Thresholds, informality, and partitions of compliance

We use ‘taxpayers’ as shorthand for the universe of firms or individuals (not restricting it to those who actually do or should pay tax).

There are other considerations in the optimal choice of threshold not addressed here. It may for instance be desirable to tax smaller firms, even if the costs of doing so exceed the revenue raised, in order to reduce the distortion of competition between taxed and untaxed firms (Keen 2013). Some also see political economy benefit in levying some charge on even the smallest taxpayers as a way of encouraging them to hold policy makers accountable (see for example OECD 2008). We abstract from these considerations here.

It is kinks that are exploited in the seminal work of Saez (2010) on the estimation of elasticities of taxable income.

Arrangements of this kind are sometimes also referred to as ‘slab’ or ‘cliff’ structures.

It is an essentially universal empirical finding that compliance costs relative to some indicator of size tend to fall with that indicator, and quite sharply at smaller sizes, so that any reasonable approximation of compliance costs will include a substantial fixed component. See, of many possible examples, European Commission (2004) and, for developing countries, Coolidge (2012). There is of course a large and growing literature on different types of tax or regulatory regimes which induce kinks and discontinuities of different types in incentive structures: see for example, in addition to Saez (2010), Bastani and Selin (2012), Almunia and López-Rodríguez (2013) and Garicano et al. (2013).

The perspective that we take on informality in this paper is thus very much tax-driven. There are of course others. There is, in particular, a long-standing interest in informality from a labor perspective: see the discussion in Kanbur (2009) and Chatterjee and Kanbur (2013). These differing perspectives can lead to quite different notions of ‘informality.’ For instance, OECD (2009), focusing on employment aspects, speaks of ‘Shoe shine workers in Cairo, street vendors in Calcutta: this is informal employment.’ That is perfectly reasonable from a labor market perspective; from a public finance perspective, however, it is far from clear that one would actually want these groups to charge VAT or remit income tax, and they may indeed be fully (or almost) tax compliant. Others will think of informality spanning a range of aspects of behavior, associated for instance with limited book-keeping, heavy reliance on cash transactions and the like. All this creates further difficulties and imprecision in the use of the term.

For definiteness, the discussion is for the most part cast in terms of ‘individuals’ or ‘firms’ and ‘income,’ but clearly many interpretations are possible.

This is in the spirit of related treatments in which entrepreneurs differ in ability and make some costly input choice (such as Dabla-Norris et al. 2008; Keen and Mintz 2004). This approach would lead to cut-offs of the kind discussed below but defined in terms of ability rather than potential income. The simpler representation of output decisions here facilitates analysis of the somewhat involved choice between the multiple regimes about to be described.

This of course is in order to abstract from distinct effects arising from the shape of the tax schedule. For developing countries, there is evidence—now rather dated, but still plausible (Gauthier and Gersovitz 1997; Gauthier and Reinnika 2001)—that larger firms tend to benefit more from exemptions, which would reinforce the pattern of compliance derived below.

In this case (and ignoring input costs) \(Y \)would be interpreted as potential sales revenue, with the assumption that this is independent of the tax system corresponding to an assumption that the consumer price is fixed—as would be the case, for instance, in a small economy open to trade in the commodity/ies of interest.

To keep things manageable, we preclude the possibility of splitting activity between more than one unit below the threshold (the legality of which will depend on the grouping rules for the tax in question).

For the welfare part of the analysis, it is assumed that these costs imply a real reduction in income, and are not simply a transfer.

Note the assumption here that the net income of those who entirely vanish from the tax system is independent of the threshold (one implication being that this category of behavior cannot plausibly be interpreted as including artificial splitting into more than one unit below the threshold)

Not all models of concealment imply an increasing \(\Gamma (Y)\): in the model of corrupt tax inspection in Hindriks et al. (1999), for example, the relationship between the equilibrium bribe and true income has an inverse-U shape. But nor is the present assumption entirely implausible: an increasing \(\Gamma \)is implied, for instance, if concealment costs are quadratic in the amount concealed. The general approach to modeling concealment costs here is in the spirit of, and discussed further in, Slemrod (2001).

For instance: adjusting is preferred to concealing at all income levels below \(\theta _{AC} \) defined in (3.11) below. Clearly \(\theta _{AC} >Z/(1-\lambda T)\), so that a sufficient condition for \(\theta _{AC} \) to exceed the highest income level, \(Z/\lambda \), at which mechanical under-declaration would put the taxpayer under the threshold is that \(\lambda >1/(1+T)\).

The interval on the right of (2.6) is larger, and the assumption in that sense more plausible, the greater is the excess of the proportionate loss of income from bounding, \(\gamma \), over the tax rate \(T\).

As a tie breaker, we assume that those indifferent between regimes select that preferred by those with slightly higher incomes.

This is certainly a simplistic view of administrative activity, which would, for example, appropriately also involve verifying claims of income below the threshold. But it captures a central cost concern of any tax administration. [Goyette (2012) provides an intriguing analysis of how the VAT threshold is implemented in Uganda, finding it to be focused more on employment than the turnover test by which the requirement to register is formally defined].

Ebrill et al. (2001) discuss and illustrate the applicability of this result. (In its original form, focused directly on the VAT, this also includes in the denominator the ratio of value added to sales, since value added is the effective base when a firm whose suppliers are subject to VAT is itself brought into the VAT).

This, it should be noted, is a simplified version of the most general problem considered in Keen and Mintz (2004), which goes further in taking account of taxed inputs and allowing output to depend on a labor input to which some disutility is attached.

Using \(\theta ^{\prime \prime }( Z)=0\) and simplifying, the second order condition is that \(W^{\prime \prime }( Z)=f( \theta )\theta ^{\prime }( {1-\theta ^{\prime }})-f( Z)-f( \theta )( {\theta ^{\prime }})^2-( {\theta -Z})f^{\prime }( \theta )\theta ^{\prime }<\) 0, for which it is sufficient that \(f^{\prime }( \theta )>0\).

The simulations in Keen and Mintz (2004), for the more complex of their settings noted above, indeed find thresholds optimally higher than \(Z^{KM}\); and not only for concave \(F\) but also for uniform (which in the present framework implies an optimal threshold unambiguously lower).

The proof, which is cumbersome, is omitted.

Note that the concern here is with multiple obligations, not with a single obligation that may take different forms (such as quarterly versus annual reporting for the VAT).

See for instance the description of small business tax regimes in Inter-American Development Bank (2013).

That \(\theta >Z_2 \), as drawn (and used in proving Proposition 6 below) follows from (4.2) and (4.1).

That \(\theta _1 <Z_2 \) follows from (4.3) and the negation of (4.2).

That \(\theta _2 >Z_2 \) follows from (4.5) and \(T_2 >0\).

As a way of thinking about the VAT, the model also neglects the links between firms that recent work suggests can be important in propagating or curtailing forms of non-compliance under the VAT (De Paula et al. 2010; Pomeranz 2011).