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Honesty in a regulatory context – good thing or bad?
European Economic Review 45 (2001) 215}232
Honesty in a regulatory context } good thing or bad? Anthony Heyes* Department of Economics, Royal Holloway College, University of London, Egham Hill, Surrey, TW20 OEX, UK Received 1 May 1998; accepted 6 December 1999
Abstract It is often taken for granted that if more "rms were innately honest or ethical this would be a good thing. We use the example of pollution policy to dispute such a claim. If regulation is by pollution tax social welfare is non-monotonic in population honesty. The choice of policy instrument may itself be characterised by &reversals', with commandand-control methods being preferred for intermediate values of population honesty, a tax system being preferred at the extremes. This means that if } because of the spread of ðical shareholding' or for whatever reason } the honesty of the corporate population increases through time, we should not be surprised to see at "rst a switch away from market-based instruments, and then a switch back. Though environmental regulation is chosen as a context, the implications are more general. 2001 Elsevier Science B.V. All rights reserved. JEL classixcation: K4; K2; H8 Keywords: Pollution control; Honesty; Incentives
1. Introduction It is often taken for granted that if more "rms were innately honest or ethical in the way they behaved this would be a good thing. In this paper we use the * Fax: #44-1784-439534. E-mail address: [email protected] (A. Heyes). 0014-2921/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 4 - 2 9 2 1 ( 9 9 ) 0 0 0 7 6 - 8
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example of environmental regulation to show that such a claim cannot, in general, be sustained. If regulation is by pollution tax we show that } once optimal agency response is taken into account } social welfare is non-monotonic in the proportion of "rms that report emissions honestly. The choice of policy instrument may itself be characterised by &reversals' with command-and-control methods being preferred for intermediate values of population honesty, a tax system being preferred at the extremes. A heterogeneity argument underlies the main result. Consider a simple model of a tax regime based on (imperfectly veri"ed) self-reports in which tax plays an incentive role, as in the case of a tax designed to internalise an externality. It is not too surprising that such a regime may perform best } once optimal agency response is factored in } either when everyone is inherently honest or when everyone is inherently dishonest. When everyone is inherently honest the agency can achieve "rst-best by setting the tax-rate equal to marginal damage (i.e. at its Pigouvian level). Supposing, instead, that everyone is inherently dishonest and is able to get away with under-reporting some fraction m of their true emissions, the agency can achieve the same outcome simply by raising the tax-rate to (m/[1!t]) such as to maintain the e!ective rate. The regime performs less well when the population is a mixture of some who are routinely honest (i.e. do not exploit opportunities for evasion presented to them) and others who are not. Whilst the framework developed in this paper is somewhat more complex than this } incorporating di!erences in compliance costs, endogenous monitoring e!ort on the part of the EPA, etc. } the basic story is unchanged. The model is consistent with some stylised features of American regulatory history. It may, for example, provide a defence of the EPA's apparent willingness to tolerate a culture of under-reporting amongst those it is supposed to police. Though environmental regulation is used as an example for the purposes of exposition, the results are likely to be of more general interest. It is conventional in economics to model agents as rational cheaters } undercomplying with laws or under-reporting tax liabilities when enforcement parameters are such as to make such behaviour "nancially pro"table. There is compelling empirical and anecdotal evidence, however, to suggest that some
Thus, Cowell (1990) de"nes the rational taxpayer to be one predisposed to dishonesty: `2 the expression predisposed to dishonesty is used because we do not impute to the taxpayer any views about duty, honor or civic pride that would compel him to put some responsibility to the state ahead of his own money-grubbing interests2. Whilst virtue for its own sake may be laudable it is unexciting in terms of economic contenta (Cowell, 1990, p. 50). For two examples (amongst many) of the rational cheater in the environmental regulatory context see Harford (1987) and Heyes (1996).
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individuals and "rms are inherently honest or ethical. A feel for the scale of &honesty' in a compliance context can be had by setting all of the enforcement parameters (size of penalty, probability of apprehension, etc.) in econometrically estimated compliance functions equal to zero. So doing invariably implies a positive level of &unenforced' compliance which can be substantial (see, for examples, Magat and Viscusi, 1990; Gray and Deily, 1996). Limited attempts have been made to model the implications of routine honesty in enforcement contexts. Graetz et al. (1986) included a sub-group of routinely honest agents (&habitual compliers') in a standard income tax enforcement framework. Varying the prevalence of routine honesty in their model has no e!ect on optimal policy nor expected net tax revenue. Erard and Feinstein (1994) use numerical simulation to show the e!ect of including a sub-group of routinely &honest' taxpayers in a somewhat di!erent model. The model presented here is substantially di!erent } both in terms of set-up and results } from these. Tax here is going to have real e!ects } indeed that is the point of its use. In Erard and Feinstein (1994) and Graetz et al. (1986) agents are born into a model with an endowment, the size of which is privately observed, and the tax regime is designed to minimise dissembling. In the current model the tax-setting agency is not motivated by revenue-generation, nor does it care about dissembling per se. Rather, its objective in levying the tax is to internalise an externality and to create the &right' incentives for clean production. The existence of real impacts enriches the scope for welfare analysis substantially. Those welfare results turn out to exhibit interestingly non-monotonic features. These are not only signi"cant in their own right but also motivate study of the role of routine honesty for the comparative performance of alternative instruments and provide the scope for instrument &reversals'.
2. Model Each "rm in a population has access to an established pollution-control technology which allows it to restrict its emissions of some noxious substance to a level x at cost c(x) where c (x)(0, c (x)'0, ∀x50. We will refer to this as V VV See, for examples, Graetz et al. (1986), Levi (1988), Erard and Feinstein (1994), and many of the citations there-in. It is useful to distinguish individual from corporate honesty. The former may, however, be a key determinant of the latter. In the speci"c context of honesty of environmental reporting practices in the US Dimento (1986) emphasises `the individual idiosyncracies of top managementa (Dimento, 1986, p. 84). It is possible that a "rms motives for honesty may be self-serving. It may, for example, have employees or clients particularly unwilling to tolerate unethical behaviour. The term &pollution charge' is also often used. Revenue is implicitly assumed to be recycled in some welfare-neutral way.
