Bureaucratic Efficiency and Democratic Choice Randy Cragun December 12, 2012
Results from comparisons of inequality databases (including the UN-WIDER data) and red tape and corruption indices (such as those from Business International now published by The Economist Intelligence Unit) have consistently found positive relationships between inequality and corruption and inequality and red tape (Apergis, Dincer, and Payne, 2010; Huther and Shah, 1999; Judge, McNatt, and Xu, 2011; Lambsdorff, 1999; Mauro, 1995; You, 2005). Most effort has been placed on explaining corruption, but to the extent that red tape (as opposed to corruption) is not a hidden activity, the potential gains from policies combating this supposed inefficiency may be high. Previous work on red tape has cast it as arising as a sorting mechanism under incomplete information (Banerjee, 1997), a result of poor performance incentives for bureaucrats (Banerjee, 1997), or as a means of reducing corruption (Wilson, 1989). However, we ought first to attempt to explain bureaucratic efficiency without notions of imperfect information or conflict within the firm. In this paper, we wish to give red tape a little more respect than usual: here red tape is the differential cost of producing government services under different managers or the difference between tax receipts and government spending and transfers. Those who manage government resources are chosen rationally and produce government resources out of tax receipts using the most efficient means available to them. In this way, we can treat government production similarly to how we treat private production. We show that red tape is increasing with inequality.
Model There are a large number of price takers. Individuals have common convex preferences over consumption and leisure ordered by ( ) such that. They choose how to allocate a unit of time between leisure and labor ( ). People have different levels of productivity ( ] and income units of. The distribution of is common knowledge, as is the productivity level of each person. There is no saving. Consumption for the individual is ( ) (1) where is the tax rate and is a government rebate. The ruler chooses the tax rate that is used to pay for a uniform rebate with some waste, which is a proportion of tax receipts. The ruler s productivity determines the proportion of tax receipts that can be used for transfers. I.e., the government budget constraint (or production function for government services) is 1 (2) where is per capita income and is the productivity of the ruler. is excluded from the sample space, because it induces for any level of. Note that the salary of the ruler is assumed to be negligible in the government budget. 1 An alternative specification could let the value of the rebate depend on the ruler s production, which is a function not only of his productivity but also of his work effort. However, this is a simple model of the case where the ruler is easily removed from office. We are viewing the democratic ruler as a public employee hired from a perfectly competitive market. Thus, he works as much as any other person of his type. As we will see, labor income (production) is ordered by productivity, so the specification here is just a useful simplification. In order to relax this (admittedly extreme) structure a little, we could allow the ruler and the voters to contract some level of pay and work effort. Under this case, the ruler s pay could not be a negligible portion of the budget, because if it were, for any given ( ) if, the people would always want to offer the ruler a higher salary to increase the amount of the rebate (since the marginal cost of doing so would be zero).
The order of play is thus: 1. Voters elect a ruler from among themselves. 2. The ruler chooses the tax rate. 3. Each person chooses their, the tax policy is implemented, and the rebate is dispersed. Equilibrium Consumer problem: For a given ( ), an individual with ability chooses his work effort to satisfy ] ( ) ] (3) which is given by ( ) ( ) ] ( ) ] (4) Then those with lower than ( ) ( ) ( ) ( ) (5) do not work and consume. Person earns income ( ). Consumption is a normal good, so is increasing in. Leisure is also normal, so is decreasing in (formal proofs of these results were derived by Meltzer and Richard, 1981). Increasing decreases the marginal cost of leisure and also makes the individual less wealthy, which decreases, so is decreasing in. ( ), since no person wishes to work if her entire income is taxed.
