This paper is based on an essay from my doctoral dissertation, submitted to the Department of Economics at the University of Pittsburgh in December 1990. I would like to acknowledge stimulating discussions with and numerous helpful comments from James Gassing, Max Corden, Avinash Dixit, Burkhard Drees, Douglas Gale, Edward Green, James Gordon, Josephine Olson, Joel Slemrod, Jan Svejnar, Neil Vousden, and the participants in an IMF seminar. Any errors are my own.
For similar opinions see Corden (1974, ch. 4), Sandmo (1976, p. 52), Atkinson and Stiglitz (1980, p. 455), Mirrlees (1986, p. 1199), Stiglitz (1987, p. 1038), Musgrave (1987, p. 259), Diamond (1987, p. 644), and Slemrod (1990, p. 163). One notable exception is Harry Johnson (1965, p. 7), who dismissed administrative costs as “of practical rather than theoretical consequence.”
The share of trade tax revenue in total tax revenue in developing countries in the mid-1980s ranged between 3.6 percent and 79 percent, the average for a group of middle-income countries being 23.2 percent. The corresponding extremes for the former socialist countries of Central and Eastern Europe were 1.6 percent and 16.1 percent, and the average was 6.4 percent. The average for the OECD countries was 1.3 percent (International Monetary Fund (1989)).
“Optimally” here refers to the requirement that tariffs raise a given amount of revenue at the smallest possible cost in terms of social welfare.
Commodity taxes also could be levied at a third point in this model -- the point of production. From the perspective of collection costs this is an intermediate case between the low-cost trade taxes and the high-cost consumption taxes. By assuming away this case we are forgoing some interesting theoretical questions, but because we are not constructing a theory of collection costs per se, but rather developing a case for such a theory, no loss of generality follows from this assumption.
The theorems in question state that if the government must raise a given amount of revenue without using the lump-sum taxes and wants to minimize the deadweight loss of the tax system, then, under the above assumptions, it should not impose differential factor taxes or other taxes that affect the production efficiency of the economy. The intuition behind this result is that, with no constraints on commodity taxes, any set of after-tax prices, including the optimal one, can be achieved with commodity taxes alone. The assumption of zero-profit income also plays a role in normalization and the choice of untaxed good (see below).
Opportunity losses suffered by taxpayers who choose to rearrange their activities as part of an avoidance or evasion effort represent distortion costs (excess burdens) in the traditional sense and hence do not constitute a component of collection costs.
Ideally, optimal tax rates and tax bases should be determined simultaneously for all taxes, but in our case this would make the government’s optimization problem too complicated. Yitzhaki (1979) solves this problem in a two-good (taxed/untaxed) model with the Cobb-Douglas utility and the recycling of tax revenue via lump-sum transfers. He obtains an intuitively plausible result that, in an optimum, the marginal cost (in terms of the utility loss) of raising an additional dollar of revenue via the tax base must equal the cost of raising this amount via the tax rate.
A more satisfactory modeling strategy would be to include such considerations as the resource costs of avoidance or evasion explicitly and not through a reduced form function for collection costs. Then one could pose questions such as, Is it better to go to third-best instruments such as tariffs or to step up enforcement activity for commodity taxes? (I am indebted to Professor Dixit for this remark.) However, factors determining collection costs are inherently difficult to model explicitly, and because the focus of this paper is to show that collection cost considerations can radically alter some long-held views on optimal commodity taxation, we opt for a simpler model.
For a discussion of the necessity of these conditions, see Diamond and Mirriees (1971 b), Section X.
These expressions are obtained as follows (for simplicity, we ignore collection costs):
For example, let σ22 = −1, σ11 = −, k = 1, (b1/C1) = 0.5, and (b2/C2) = 0.8. Then σ22/σ11 = 0.5, while (−k + b2/C2) / (−k + bl/C1) = 0.4.
σ10 and σ20 denote the compensated cross-elasticities of goods 1 and 2 with respect to the price of labor (commodity 0), i.e., with respect to the wage rate.
Notice that both goods cannot be substitutes for labor. We defined the commodity “labor” so that si0 = −s0i, i = 1, 2 and because the own-price effects are negative (−s00 < 0), at least one more element in the first row of the Slutsky matrix, −s01 or −s02, must be positive.
We are assuming only that the supply curves slope upward (X11 > 0 and X22 > 0) and that resources are limited, so when output in industry i increases, it must be on account of resources drawn from industry j (i.e., Xij < 0, i≠j). In our model, labor supply is ultimately limited by the time endowment T. Before that limit is reached, more labor could be supplied to both sectors by reducing leisure, so we must assume that X12 and X21 are not positive.
This term is positive, because λ (the marginal utility of income) and η (the marginal social value of a decrease in
A special case occurs when |−ϕ1|/Z1 = −ϕ2/Z2; then the reduction in domestic consumption/excess demand ratio should be smaller for the good with higher collection costs: if a1/Z > a2/Z2, then |(−ϕ1 + a1),/Z1| < (−ϕ2 + a1)/Z2.
Although the substitution term z22 is negative, the own-price elasticity of excess demand for exportables ζ22 is positive, because when the price of exportables increases, the domestic demand (which is lower than the domestic supply to begin with) decreases, while the domestic supply increases, thus increasing the excess supply, i.e., making the (negative) excess demand more negative.
This proposition is the missing part in the analysis of Riezman and Slemrod (1985). The result is indicated in a footnote as a direct implication of the first-order conditions for optimality, but it is not proved, nor does it follow trivially from these conditions. Interestingly, although many authors have derived the third-best properties of tariffs, none of them have done so directly, by comparing the changes in compensated demand caused by alternative taxes. Instead, most authors impose the requirement that the government expenditure must be financed using trade taxes alone. As a result, domestic producer prices no longer equal world producer prices, and domestic and foreign rates of transformation are no longer equal. (See, e.g., Dixit, 1985, pp. 339-340.)
Unlike Corden (1974, 1984), and Riezman and Slemrod (1985), who use the term “first-best” when describing a revenue-raising tax package in which tariffs figure alongside domestic consumption taxes, we use the more appropriate term “second-best,” as the first-best lump-sum taxes have been ruled out by assumption.
We adopt the convention that labels the demand as “inelastic” if the absolute value of its price elasticity is less than 1. For example. if σ22 = 1.5 and σ11 = 0.9, i.e., if σ22 < σ11, we nevertheless consider the demand for good 1 to be inelastic, because |σ22| > |σ11|.
Riezman and Slemrod (1985, 1987) tested the hypothesis that the use of tariffs as a revenue-raising device depends on the relative collection costs of tariffs versus other taxes and found that all three indices of relative collection costs -- degree of literacy, population density, and labor-force participation rate of women -- had the predicted negative sign and were statistically significant.