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the &backstop' technology. The intensity of its application is assumed to be directly veri"able by the Environmental Protection Agency (EPA). For each "rm we can also de"ne the &least cost' abatement method to which it has access. The least cost technology allows it to control its emissions of the same noxious substance at a cost h .c(x) where h is distributed according to G G a density function f de"ned on the support [0,1], where f '0 for all x on that support. The associated cumulative will be denoted F. Some (but not all) "rms, then, are assumed to have access to a lower cost abatement technology than the backstop. Abatement by methods other than the backstop is not, however, directly veri"able by the EPA. It may involve application of new and/or context-speci"c technologies and/or practices that are inherently less transparent to an outsider. The EPA can either regulate by command-and-control (CC), or it can levy a pollution tax. Its objective is to minimise the sum of industry costs and environmental damage. The damage function is linear in aggregate emissions with the constant unit damage denoted d. In the stylised world described here CC means } given the unveri"ability of the alternatives } requiring use in some &amount' of the backstop technology. Under a tax regime the agency sets a tax t per unit of emissions and then requires each "rm to report its output of emissions. The report is assumed subject to some sort of (imperfect) veri"cation procedure. In particular, a "rm that chooses to do so is assumed able to &hide' (get away with not reporting) some fraction m of their true emissions, where m is some measure of the tightness or accuracy of the monitoring regime in place. In Section 3, we treat m as exogenous. Though unrealistic this allows for exposition of the key insights of the paper in the &cleanest' and most intuitive way. The model and results are generalised in Section 4 in which the m is endogenised and modelled as dependent upon the EPA's monitoring e!orts in the manner used by Xepapadeas (1995, 1997) and others in analogous contexts. Whilst endogenising the monitoring/enforcement programme creates } unsurprisingly } additional ambiguity in some places, the key results are preserved. The unconventional assumption in the model is with regard to the reporting behaviour of "rms. In particular, we assume that some proportion of "rms b are intrinsically &honest'. Honest "rms always tell the truth. The remaining fraction (1!b) are the rational cheaters of standard economic analysis, choosing the extent of under-reporting on the basis of expected "nancial costs and bene"ts
For some "rms h "1, the least cost technology is the backstop technology. The backstop G technology being universally available means h cannot exceed 1. G &Technology' should be interpreted broadly to encompass any method of abatement. It may, for example, take the form of changes in composition of inputs, work practices, etc.
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from such behaviour. The EPA knows b } the propensity to honest reporting across the population } but cannot tell which "rms are which. Comparative statics (positive and normative) with respect to b are a particular focus of the analysis.
3. The simple story } exogenous monitoring For the purposes of exposition we will start with the assumption that m is exogenous. Under a CC regime all "rms are required to use the backstop technology. The EPA stipulates and enforces the intensity of application associated with xH where, for the representative "rm !! xH 3min+c(x)#dx,. (1) !! Expected per "rm social loss under CC is, then, S¸(xH )"c(xH )#dxH , (2) !! !! !! where xH is implicitly de"ned by c (xH )"!d. Under a CC regime regulation !! V !! is input-based and b is not relevant. The EPA sets (optimally) the pollution target to be satis"ed and the technology to be used in achieving it, and polices it directly. Note that for a given distribution of abatement e!ort choice of technique is not cost-e!ective } "rms with h (1 have to use the backstop technology G despite knowing a cheaper way of doing the same thing. Furthermore, the distribution of e!ort across "rms is ine$cient } no mechanism exists for "rms with lower marginal compliance costs to reduce emissions more than do those with higher marginal costs. The calibration of the CC regime and the level of welfare delivered do not depend upon b. Consider, next, a tax-based regime. If "rm i is dishonest (denoted D) } a rational cheater of the sort familiar to economic modellers } then it chooses
In adopting to this approach we are following Graetz et al. (1986) and Erard and Feinstein (1994). The fraction of "rms b could be called &pathologically' honest. Our motivation here is expositional. If m is a measure of monitoring intensity, however, such an assumption could be motivated by the agency having a "xed monitoring/enforcement budget. Such an assumption } though unsatisfying in many ways } is a common one in the enforcement literature. These are the two &usual' shortcomings associated with CC (see e.g. Baumol and Oates, 1988, pp. 171}180). CC regimes are tied to the use of the backstop technology and do not, by construction, perform well under technological heterogeneity of the sort here.
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x to minimise the sum of abatement expenditures plus tax payments, i.e. G to minimise F(x , t"D)"h c(x )#t(1!m)x . G G G G H The interior solution x (t"D) is implicitly de"ned by G !(1!m)t c (xH(t"D))" . V G h G The analogous problem faced by an honest "rm is to minimise F(x , t"H)"h c(x )#tx G G G G H such that x (t"H) is characterised by
(3)
(4)
(5)
!t c (xH(t"H))" . (6) V G h G Eq. (6) is conventional in the case of a fully enforced tax. Eq. (4) is the same condition adapted to take account of the fact that the e!ective marginal tax rate for a D is (1!m)t. It is apparent that, other things being equal, a D emits more than an H, since the e!ective tax rate it faces is lower. Choice of technique in equilibrium is cost-e!ective } each "rm chooses the least cost way of doing the abatement it is doing. Combining (4) and (6) implies that marginal abatement costs are not equalised across "rms } the distribution of abatement e!ort across "rms remains ine$cient. The incentive e!ects of tax changes are qualitatively conventional. Implicit di!erentiation of (4) and (6) yields !(1!m) *xH(t"D) G " *t h ) c (xH(t"D)) G VV G
(7)
and *xH(t"H) !1 G " , (8) *t h ) c (xH(t"H)) G VV G respectively. Both derivatives are negative: A marginal increase in t induces a decrease in emissions from both types of "rms, the reduction is greater, ceteris paribus, for an H. If tax is the chosen instrument, then, the EPA's problem is to set t to minimise an expected social loss function: ¸(t"b)"b¸(t"H)#(1!b)¸(t"D),
(9)
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221
where
[h c(xH(t"H))#xH(t"H)d] f (h) dh (10) G G G and ¸(t"D) is de"ned analogously. The optimal tax is implicitly de"ned as a function of b by the "rst-order condition associated with the EPA's problem: ¸(t"H)"
b
d¸(tH(b)"H) d¸(tH(b)"D) #(1!b) "0, dt dt
(11)
which, after substitution and simpli"cation becomes
(1!b)
*xH(tH(b)"D) G f (h) dh(tH(b)(1!m)!d) *t
*xH(tH(b)"H) G f (h) dh(tH(b)!d). (12) *t It is straightforward to infer from this that tH(1)"d } if all "rms are honest the optimal tax is Pigouvian } and that this achieves "rst best for the usual reasons. If all "rms are dishonest, the picture is more complicated. If all "rms were D's the EPA could achieve "rst best by setting a tax t"d/(1!m) such that every "rm faced an ewective tax rate d. Implicit di!erentiation yields "!b
sgn
dtH(b) * d¸(tH(b)"b) "sgn ! db *b dt
(0
(13)
} the optimal tax is everywhere decreasing in b. This is intuitive. 3.1. Honesty } good thing or bad? Of interest to us here are the welfare impacts of variations in the parameter b. Fully di!erentiating ¸(tH(b)"b) with respect to b implies (after application of the envelope theorem) d¸(tH(b)"b) "¸(tH(b)"H)!¸(tH(b)"D). db
(14)
There is some abuse of notation here. ¸(t"H) is used to mean the expected social loss generated by an honest "rm given a tax t, whilst ¸(t"b) is used to mean expected social loss per "rm for a particular value of b. The interpretation at any point should be transparent.