Political Problem: The value of the rebate is zero for both and and is positive for at least one value between these (since zero consumption is the worst possible outcome for any person), so we assume that for each there is a tax rate that maximizes the rebate. Then each rebate production function (or government budget constraint) forms a sort of Laffer curve, as in Figure 1, which we assume for simplicity to be strictly concave to the -axis. For a higher, a greater rebate can be produced at any, as can be seen in the shift to a higher curve in Figure 1. However, this shift is not straight Figure 1: Government budget constraints. Higher curves are associated with higher ruler productivity. up. Since a low productivity ruler is bad at producing, a small increase in will have little impact on. As increases, the impact of on increases, so is decreasing in. does not uniquely determine, but no ruler would choose a tax rate above, since this would both decrease his effective wage and his rebate. Thus only the left side of the rebate production function is relevant and is uniquely determined by ( ]. If each ruler has a favorite (call it ), then choosing a ruler (choosing ) determines all outcomes. Consider an individual s indifference curves in the ( ) space as in Figure 2. The central observation to be made about this preference mapping is that as becomes larger relative to the individual s overall wealth, the indifference curves become less steep. This is because a
higher reduces the importance of labor income, so changes in have little impact on wealth. This produces a few important results: 1. The indifference curves are concave to the -axis and convex to the -axis. As increases along an indifference curve, people substitute away from labor, so is a larger portion of their wealth. Figure 2: Indifference mapping for a single person. Utility is increasing to the North-West. 2. If is sufficiently low, as and increase along the indifference curve, the individual reaches a point where ( ) and additional increases in do not affect her wellbeing. Beyond this point the indifference curve is flat. Note that for any this point is reached at least by. 3. Higher indifference curves (increasing while holding fixed) are flatter. 4. More productive people have steeper indifference curves. As the labor income of the person increases, changes in represent a smaller portion of wealth and changes in exert a greater effect on wealth. This effect can be seen in the transition from the red preference field to the blue preference field in Figure 3. The shift in the point of tangency with the rebate production curve illustrates the result that for a fixed a higher induces a weakly lower favorite (strictly lower if ).
Meltzer and Richard (1981) proved the result of point 4. They showed that if, each person has a favorite value of and these choices are inversely ordered by pre-tax labor income, which is ordered by productivity. The same argument shows that optimal choices of t are inversely ordered by constant. for any Figure 3: Indifference curves for a low productivity person (red) and a high productivity individual (blue). In contrast, if increases, each person may desire a higher. At the same tax rate each person is wealthier because the rebate increases. Thus each person will work less and consume more. Because they work less and have higher non-labor income, increases in have a smaller effect on their wealth. But increases in have a larger impact on when is higher, so there may be times when each person will want a higher. Notice, however, that for near, a higher constraint has a lower slope since is decreasing in. The preferred level of will certainly not rise if falls below the initial favorite. On the other hand, with near, a higher constraint has a higher slope, so the preferred tax rate for any given individual is more likely to rise as increases. As we will see, when inequality is high, the decisive voter is more likely to desire a near. Thus we have that: 5. A higher induces a lower preferred when is fixed.
6. A higher may induce a higher or lower preferred t for any given person (but more productive workers are more likely to see their preferred increase). We assume that effect 5 dominates effect 6. In other words, we are asserting that as increases, the tax rate preferred by the ruler ( ) decreases. This is equivalent to claiming that the shift in indifference curves when increases and the fall in from an increase in are large compared to the shift up in the government budget constraint. We believe the case is compelling, but further study should evaluate this claim more rigorously 2. It is important here to remind the reader that when is low,, since the ruler does not work. Consider also the fact that a ruler with above-average pre-tax labor income must prefer, since taxing would redistribute wealth away from him to the poor. Thus there exists a locus of ( ) choices as seen in the thick purple curve in Figure 4. initially rises and then falls as increases and is inversely ordered by. Figure 4: Rulers' policy choice locus. Each light pink indifference curves is for a ruler of a different ruler type and is associated with one budget constraint. The policy choice locus is the thick purple curve. 2 An initial attempt with Cobb-Douglas preferences suggested that the each ruler s indirect utility of taxation function had as many modes as there were productivity types. This might undermine the assertion here, but as the number of types diverges, the function might become unimodal.
Each voter chooses her favorite point on the rulers policy locus as in Figure 5. It is easy to see that the ideal policy (a choice of ) for any voter whose income is below the mean satisfies because the ( ) locus is never tangent to a government budget constraint. We assume for simplicity that the policy space over which voters are choosing is { ( )}, where is the lowest ruler productivity that induces Figure 5: Each voter chooses their favorite point on the policy locus. Indifference curves are shown for a low x voter (red) and a high x voter (black).. Then is the favorite policy of each voter with income above the mean. We can also see that there is some such that if and only if and that ( ) { ( ) ( ]} and { ( ]}, where is the for a ruler of type and ( ) is the rebate chosen by a ruler of type. Thus no person will have a favorite policy, because they can get a lower tax rate and a higher rebate from a ruler of type. However, even above this point, if the ruler choice locus is still downward sloping, they can still get a lower tax rate and higher rebate as long as, where is the tax rate that maximizes the rebate on the ( ) locus. Thus the favorite policies of voters are bounded above by some that would incude. Again, only the left side of the ( ) locus matters. Then there exists a set of low productivity voter types for whom is the optimal choice. This set corresponds to the set of voters whose indifference curves are flat at the point on the ( ) locus chosen by.
