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«Abstract. This paper investigates analytically the welfare effects of black-market activities undertaken by firms to evade taxes. The desirability of ...»

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Efficient Black Markets?

Abstract. This paper investigates analytically the welfare effects of black-market activities

undertaken by firms to evade taxes. The desirability of a black market is linked to the attributes

of goods supplied by black-market firms. The analysis identifies cases where a black market

increases (reduces) the distortionary impact of taxation on the allocation of resources across the

goods that the government is attempting to tax, leading to a welfare gain (loss).

Keywords: black market, underground economy, shadow economy, tax evasion, optimal taxation JEL codes: H21, H26

1. Introduction By their nature, black-market activities are difficult to measure. Nevertheless, there is widespread agreement that black-market activities account for a significant portion of GDP in many countries.1 Less clear, however, are the welfare effects of such activities, particularly those motivated by tax evasion. In his leading undergraduate text on public finance, Rosen (2005, p. 353) states a second-best argument for why a black market, or an "underground economy," might be efficiency-enhancing in some cases: "Then under certain conditions, the existence of an underground economy raises social welfare. For example, if the supply of labor is more elastic to the underground economy than to the regular economy, optimal tax theory suggests that the former be taxed at a relatively low rate." But Slemrod and Bakija (2000, p. 156) expound an alternative view: "…because tax evasion depends on opportunities that are tied to particular activities, it provides an incentive--which is inefficient from a social point of view--to engage in those activities for which it is relatively easy to evade taxes."2 The first view focuses on the potential for the black market to increase incentives to provide resources to taxed activities, whereas the latter view emphasizes the distorting effect of the tax system on the allocation of resources across different taxed activities.3 The relative merits of these two views might seem to be purely an empirical matter, but the current paper argues that surprisingly sharp results can be obtained by placing both views Other terms for the “black market” are the “underground economy” and “shadow economy.” As reported by Schneider and Enste (2000), estimates of the size of the shadow economy as a percentage of GDP in the 1990-93 period ranged from between 8-10% for the U.S., Austria, and Switzerland to 24-30% for Greece, Italy, Spain, Portugal and Belgium. But fractions above two-thirds of GDP have been calculated for Nigeria, Egypt and Thailand. There are several reasons for the growth of the shadow economy, but the authors single out tax evasion as one of the most important. For recent reviews of the tax evasion literature, see, Andreoni, Erard and Feinstein (1998), and Slemrod and Yitzhaki (2002).

Many other studies emphasize the efficiency losses from tax evasion. See, for example, Usher (1984), Yitzhaki (1987), Slemrod and Yitzhaki (1995), Feldstein (1995), and Palda (1998).

Using data from 1980, Alm (1985) estimated the efficiency losses from the diversion of resources into the underground economy to lie between 100 billion and 220 billion dollars per year, where the latter figure represented nine percent of GDP. Both Alm's calculations and Kesselman's (1989) qualitative results about the extent and incidence of tax evasion are based on general equilibrium models in which tax evasion is associated with the production of particular goods. In our model, such goods are determined endogenously.

within a single model. Following Slemrod and Bakija, we model a set of activities that differ in the expected rewards from operating in the black market. In particular, our activities are distinguished by the levels of assets that the tax authority is able to seize in the event that tax evasion is discovered. Low-asset activities self-select into the black market because the potential fine from detection is relatively low. For simplicity, the model abstracts from the myriad other considerations behind the decision to enter the black market; in particular, all firms are randomly audited for tax purposes. Following Rosen, we next assume that the tax system distorts the decision of whether to devote resources to any taxed activity. In particular, activities are ranked by a continuous parameter called "quality," interpreted here as the attribute of a good produced by firms. Each consumer purchases at most a unit of a variable-quality good, with choices based on a heterogeneous "taste" parameter. Recognizing the costs involved in administering a qualitydifferentiated tax system, we assume that the government's expenditure needs are met by taxing all variable-quality goods at a uniform statutory rate. Such a tax system causes consumers with low tastes for quality to drop out of the market -- that is, they devote no resources to purchasing variable-quality goods, whereas those who remain reduce the qualities of the goods that they purchase.

With such a setup, we provide conditions that determine whether the black market consists of low- or high-quality goods. In the latter case, neither the Slemrod-Bakija nor Rosen arguments are relevant: a small black market (maintained through an appropriately low expected fine) does not distort consumption towards too much quality, because quality choices are already too low under a uniform tax; and it does not bring new consumers into the market for variablequality goods. This case illustrates how a black market can be desirable, even in the case where audits are costless, because it partially corrects the distorting effect that a uniform tax system has on the allocation of resources across taxed activities.





In stark contrast, both the Rosen and Slemrod-Bakija arguments appear relevant when the black market contains low-quality goods: allowing it to flourish brings some consumers back into the market for variable-quality goods, but it also distorts the choices of some existing consumers away from higher-quality "legal goods" and towards the lower-quality goods in the black market.

But we demonstrate analytically that these conflicting welfare effects do not favor a black market.

Thus, the potential for black markets to misallocate goods is found to depend systematically on where the black market is located. Black markets containing high-quality goods improve the allocation. With low-quality goods, the misallocation is so severe that it offsets any welfare gains from the ability of black markets to draw resources into taxed activities as a whole.

Rosen emphasizes the importance of black markets with low-income participants, noting that, "many observers believe that the underground economy is a crucial part of life in American inner cities." To the extent low-wage labor is relatively elastic, his second-best argument then suggests that black markets may satisfy both efficiency and equity goals. Our model does not deal with this potential equity argument, because it follows the optimal commodity tax literature by focusing on efficiency issues (i.e., risk-neutral firms and consumers). But if our low-quality goods are viewed as goods consumed by low-income taxpayers, our results raise the possibility that a government's efficiency and equity goals may be at odds with regard to black markets.