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When enforcement e!ort is exogenous (the current case) ¸(tH(0)"D)" ¸(tH(1)"H). It is also apparent from the structure of the model that d¸(tH(1)"1) ¸(tH(1)"D)'¸(tH(1)"H)N (0 db
(15)
d¸(tH(0)"0) '0. ¸(tH(0)"H)'¸(tH(0)"D)N db
(16)
and
Furthermore, it is established in an appendix that
* d¸(tH(b)"b) (0, ∀b'0. *b db
(17)
These results together imply the following: Proposition 1. For a specixed enforcement programme, ¸(tH(b)"b) is non-monotonic (more concretely inverted-"-shaped) in b. The result that increases in population honesty may (and over some range will ) be welfare-reducing is interesting. With the intensity of the enforcement programme predetermined (i.e. with m "xed) it makes no di!erence to the EPA whether all "rms are honest (b"1) or all are dishonest (b"0). In either case the "rst-best outcome is implementable } albeit that when b"0 implementation will require a higher tax. Moving to some interior value of b implies an injection of heterogeneity which makes regulation more di$cult and generates a welfare loss. The EPA sets t to balance the marginal dead-weight loss due to honest "rms doing too much abatement against that due to dishonest "rms doing too little. At the resulting t(0)'tH(b)'t(1) no "rm faces the &correct' ("rst-best) marginal incentives. The inverted-" will not, in general, be symmetric. 3.2. Changing b and choice of regulatory instrument The non-monotonicity identi"ed in Proposition 1 has potentially novel implications for instrument selection. Recall that expected social loss per "rm under a CC regime (under which the use of the backstop technology is mandatory) is as speci"ed in Eq. (2). ¸(xH ) !! and ¸(tH(b)"b) can be plotted on common axes, as in Fig. 1. It is necessarily the case that ¸(xH )'¸(tH(b)"b) for b"0, 1. The continuity of both functions in !! b then implies:
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Fig. 1.
Proposition 2. When a suzciently large or suzciently small fraction of xrms are honest a tax regime performs better than a CC regime. Most interesting is the scope for &reversals' in instrument choice which occurs if ¸(xH ) intersects ¸(tH(b)"b). !! The vertical location of ¸(xH ) depends upon the quality of the backstop !! technology (amongst other things) and } importantly for our purposes here } does not depend upon b. Thus, Proposition 3. If Max(¸(tH(b)"b))'¸(xH ) then tax performs better than CC for !! values of b suzciently large or suzciently small. CC performs better for intermediate values. This is the case illustrated in Fig. 1. Tax is the preferred instrument for values of b less than b or greater than b . Expected social loss conditional on optimal instrument selection and calibration (the lower envelope in Fig. 1) is piecewise non-monotonic in b.
4. Endogenising the enforcement programme The analysis so far has exposed the key novelties of the paper } that social loss under the optimally calibrated tax-based regime will be non-monotonic in b and that this may imply &reversals' in instrument choice (insofar, of course, as the
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Agency has discretion over choice of instrument). The signi"cance of such results will be considered in more detail in Section 5. Until now, however, enforcement has been exogenous. In reality the intensity of the monitoring/enforcement programme is likely to be under EPA control } indeed regulatory agencies put considerable time and consideration into &optimising' their enforcement programmes (see, for some discussion, Heyes, 1998). Before taking the results too seriously, then, it is important to verify that they are robust to endogenisation of this facet of Agency activity. There are a number of ways in which monitoring or enforcement could sensibly be endogenised in a model of this sort. The approach we have taken is the one that &"ts' best in the context, whilst maintaining tractability. In Erard and Feinstein's (1994) excellent model of income tax reporting and veri"cation, the tax agency is assumed to have a "xed monitoring budget. Optimal policy involves concentrating veri"cation e!orts on low-income reports (which have a greater chance of being under-reports). An increase in the proportion of pathologically honest taxpayers reduces the fraction of low income reports and makes any such report more likely to be audited. Thus, an increase in the proportion of taxpayers who are honest has the e!ect of encouraging dishonest taxpayers to cheat by less (in our notation an increase in b would tend to decrease m). Put another way, an increase in the proportion of honest taxpayers serves to &free up' the incentive compatibility constraint for their dishonest counterparts } the honest impose a form of (negative) externality on the dishonest. We choose not to follow this approach for two reasons. Firstly, this class of interaction between taxpayer motivation and enforcement e$cacy has already been well-studied. Whilst some of Erard and Feinstein's results are not fully general (being derived from numerical simulation) it seems apparent that, in a model such as ours, the mechanism they envisage would serve to increase the social return to honesty and cause a &skewing downwards' of the right-hand end of the ¸(tH(b)"b) curve in Fig. 1. The implications of this for instrument choice and policy reversals are apparent. Second, and more importantly, whilst their sort of model is ideal for thinking about income tax monitoring } relying as it does on targeted ex post veri"cation } it is unlikely to be suited to thinking about pollution taxes. &Monitoring' in the context of an income tax return means, largely, checking the return against a paper trail (or other ex post veri"able evidence). It is an inherently responsive
As usual in models of this sort there is no really convincing story as to how that budget has been set and why its size should be "xed (why, in particular, its size should not be sensitive to the marginal social value of enforcement spending). Certainly, in the context of a large Agency such as the EPA in the US one might expect intra-agency budget allocations to adjust to re#ect (perhaps imperfectly) marginal productivity. Much of interest remains exogenous in "xed budget models of this sort.
