# TAX ARBITRAGE: Introducing limitations 4

When the tax-exempt asset is an argument in the utility function In this subsection we will briefly discuss another permutation, which will turn out to have an interesting connection to the simple model of Section 3. Assume that the outside asset X appears as an argument in the utility function. Formally, this means that we reformulate (16), with X as an argument in the utility function, and with p- 0:

where X is now an ordinary consumption good. In practice, we may think of X as housing, or some consumer durable. This model gives a representation of how housing appears in the labor supply decision of an individual in an economy with full interest deductibility; model (16) above has a closer resemblance to a world where X is raw land (which gives a constant yield of the consumption good, but which does not appear in the utility function). Working out the first-order conditions gives us solutions for the supply of labor, £(t, w, г, X), and for the demand for housing, X(r, w, r, X). These solutions will differ from those in section 3 in the sense that both first-order conditions of (24) will involve marginal utilities. Several implications follow.

# TAX ARBITRAGE: Introducing limitations 3

Everybody with a full income w + rX less than the right-hand side of (22) will be in a constrained optimum, while everybody with a full income that is greater than or equal to the right-hand side will be in an unconstrained optimum. Inherently poor individuals will face a binding credit constraint and a nonlinear tax system, and they will supply labor according to (21). Inherently rich individuals will face a perfect capital market and a linearized tax system, and they will supply labor according to (19).

We can now integrate (20) over all unconstrained individuals to obtain aggregate land demand. In equilibrium, this has to be equal to the total quantity of land available (which we for simplicity set equal to unity) read more:

where F(w, X) now is a joint cumulative distribution function. Equation (23) gives a solution for the endogenous variable r , or rather for the price of land, since r =rP.

# TAX ARBITRAGE: Introducing limitations 2

The complementary slackness condition (18) has important implications for the shape of the labor supply function. Individuals who face a binding quantity constraint in the credit market react to different labor supply incentives than individuals who are at an interior portfolio optimum.

Consider first the case of an interior solution, when (18) holds as an equality. For individuals for which X > 0, tax arbitrage is driven to the point where the after-tax return on the taxable asset equals p. For these workers, the constraint on short sales is not an issue, and labor supply is determined in a way that parallels our previous analysis. The relevant marginal tax rate is the yield ratio p / r , the same for everyone. It is easy to show that the behavioral functions take the form

i.e., the tax system is linearized. Compared with the analysis in section 3, the only novelty is that (19) and (20) include a wealth effect from the initial land endowment.

# TAX ARBITRAGE: Introducing limitations

Outside assets and constraints on short sales

As in the previous section, we model a situation when the only reason for asset trade is the desire to avoid taxation when marginal tax rates differ across individuals. But we now assume that the tax exempt asset is an outside asset in fixed total supply, and that this asset (which we for simplicity refer to as land) can not be sold short. We assume that land is productive, in the sense that each land unit produces p units of the consumption good further.

The introduction of land means that there is an additional layer of heterogeneity in the model. Each individual is now identified by the vector (w, X), where X is the initial land endowment.

# TAX ARBITRAGE: Efficiency and tax incidence 3

We see, first, that one has to take the non-negativity constraint on labor supply seriously. By (15), t can be negative for small values of w. We have therefore simply assumed that the parameters are such that labor supply will be positive, the parameter configurations in the (v, k) space not satisfying this being in the upper left part of Figure 2. For other, admissible, parameter configurations, we see that it is easy to find cases where both high- and low-income earners would gain from the introduction of tax arbitrage, i.e., where both Дя and AL are positive. Finally, a word of caution is warranted.

In this model, we have assumed that tax arbitrage is costless, and it is therefore hardly surprising that one can find cases where the introduction of such arbitrage is welfare-enhancing in the sense of Pareto. In practice, there are real resource costs associated with most tax avoidance schemes, ranging from transactions costs and legal fees to costs associated with an inefficient allocation of risk, consumption, and productive capital. For example, since much tax avoidance activities involve real estate, an important cost probably consists of an oversized housing sector, and the possibility that the introduction of tax arbitrage leads to a Pareto improvement then becomes correspondingly smaller.

# TAX ARBITRAGE: Efficiency and tax incidence 2

Thus the average individual would not be unharmed by the introduction of tax arbitrage. Even if she does not engage in asset trade, she would be harmed by the tax increase and thus suffer a fall in utility. The distribution of Л over income groups would therefore look like the dashed curve in Figure 1, showing a utility loss in the middle of the income distribution.
On the other hand, we can not rule out that the introduction of tax arbitrage leads to a budget surplus rather than a deficit. This would happen if the reduction of marginal tax rates for people with high wage rates leads to such a large increase in the labor supply among those people that it outweighs the fall in labor supply among those with low wage rates.12 Then the tax base would increase, and the government could reduce taxes. Thus the average individual would gain from the introduction of tax arbitrage, as would everybody else. The distribution of utility gains would then look like the dotted curve in Figure 1.

# TAX ARBITRAGE: Efficiency and tax incidence

Let us first consider a regime where no tax arbitrage is possible. The indirect utility of an individual with a wage rate w, i.e., the utility resulting from labor supply (1) and its corresponding consumption, is denoted by V(w) . Similarly, the indirect utility of the same individual under a regime where tax arbitrage is possible (i.e., the utility resulting from labor supply С and its corresponding consumption) is denoted by VA {w), where the subscript stands for ’’arbitrage”. The change in utility from introducing arbitrage is thus A = Va (w) – V(w) more.

# TAX ARBITRAGE: The Simple Model 5

Here, 0<v<l, and a lower value of v means a higher degree of progressivity, in the sense of disposable income being a more concave function of taxable income. For a given v, we use the parameter p to ensure a balanced budget, and for simplicity, we only deal with a purely redistributive tax system. One can easily show that within our tax arbitrage model, where everybody has the same taxable income, this implies

This corresponds to the supply function of the standard model (1), and it exhibits the well-known property that with logarithmic preferences and no initial wealth, labor supply is independent of the wage rate w.

# TAX ARBITRAGE: The Simple Model 4

We can obtain some characterizations of the equilibrium. Integrating (5) over all individuals, and using the Miller equilibrium condition (8), yields B(p !r)~ wt, where w£* is the average labor income in the economy. Substituting this back into (5), we obtain the individual’s demand for tax deductions in general equilibrium:

As we should expect, individuals with a higher-than-average labor income have a positive demand for tax deductions, while the opposite holds for those with lower-than-average income. Individuals with average labor income will not participate in the arbitrage process. Also, when the tax system is purely redistributive, and when the government’s budget is balanced, there is a simple relation between the curvature of the tax schedule and the relative asset yield. An often adopted measure of the degree of tax progression is the measure of residual tax progression more:

Our assumptions about the marginal tax rate imply that 0 Continue reading

# TAX ARBITRAGE: The Simple Model 3

This is intuitively reasonable. With unlimited tax arbitrage, high-income individuals issue taxable claims and hold tax-exempt claims, while low-income individuals hold taxable claims and issue tax-exempt claims. This process continues until all taxable incomes, and hence all marginal tax rates, are equalized. From an efficiency point of view, we may also note that this implies that

In the presence of tax arbitrage, individual marginal rates of substitution between consumption and leisure are proportional to the marginal rate of transformation (i.e., the wage rate). The factor of proportionality is to be regarded as a tax wedge, since p and r are unequal.
Combining (3), (4), and the budget constraint in (2) gives us labor supply t and asset demand X (or, rather, the demand for interest deductions rX):