As described in the next section, our model departs from the optimal commodity tax literature by making adverse-selection problems a major part of the analysis. In particular, the black market is designed so that those firms that select it are the ones that the government desires to tax relatively lightly.4 Section 3 uses the model to determine whether the black market contains high- or low-quality goods. Our main proposition on the benefits of black-market There are now sizable literatures that incorporate tax evasion into models of optimal commodity taxation and optimal income taxation. See Slemrod and Yitzhaki (2002) for a review. For optimal commodity tax models, see Yitzhaki (1979), Wilson (1989), Boadway, Marchand, and Pestieau (1994), Cremer and Gahvari (1993) and Kaplow (1990). In contrast to our work, none of these papers consider the choice of risk-neutral firms between legal and black-market activities.

activities appears in Section 4. At the end of Section 4 we discuss some extensions of the analysis, and Section 5 concludes.

–  –  –

Consider an economy with a continuum of consumers, indexed by a taste parameter, α.

Each consumer is endowed with E units of a composite commodity, or “endowment good,” which may be interpreted as labor. To earn income, consumers supply this good to competitive private firms and the government at a price normalized to equal one. This income is used to purchase zero or one unit of a variable-quality good, at a price equal to P(θ) for a quality-θ good, and E – P(θ) 0 units of a homogeneous consumption good. In addition, all consumers receive the same G units of the public good. Utility is then given by

–  –  –

for a type-α consumer, where v is concave and σ is strictly concave. The parameter α possesses a continuous distribution, h(α), on [0,1], and the population is normalized to equal one. From (1), higher values of α represent a greater marginal willingness to pay for quality. Quality is treated as a continuous variable, in which case utility maximization yields the following first-order

condition at each θ 0 where P(θ) is differentiable:

–  –  –

By the second-order condition, the chosen θ is an increasing function of α. Under our subsequent assumptions about the cost structure, consumers with values of α below some positive level choose not to consume variable-quality goods.

The homogeneous consumption good is produced from labor via a linear technology. In contrast, there are two ways in which the variable-quality firms use the endowment good. First, it is sold directly to these firms as labor. Second, consumers may transform it into capital at a oneto-one rate, and then this capital is invested in these firms. For our purposes, the critical difference between labor and capital is that some of the capital remains after production has taken place (i.e., capital is durable), whereas an hour of labor services spent in production is an hour that is unavailable for other uses. Each unit of capital depreciates at rate δ, leaving 1 - δ units that can be transformed into numeraire consumption at the end of the production process. The consumer must be indifferent between supplying labor or capital. With the wage rate equal to one, the payment for each unit of capital must also be one.

The variable-quality goods are produced using a fixed-proportions technology, with each unit of a quality-θ good requiring W(θ) units of labor and A(θ) units of capital. (We later allow for substitutability in production.) Both W(θ) and A(θ) are increasing and convex in θ, and they also converge to a positive number as θ goes to zero. Thus, some costs are independent of quality. After the production and sale of output, the firm is left with assets of P (θ ) + (1 − δ ) A(θ ).

Since equilibrium profits equal zero under perfect competition, factor payments, W(θ) + A(θ), exhaust these assets in the absence of taxes. It follows that P(θ) = W(θ) + δA(θ) ≡ C(θ).5 For simplicity, we are assuming a zero interest rate over the production period, in which case the user cost of capital is the rate of depreciation.

With some costs independent of quality, the average cost of utility, C(θ)/v(θ), goes to infinity as the quality level goes to zero. It follows that nobody buys goods with qualities close to zero, and consumers with sufficiently low values of the taste parameter, α, choose not to consumer variable quality goods. We assume that C(θ)/v(θ) is U-shaped in quality.

The manner in which A(θ)/W(θ) varies with θ plays an important role in our analysis, for it determines which goods are drawn to the black market. There is no natural assumption to make concerning this issue. It is easy to think of examples in which the capital intensity of the production process is increasing in quality and others in which it is decreasing in quality. For an Zero profits would also hold if we instead assumed that firms are engaged in Bertrand competition, with more than one firm producing each good, or if we assumed a contestable market.

example of the former, consider the market for landscaping services, where it appears that capital intensity increases with the quality of the services provided. At the high end of the quality spectrum are the large outfits that come in and use heavy equipment to clear brush, grade a tract, and spread grass seed. At the other end of the spectrum are small teams of workers who rely largely on their own labor. In contrast, we would argue that the market for furniture provides an example in which capital intensity is decreasing in quality. Low-quality furniture is mass produced in large factories relying heavily on machinery and assembly lines, while high-quality furniture is often hand-crafted by artists who rely primarily on their own labor to produce the final product. Since there is no natural assumption to make concerning this issue, we consider both cases – that is, we examine the case in which A(θ)/W(θ) is increasing in θ and the case in which it is decreasing in θ. We derive remarkably similar positive results in both cases, but starkly contrasting normative ones.

To introduce taxes into the model, assume that the government finances its expenditure needs by imposing a tax at a constant rate, t, on the revenue from the sale of variable-quality goods. A discriminatory tax scheme (in which t depends on θ ) is assumed not to be available, perhaps because the informational requirements would be too costly. By auditing a firm, the government is assumed to learn the value of a firm's assets, but the value of θ cannot be deduced from this information because the government does not know the number of customers the firm has served.

By the zero-profit requirement, the price of a quality-θ good in the absence of tax evasion, or the “legal price,” is given by

–  –  –



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