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activity which makes it natural to model the Agency as moving second and able to condition its action upon the content of a particular return. In the pollution tax context there will not, in general, be such a paper trail. Monitoring must occur at the moment of emission (by installed or remote monitoring equipment, on-site inspections, etc.) if it is to occur at all, such that it makes sense to suppose that the Agency is obliged to choose the &intensity' of its monitoring programme (e.g. the quality of monitoring equipment it installs) ex ante. That monitoring programme is then part of the regulatory environment in which "rms make their emissions and reporting decisions. We follow Xepapadeas (1995, 1997) in endogenising the EPA's compliance programme by supposing that the Agency can erode the fraction of emissions that can be &hidden' by a dishonest "rm by increasing its monitoring e!ort. The unobserved or evadable portion of emissions, m, then, is assumed to be a decreasing function of the intensity of the EPA's monitoring e!ort, e. Thus, we can write m(e) where m(e)'0, m (e)(0. We assume further that m (e)'0; mP1 as ePR; m P!R as eP0. These are all plausible (and standard) assumptions. The former implies diminishing returns to monitoring e!ort. The latter serve to ensure that the solution to the EPA's problem will involve an interior choice of e for b'0. Under a tax-based regime, then, the EPA's problem is to choose both a tax rate and a level of monitoring intensity to minimise ¸(t, e"b) where
¸(t, e"b)"ek#b
[h c(xH(t"H))#xH(t"H)d] f (h) dh G G G
[h c(xH(t, e"D))#xH(t, e"D)d] f (h) dh, G G G where k is the unit cost of monitoring e!ort, xH(t, e"D) is de"ned by #(1!b)
(18)
!(1!m(e)).t c (xH(t, e"D))" (19) V G h G and xH(t"H) remains as de"ned by Eq. (6). The "rst-order conditions associated G with an interior solution to the EPA's problem are then
*xH(tH(b)"H) G (d!tH(b)) f (h) dh *t *xH(tH(b), e"D) G (1!b) (d!tH(b)(1!m(e))) f (h) dh *t
¸ (tH(b), e"b)"0"b R
(20)
Other authors who model enforcement e!ort as being pre-committed in this way include Nowell and Shogren (1994) and Alvenhaus (1991). See Xepapadeas (1997, pp. 138}140) for an advanced textbook discussion of some of the modelling issues involved.
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and
¸ (t, eH(b)"b)"0"k#(1!b) C
*xH(t, eH(b)"D) *e
;(d!t.(1!m(eH(b)))) f (h) dh
(21)
Eq. (21) is the simple analogue of 12 in the m-"xed case. Eq. (22) characterises the intensity of the EPA's monitoring programme, conditional on t and b. It dictates that monitoring e!ort is increased up to the point at which its marginal cost (k) equals the marginal social bene"t in terms of reduced emissions from dishonest "rms. (The behaviour of honest "rms is, of course, insensitive to variations in e.) Though it is the welfare analysis which is of primary interest we start by reporting (brie#y) the main positive results } the comparative static impact of changes in b upon tH and eH. Application of Cramer's Rule to the system of equations (20) and (21) implies dtH !¸ ¸ #¸ ¸ R@ CC RC C@ " "D" db
(22)
deH !¸ ¸ #¸ ¸ RR C@ CR R@ " db "D"
(23)
and
where
¸ ¸
RR
¸
CR , RC CC such that "D"'0 in the vicinity of equilibrium. ¸ and ¸ are both positive by RR CC the second-order conditions for a minimum. Further partial di!erentiation of Eqs. (20) and (21) yields expressions for ¸ , ¸ and ¸ which, after some CR C@ R@ manipulation, can be signed as negative, positive and positive, respectively. D"
¸
These also combine to imply two partial impacts of potential interest: *tH(b)/*e'0 and *eH(b)/*t'0. The "rst says that in settings where e is "xed (e.g. where the EPA's monitoring budget is exogenously "xed) an increase in that e will generate an increase in the optimal tax. This is e!ectively the m-"xed case of Section 3. The second implies that in contexts where t is "xed exogenously (e.g. by statute), an increase in that t will generate an increase in optimal monitoring intensity. Both partials are unsurprising. I am grateful to a referee for pointing out that in some contexts these partials may be of more practical interest than the equilibrium derivatives in 22 and 23.
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We can now note that substituting terms with these signs into 22 and 23 implies that both equilibrium derivatives are negative: Proposition 4. Assuming an interior solution to the EPA's problem, tH and eH are both strictly decreasing in b. As a greater portion of regulatees are inherently honest optimal policy implies not just cutting the tax rate (as in the m-"xed case } and for the same set of reasons) but also reducing the intensity of the monitoring programme. Both monitoring intensity and higher-than-Pigouvian taxes are used (at a cost) as tools to coax dishonest "rms closer to the e$cient rate of emission. As the preponderance of dishonest "rms in the population goes down the Agency gradually &eases o! ' on its use of both tools. The speci"cation of m(e) implies, more speci"cally, that from a base of eH(0)"0, eH rises continuously and monotonically in b up to some ("nite) eH(1). It is interesting to note that (as in Erard and Feinstein, 1994) the honest "rm imposes an externality upon the dishonest. In contrast to Erard and Feinstein, however, the externality here is positive. The presence of an additional honest "rm induces an incremental cut both in the tax rate and in monitoring intensity, both of which advantage the dishonest. Growth in the propensity to honesty in the population will cause the equilibrium behaviour (both in terms of volume of emissions, and proportion reported) of the dishonest to get worse. The di!erence arises from the di!erent sequencing of moves in the two models. In particular, the assumption here is that the EPA moves "rst. This, as we have argued, is justi"ed by fundamentals and constitutes an important di!erence between how we should think about the enforcement aspects of income and pollution taxes. 4.1. Honesty and welfare } still non-monotonic? The most interesting feature of the m-"xed case was the non-monotonicity of welfare in b under a tax-based regime, and the scope for &reversals' in instrument choice which that non-monotonicity implied. These features are preserved in the m-endogenous case, though the characterisation of social loss is (unsurprisingly) less &clean'. It remains apparent from the structure of the model that d¸(tH(1), eH(1)"1) ¸(tH(1), eH(1)"D)'¸(tH(1), eH(1)"H)N (0 db
(24)
Recall that in Erard and Feinstein more honest taxpayers meant a lower proportion of low-income returns and therefore a greater probability that any given low-income return (which would include a higher than proportionate fraction of dishonest (under-) reports) would be audited.