Note that if is the optimal policy for a person of type and is the optimal policy for a person of type, then and this inequality is strict if. Thus productivities weakly order optimal choices of ruler productivity. The median productivity voter is decisive. Due to standard assumptions of completeness of preferences and local non-satiation, any movement along the ( ) locus further away from the optimal point lowers utility for the voter. Thus preferences are single peaked over. Preferences over are a strictly monotonic and one-for-one transformation of preferences over { ( )}3, so preferences over the policy space (ruler productivities) are single-peaked. Inequality We can think of income inequality as divergence between the average labor income and the labor income of the person with median productivity. As the decisive voter s income falls relative to the average income (holding average income constant), his favorite falls and favorite rises, as in Figure 5. Conclusions It is apparent immediately that if there is any taxation and redistribution in the economy that there is also some waste in the sense that the total rebate does not equal the total tax receipts. However, the outcome here is also inefficient in the sense that in order to achieve a higher tax rate, a lower productivity decisive voter chooses a government budget constraint 3 An alternate proof allowing the policy space to vary over all productivities is possible if the median voter has a favorite policy in the interior of the policy space used here, but this proof is not included here because it is lengthy.
with a lower rebate for each tax rate. If when the median voter s income falls relative to the mean the voters and rulers could contract to raise the tax rate just a little while keeping the same ruler, every person would be better off. If the income of the decisive voter rises relative to the mean, we see a fall in and a shift to a government budget constraint with higher rebates for each tax rate, so we get less tax distortion and more efficient bureaucracy (or less red tape). Additional Thoughts Some readers might complain that the operationalization of red tape used here is not satisfactory. Red tape is typically seen as a purely wasteful process that is added on top of the costs of truly productive inputs to the government production function. However, there seems to be no a priori reason for this characterization other than prejudice from long days waiting in line at the Department of Motor Vehicles. This paper shows that government production of tax rebates is less efficient when inequality is higher without resorting to assumptions that governments produce inside the production frontier. These results apply only to the case of a democracy. According to You (1995), corruption seems to increase with inequality only in democracies, and we might expect a similar result for red tape, since corruption and red tape tend to be highly correlated and have typically been seen as arising from similar inefficiencies. Further research should focus on the outcomes in a dictatorship when government resources are produced from tax receipts and the dictator s productivity and work effort. Preliminary thoughts might suggest that a dictator would use higher rebates and lower taxes to appease the people and keep them from revolting.
However, a less productive ruler might be less capable of offering a sufficiently low tax rate for a given rebate. It is unclear how income inequality would affect the dictator s constraints and incentives. This paper assumes wages are fixed. Each person has a particular level of productivity in creating a homogenous good. In reality, the wage rate should be endogenous the model. A more complicated but interesting model would more fully specify the government resource production function and would recognize the opportunity cost inherent in the wages of each input (including the wage of the ruler). In such a model, it would not be true that every person would always want a higher for a given, since a more productive ruler would be more costly.
References Apergis, N., Dincer, O. C., and J.E. Payne. (2010). The relationship between corruption and income inequality in U.S. states: Evidence from a panel cointegration and error correction model. Public Choice, 145. Banerjee, Abhijit V. (1997). A theory of misgovernance. The Quarterly Journal of Economics, 112(4). Huther, J., and Anwar Shah. (1999). Applying a simple measure of good governance to the debate on fiscal decentralization. The World Bank, Policy Research Working Paper Series: 1894. Judge, W. Q., McNatt, D.B., and Weichu Xu. (2011). The antecedents and effects of national corruption: A meta-analysis. Journal of World Business, 46. Lambsdorff, J.G. (1999). Corruption in empirical research. 9 th International Anti-Corruption Conference, World Bank. Mauro, Paulo. (1995). Corruption and growth. The Quarterly Journal of Economics, 110(3). Meltzer, A. H., and S. F. Richard. (1981). A rational theory of the size of government. The Journal of Political Economy, 89(5). Wilson, J. Q. (1989). Bureaucracy: What Government Agencies Do and Why They Do It. Basic Books: New York. You, Jong-sung. (2005). A comparative study of inequality and corruption. American Sociological Review, 70.