stresses that the problem becomes worse when regulations lack simplicity and transparency.
Ades and Di Tella (1995) also argue that, in evaluating the effects of industrial policies, it is necessary to take into account the fact that they generate corruption as an unintended by-product.
One way in which the growth rate may be affected even for a given investment rate is through changes in the allocation of resources among sectors (Easterly, 1990), and perhaps—more specifically—between the formal and informal sectors (Loayza, 1996).
The ICRG index covers all the 106 countries in the sample, while the BI index covers only 67 countries.
The index of ethnolinguistic fractionalization has a correlation coefficient of 0.39 (significant at the conventional levels) with the corruption index.
The simple correlation coefficients are 0.46 and 0.38 respectively, both significant at the conventional levels.
Strictly speaking, ethnolinguistic fractionalization and colonial dummies are only likely to be valid instruments for a country’s degree of institutional efficiency in a broader sense. Nevertheless, they are used in this paper mostly in order to address endogeneity problems that might be due to the subjective nature of the indices.
The analysis in this paper relies only on cross-sectional regressions using averages of the data over the sample period, as a country’s degree of institutional efficiency typically evolves rather slowly. At the same time, Mauro (1993) shows that the relationship between investment and corruption is significant in a fixedeffects panel.
The specification chosen here is the base regression in Levine and Renelt (1992) and includes initial per capita GDP, the initial secondary education enrollment rate, and the population growth rate.
Concerning the overall level of government expenditure, Levine and Renelt (1992) show that it does not seem to bear any robust relationship with economic growth. Previous work on the composition of government expenditure has been relatively limited. Devarajan et al. (1993) find that there is no clear relationship between any component of government expenditure and economic growth. Easterly and Rebelo (1993) do find some significant relationships: public investment on transport and communications is positively associated with economic growth, though not with private investment; public investment in agriculture is negatively associated with private investment; general government investment is positively correlated with both growth and private investment; and public enterprise investment is negatively correlated with private investment.
The reason why the various components of government spending are analyzed as a share of GDP is that the generalization of the Barro (1991) that is derived in the Appendix, which provides a useful theoretical benchmark, implies that if bribes could be levied just as easily on all income (rather than more easily on some government expenditure components than others), then the various components of government as a ratio to GDP should be unrelated to corruption.
Easterly and Rebelo (1993) provide a literature review on Wagner’s law and show that, in a panel of countries, several components of public spending rise (as a ratio to GDP) as income per capita rises.
This analysis is a first pass at the data. Future research could introduce additional control variables, such as the demographic structure of the population (a higher share of people in schooling age implies higher education expenditure), and indicators of the relationship with neighboring countries (the possibility of war raises defense spending).