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and d¸(tH(0), eH(0)"0) ¸(tH(0), eH(0)"H)'¸(tH(0), eH(0)"D)N '0. db
(25)
If the Agency has calibrated its tax/monitoring policy on the basis that all "rms are dishonest then the substitution (in a large population) of one dishonest by one honest "rm is welfare-reducing (in particular, that &pioneer' honest "rm will under-emit). The same applies to the substitution of one honest by one dishonest "rms if policy is geared for b"1. The continuity of ¸(tH(b), eH(b)"b) in b then implies: Proposition 5. Expected social loss under an optimally calibrated and monitored tax-based regime } ¸(tH(b), eH(b)"b) } is non-monotonic in b. In particular, there will be some range of values of b su$ciently small (but positive) where social loss is increasing in b, and some interval of values b su$ciently large (but less than one) where social loss is decreasing in b. This is captured by the left- and right-hand ends of the social loss function in Fig. 2. Given the greater generality of the current version of the model, however, we cannot tie-down the shape of the function for intermediate values of b. In particular, and unsurprisingly, it will not generally be the case that
* d¸(tH(b), eH(b)"b) *b db
is negative over the whole unit interval. In terms of instrument reversal the same comments apply as in the m-"xed case. The social loss under a CC regime does not depend upon b such that ¸(xH ) can be superimposed as a horizontal line in Fig. 2. The vertical location !! of that line relative to ¸(tH(b), eH(b)) will depend, as before, upon the distribution of h (amongst other things). In the current case it would also be pertinent to G insert any per-"rm cost associated with the implementation of the CC regime, which would imply an upward displacement of ¸(xH ). It is apparent that the !! non-monotonicity of the social loss function still generates the possibility of instrument reversals, as in the m-"xed case.
5. Implications The key advantage attributed to pollution taxation is the technological #exibility it o!ers to those regulated } empowering them with choice of technique } and its implied ability to &handle' technological heterogeneity (Baumol and Oates (1988) provide the de"nitive textbook analysis). This is captured in the model presented here } in the absence of the variation in "rms technological
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Fig. 2.
&outside options' command-and-control would invariably be the preferred method of regulation. The novelty in our analysis is to incorporate another type of heterogeneity } what we might refer to as &motivational heterogeneity' } which a tax-based regime is comparatively bad at handling. Whether or not the monitoring/enforcement programme of the EPA is modelled endogenously, it turns out that command-and-control may be preferred as a regulatory instrument for (and only for) interior values of b. The implications of the analysis depends upon the interpretation applied to b. Suppose that b evolves exogenously through time, in#uenced by broader social trends, etc., then we should expect a responsive regulatory agency to adjust to take account of such evolution. This response might involve recalibrating a given instrument or } if one of the critical thresholds is traversed } switching between instruments. A long-term upward trend in the evolution of b } driven by, for example, the spreading in#uence of ethical investors } may generate &reversals' in instrument choice, with an initial switch away from market-based instruments followed by a later switch back towards them. What of regulatory attitudes towards changes in b? This depends upon the starting point and the size and direction of the change } certainly the simple view that more honesty is always good cannot be sustained. Starting from b"0 (the &default' assumption in conventional economic analysis) marginal increases in the parameter are an impediment to the agency in its work such that &pioneer' ethical "rms might legitimately be regarded as a nuisance, &throwing a spanner' into the regulatory process. Increases in population honesty are only welfareimproving at the margin once a certain critical prevalence has been achieved.
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Such a recognition has particularly interesting implications in contexts where b } rather than being exogenous } is something that the regulatory agency might have scope to in#uence, e.g. through &good citizenship' campaigns. A policy aimed at encouraging increased honesty from a low base is only welfareimproving if it can work on a big enough scale to get over the hill and far enough down the other side of the inverted-" in Fig. 1. The analysis provides a possible e$ciency-interpretation for the USEPA's apparent willingness to tolerate widespread misreporting of environmental performance by those in its charge (as evidenced by Yaeger, 1991, and others). This is alternative to the standard view that any such tolerance must necessarily indicate incompetence, sloth or regulatory capture on the part of the agency. The analysis could, of course, be extended in a variety of ways. Perhaps most importantly: E &Honesty' could be modelled in a non-binary way (di!erent agents could, for example, be assumed to get di!erent marginal disutilities per unit of underreporting). E The EPA's monitoring and enforcement programme could be modelled in a variety of alternative ways (including, for example, speci"cation and optimisation of speci"c expected penalty functions). E The possibility of &social norm' in#uences on behaviour } for instance that a "rm may be more willing to comply if it believes that others are going to (honesty may be &infectious') or if it believes that non-compliance by other "rms will be adequately punished (as suggested by Scholtz, 1984) } could be incorporated. E There may also be interdependence in compliance decisions when "rms face each other as rivals in a product market. The only way "rms in a very competitive industry could &a!ord' honesty would be if dishonest rivals faced a signi"cant probability of being caught and punished. E Perhaps most interesting would be to model repetition } under which the EPA might have the ability to target its enforcement e!ort according to the previous performance of individual "rms (as in, for example, Harrington, 1988). Such extensions, however, could be expected to enrich rather than to negate the sorts of insights presented here. I am grateful to a referee for highlighting these possibilities. The former type of &motivational externality' has been explored by Haltiwanger and Waldman (1991, 1993). They suppose that some fraction g of a population of agents are &responders' who choose to behave opportunistically (anti-socially) if (and only if ) they observe opportunistic (anti-social) behaviour by others. Frey (1994) has explored the (he asserts negative) interaction between the intensity of regulatory compulsion and the propensity for voluntarism. Such e!ects could be added to the model here.
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Acknowledgements I am grateful to two referees and seminar participants at Tilburg University for helpful comments. Errors are mine.
Appendix Di!erentiating (9) and applying the envelope theorem yields d¸(tH(b), b) "¸(tH(b)"H)!¸(tH(b)"D). db
(A.1)
Di!erentiating yields
* d¸(tH(b), b) *tH *¸(tH(b)"H) *¸(tH(b)"D) " ! . *b *b *t db *t
(A.2)
Let the expression in brackets on the right-hand side of (A.2) be denoted X. The left-hand side of (A.4) will be opposite in sign to X (since *tH/*b(0). Now, *¸(tH(b)"D) *xH(t"D) "! (t(1!m)!d), *t *t
(A.3)
whilst (11) implies *¸(tH(b)"H) (1!b) *¸(tH(b)"D) "! *t b *t
(A.4)
such that
(1!b) *xH(t"D) X"! (t(1!m)!d) ! !1 . *t b
(A.5)
Note from the planner's "rst-order condition that (t(1!m)!d)(0 such that X'0. The inequality in (13) follows directly.
References Alvenhaus, R., 1991. Monitoring the emission of pollutants by the inspector leadership method. In: R. Pethig (Ed.), Con#icts and Cooperation in Managing Environmental Resources. Springer, Berlin. Baumol, W., Oates, W., 1988. The Economic Theory of Environmental Policy, 2nd Edition. Cambridge University Press, Cambridge, England. Cowell, F.A., 1990. Cheating the Government: The Economics of Evasion. MIT Press, Cambridge, MA.
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Dimento, J., 1986. They Treated Me Like a Criminal.. University of Pittsburgh Press, Pittsburgh. Erard, B., Feinstein, J.S., 1994. Honesty and evasion in the tax compliance game. RAND Journal of Economics 25 (1), 1}19. Frey, B.S., 1994. Pricing and regulating a!ect environmental ethics. Environmental and Resource Economics 2, 399}414. Graetz, M.J., Reinganum, J.F., Wilde, L.L., 1986. The tax compliance game: Towards an interactive theory of law enforcement. Journal of Law, Economics & Organisation 2, 1}32. Gray, W.B., Deily, M.E., 1996. Compliance and enforcement: Air pollution regulation in the US steel industry. Journal of Environmental Economics and Management 31, 96}111. Haltiwanger, J., Waldman, M., 1991. Responders versus nonresponders: A new perspective on heterogeneity. Economic Journal 101, 1085}1102. Haltiwanger, J., Waldman, M., 1993. The role of altruism in economic interaction. Journal of Economic Behavior and Organization 21, 1}15. Harford, J.D., 1987. Self-reporting of pollution under imperfectly enforceable pollution standards and taxes. Journal of Environmental Economics and Management 14, 26}43. Harrington, W., 1988. Enforcement leverage when penalties are restricted. Journal of Public Economics 37, 29}53. Heyes, A.G., 1996. Cutting environmental penalties to protect the environment. Journal of Public Economics 60 (2), 251}265. Heyes, A.G., 1998. Making things stick: The economics of enforcement and compliance. Oxford Review of Economic Policy 14 (4), 50}63. Levi, M., 1988. Of Rule and Revenue. University of California Press, Berkeley, CA. Magat, W., Viscusi, W.K., 1990. The e!ectiveness of EPA's regulatory enforcement: The case of industrial e%uent standards. Journal of Law and Economics 33, 331}360. Nowell, C., Shogren, J., 1994. Challenging the enforcement of environmental regulation. Journal of Regulatory Economics 6, 265}282. Scholtz, J.T., 1984. Cooperation, deterrence, and the ecology of regulatory enforcement. Law and Society Review 18 (2). Xepapadeas, A., 1995. Observability and choise of instrument mix in the control of externalities. Journal of Public Economics 56, 485}498. Xepapadeas, A., 1997. Advanced Principles in Environmental Policy. Edward Elgar, Cheltenham, England. Yaeger, P.E., 1991. The Limits of the Law: Public Regulation of Private Pollution. Cambridge University Press, New York, NY.
Honesty in a regulatory context } good thing or bad? Anthony Heyes* Department of Economics, Royal Holloway College, University of London, Egham Hill, Surrey, TW20 OEX, UK Received 1 May 1998; accepted 6 December 1999
Abstract It is often taken for granted that if more "rms were innately honest or ethical this would be a good thing. We use the example of pollution policy to dispute such a claim. If regulation is by pollution tax social welfare is non-monotonic in population honesty. The choice of policy instrument may itself be characterised by &reversals', with commandand-control methods being preferred for intermediate values of population honesty, a tax system being preferred at the extremes. This means that if } because of the spread of ðical shareholding' or for whatever reason } the honesty of the corporate population increases through time, we should not be surprised to see at "rst a switch away from market-based instruments, and then a switch back. Though environmental regulation is chosen as a context, the implications are more general. 2001 Elsevier Science B.V. All rights reserved. JEL classixcation: K4; K2; H8 Keywords: Pollution control; Honesty; Incentives
1. Introduction It is often taken for granted that if more "rms were innately honest or ethical in the way they behaved this would be a good thing. In this paper we use the * Fax: #44-1784-439534. E-mail address: [email protected] (A. Heyes). 0014-2921/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 4 - 2 9 2 1 ( 9 9 ) 0 0 0 7 6 - 8
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example of environmental regulation to show that such a claim cannot, in general, be sustained. If regulation is by pollution tax we show that } once optimal agency response is taken into account } social welfare is non-monotonic in the proportion of "rms that report emissions honestly. The choice of policy instrument may itself be characterised by &reversals' with command-and-control methods being preferred for intermediate values of population honesty, a tax system being preferred at the extremes. A heterogeneity argument underlies the main result. Consider a simple model of a tax regime based on (imperfectly veri"ed) self-reports in which tax plays an incentive role, as in the case of a tax designed to internalise an externality. It is not too surprising that such a regime may perform best } once optimal agency response is factored in } either when everyone is inherently honest or when everyone is inherently dishonest. When everyone is inherently honest the agency can achieve "rst-best by setting the tax-rate equal to marginal damage (i.e. at its Pigouvian level). Supposing, instead, that everyone is inherently dishonest and is able to get away with under-reporting some fraction m of their true emissions, the agency can achieve the same outcome simply by raising the tax-rate to (m/[1!t]) such as to maintain the e!ective rate. The regime performs less well when the population is a mixture of some who are routinely honest (i.e. do not exploit opportunities for evasion presented to them) and others who are not. Whilst the framework developed in this paper is somewhat more complex than this } incorporating di!erences in compliance costs, endogenous monitoring e!ort on the part of the EPA, etc. } the basic story is unchanged. The model is consistent with some stylised features of American regulatory history. It may, for example, provide a defence of the EPA's apparent willingness to tolerate a culture of under-reporting amongst those it is supposed to police. Though environmental regulation is used as an example for the purposes of exposition, the results are likely to be of more general interest. It is conventional in economics to model agents as rational cheaters } undercomplying with laws or under-reporting tax liabilities when enforcement parameters are such as to make such behaviour "nancially pro"table. There is compelling empirical and anecdotal evidence, however, to suggest that some
Thus, Cowell (1990) de"nes the rational taxpayer to be one predisposed to dishonesty: `2 the expression predisposed to dishonesty is used because we do not impute to the taxpayer any views about duty, honor or civic pride that would compel him to put some responsibility to the state ahead of his own money-grubbing interests2. Whilst virtue for its own sake may be laudable it is unexciting in terms of economic contenta (Cowell, 1990, p. 50). For two examples (amongst many) of the rational cheater in the environmental regulatory context see Harford (1987) and Heyes (1996).
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individuals and "rms are inherently honest or ethical. A feel for the scale of &honesty' in a compliance context can be had by setting all of the enforcement parameters (size of penalty, probability of apprehension, etc.) in econometrically estimated compliance functions equal to zero. So doing invariably implies a positive level of &unenforced' compliance which can be substantial (see, for examples, Magat and Viscusi, 1990; Gray and Deily, 1996). Limited attempts have been made to model the implications of routine honesty in enforcement contexts. Graetz et al. (1986) included a sub-group of routinely honest agents (&habitual compliers') in a standard income tax enforcement framework. Varying the prevalence of routine honesty in their model has no e!ect on optimal policy nor expected net tax revenue. Erard and Feinstein (1994) use numerical simulation to show the e!ect of including a sub-group of routinely &honest' taxpayers in a somewhat di!erent model. The model presented here is substantially di!erent } both in terms of set-up and results } from these. Tax here is going to have real e!ects } indeed that is the point of its use. In Erard and Feinstein (1994) and Graetz et al. (1986) agents are born into a model with an endowment, the size of which is privately observed, and the tax regime is designed to minimise dissembling. In the current model the tax-setting agency is not motivated by revenue-generation, nor does it care about dissembling per se. Rather, its objective in levying the tax is to internalise an externality and to create the &right' incentives for clean production. The existence of real impacts enriches the scope for welfare analysis substantially. Those welfare results turn out to exhibit interestingly non-monotonic features. These are not only signi"cant in their own right but also motivate study of the role of routine honesty for the comparative performance of alternative instruments and provide the scope for instrument &reversals'.
2. Model Each "rm in a population has access to an established pollution-control technology which allows it to restrict its emissions of some noxious substance to a level x at cost c(x) where c (x)(0, c (x)'0, ∀x50. We will refer to this as V VV See, for examples, Graetz et al. (1986), Levi (1988), Erard and Feinstein (1994), and many of the citations there-in. It is useful to distinguish individual from corporate honesty. The former may, however, be a key determinant of the latter. In the speci"c context of honesty of environmental reporting practices in the US Dimento (1986) emphasises `the individual idiosyncracies of top managementa (Dimento, 1986, p. 84). It is possible that a "rms motives for honesty may be self-serving. It may, for example, have employees or clients particularly unwilling to tolerate unethical behaviour. The term &pollution charge' is also often used. Revenue is implicitly assumed to be recycled in some welfare-neutral way.
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the &backstop' technology. The intensity of its application is assumed to be directly veri"able by the Environmental Protection Agency (EPA). For each "rm we can also de"ne the &least cost' abatement method to which it has access. The least cost technology allows it to control its emissions of the same noxious substance at a cost h .c(x) where h is distributed according to G G a density function f de"ned on the support [0,1], where f '0 for all x on that support. The associated cumulative will be denoted F. Some (but not all) "rms, then, are assumed to have access to a lower cost abatement technology than the backstop. Abatement by methods other than the backstop is not, however, directly veri"able by the EPA. It may involve application of new and/or context-speci"c technologies and/or practices that are inherently less transparent to an outsider. The EPA can either regulate by command-and-control (CC), or it can levy a pollution tax. Its objective is to minimise the sum of industry costs and environmental damage. The damage function is linear in aggregate emissions with the constant unit damage denoted d. In the stylised world described here CC means } given the unveri"ability of the alternatives } requiring use in some &amount' of the backstop technology. Under a tax regime the agency sets a tax t per unit of emissions and then requires each "rm to report its output of emissions. The report is assumed subject to some sort of (imperfect) veri"cation procedure. In particular, a "rm that chooses to do so is assumed able to &hide' (get away with not reporting) some fraction m of their true emissions, where m is some measure of the tightness or accuracy of the monitoring regime in place. In Section 3, we treat m as exogenous. Though unrealistic this allows for exposition of the key insights of the paper in the &cleanest' and most intuitive way. The model and results are generalised in Section 4 in which the m is endogenised and modelled as dependent upon the EPA's monitoring e!orts in the manner used by Xepapadeas (1995, 1997) and others in analogous contexts. Whilst endogenising the monitoring/enforcement programme creates } unsurprisingly } additional ambiguity in some places, the key results are preserved. The unconventional assumption in the model is with regard to the reporting behaviour of "rms. In particular, we assume that some proportion of "rms b are intrinsically &honest'. Honest "rms always tell the truth. The remaining fraction (1!b) are the rational cheaters of standard economic analysis, choosing the extent of under-reporting on the basis of expected "nancial costs and bene"ts
For some "rms h "1, the least cost technology is the backstop technology. The backstop G technology being universally available means h cannot exceed 1. G &Technology' should be interpreted broadly to encompass any method of abatement. It may, for example, take the form of changes in composition of inputs, work practices, etc.
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from such behaviour. The EPA knows b } the propensity to honest reporting across the population } but cannot tell which "rms are which. Comparative statics (positive and normative) with respect to b are a particular focus of the analysis.
3. The simple story } exogenous monitoring For the purposes of exposition we will start with the assumption that m is exogenous. Under a CC regime all "rms are required to use the backstop technology. The EPA stipulates and enforces the intensity of application associated with xH where, for the representative "rm !! xH 3min+c(x)#dx,. (1) !! Expected per "rm social loss under CC is, then, S¸(xH )"c(xH )#dxH , (2) !! !! !! where xH is implicitly de"ned by c (xH )"!d. Under a CC regime regulation !! V !! is input-based and b is not relevant. The EPA sets (optimally) the pollution target to be satis"ed and the technology to be used in achieving it, and polices it directly. Note that for a given distribution of abatement e!ort choice of technique is not cost-e!ective } "rms with h (1 have to use the backstop technology G despite knowing a cheaper way of doing the same thing. Furthermore, the distribution of e!ort across "rms is ine$cient } no mechanism exists for "rms with lower marginal compliance costs to reduce emissions more than do those with higher marginal costs. The calibration of the CC regime and the level of welfare delivered do not depend upon b. Consider, next, a tax-based regime. If "rm i is dishonest (denoted D) } a rational cheater of the sort familiar to economic modellers } then it chooses
In adopting to this approach we are following Graetz et al. (1986) and Erard and Feinstein (1994). The fraction of "rms b could be called &pathologically' honest. Our motivation here is expositional. If m is a measure of monitoring intensity, however, such an assumption could be motivated by the agency having a "xed monitoring/enforcement budget. Such an assumption } though unsatisfying in many ways } is a common one in the enforcement literature. These are the two &usual' shortcomings associated with CC (see e.g. Baumol and Oates, 1988, pp. 171}180). CC regimes are tied to the use of the backstop technology and do not, by construction, perform well under technological heterogeneity of the sort here.
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x to minimise the sum of abatement expenditures plus tax payments, i.e. G to minimise F(x , t"D)"h c(x )#t(1!m)x . G G G G H The interior solution x (t"D) is implicitly de"ned by G !(1!m)t c (xH(t"D))" . V G h G The analogous problem faced by an honest "rm is to minimise F(x , t"H)"h c(x )#tx G G G G H such that x (t"H) is characterised by
(3)
(4)
(5)
!t c (xH(t"H))" . (6) V G h G Eq. (6) is conventional in the case of a fully enforced tax. Eq. (4) is the same condition adapted to take account of the fact that the e!ective marginal tax rate for a D is (1!m)t. It is apparent that, other things being equal, a D emits more than an H, since the e!ective tax rate it faces is lower. Choice of technique in equilibrium is cost-e!ective } each "rm chooses the least cost way of doing the abatement it is doing. Combining (4) and (6) implies that marginal abatement costs are not equalised across "rms } the distribution of abatement e!ort across "rms remains ine$cient. The incentive e!ects of tax changes are qualitatively conventional. Implicit di!erentiation of (4) and (6) yields !(1!m) *xH(t"D) G " *t h ) c (xH(t"D)) G VV G
(7)
and *xH(t"H) !1 G " , (8) *t h ) c (xH(t"H)) G VV G respectively. Both derivatives are negative: A marginal increase in t induces a decrease in emissions from both types of "rms, the reduction is greater, ceteris paribus, for an H. If tax is the chosen instrument, then, the EPA's problem is to set t to minimise an expected social loss function: ¸(t"b)"b¸(t"H)#(1!b)¸(t"D),
(9)
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221
where
[h c(xH(t"H))#xH(t"H)d] f (h) dh (10) G G G and ¸(t"D) is de"ned analogously. The optimal tax is implicitly de"ned as a function of b by the "rst-order condition associated with the EPA's problem: ¸(t"H)"
b
d¸(tH(b)"H) d¸(tH(b)"D) #(1!b) "0, dt dt
(11)
which, after substitution and simpli"cation becomes
(1!b)
*xH(tH(b)"D) G f (h) dh(tH(b)(1!m)!d) *t
*xH(tH(b)"H) G f (h) dh(tH(b)!d). (12) *t It is straightforward to infer from this that tH(1)"d } if all "rms are honest the optimal tax is Pigouvian } and that this achieves "rst best for the usual reasons. If all "rms are dishonest, the picture is more complicated. If all "rms were D's the EPA could achieve "rst best by setting a tax t"d/(1!m) such that every "rm faced an ewective tax rate d. Implicit di!erentiation yields "!b
sgn
dtH(b) * d¸(tH(b)"b) "sgn ! db *b dt
(0
(13)
} the optimal tax is everywhere decreasing in b. This is intuitive. 3.1. Honesty } good thing or bad? Of interest to us here are the welfare impacts of variations in the parameter b. Fully di!erentiating ¸(tH(b)"b) with respect to b implies (after application of the envelope theorem) d¸(tH(b)"b) "¸(tH(b)"H)!¸(tH(b)"D). db
(14)
There is some abuse of notation here. ¸(t"H) is used to mean the expected social loss generated by an honest "rm given a tax t, whilst ¸(t"b) is used to mean expected social loss per "rm for a particular value of b. The interpretation at any point should be transparent.
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When enforcement e!ort is exogenous (the current case) ¸(tH(0)"D)" ¸(tH(1)"H). It is also apparent from the structure of the model that d¸(tH(1)"1) ¸(tH(1)"D)'¸(tH(1)"H)N (0 db
(15)
d¸(tH(0)"0) '0. ¸(tH(0)"H)'¸(tH(0)"D)N db
(16)
and
Furthermore, it is established in an appendix that
* d¸(tH(b)"b) (0, ∀b'0. *b db
(17)
These results together imply the following: Proposition 1. For a specixed enforcement programme, ¸(tH(b)"b) is non-monotonic (more concretely inverted-"-shaped) in b. The result that increases in population honesty may (and over some range will ) be welfare-reducing is interesting. With the intensity of the enforcement programme predetermined (i.e. with m "xed) it makes no di!erence to the EPA whether all "rms are honest (b"1) or all are dishonest (b"0). In either case the "rst-best outcome is implementable } albeit that when b"0 implementation will require a higher tax. Moving to some interior value of b implies an injection of heterogeneity which makes regulation more di$cult and generates a welfare loss. The EPA sets t to balance the marginal dead-weight loss due to honest "rms doing too much abatement against that due to dishonest "rms doing too little. At the resulting t(0)'tH(b)'t(1) no "rm faces the &correct' ("rst-best) marginal incentives. The inverted-" will not, in general, be symmetric. 3.2. Changing b and choice of regulatory instrument The non-monotonicity identi"ed in Proposition 1 has potentially novel implications for instrument selection. Recall that expected social loss per "rm under a CC regime (under which the use of the backstop technology is mandatory) is as speci"ed in Eq. (2). ¸(xH ) !! and ¸(tH(b)"b) can be plotted on common axes, as in Fig. 1. It is necessarily the case that ¸(xH )'¸(tH(b)"b) for b"0, 1. The continuity of both functions in !! b then implies:
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Fig. 1.
Proposition 2. When a suzciently large or suzciently small fraction of xrms are honest a tax regime performs better than a CC regime. Most interesting is the scope for &reversals' in instrument choice which occurs if ¸(xH ) intersects ¸(tH(b)"b). !! The vertical location of ¸(xH ) depends upon the quality of the backstop !! technology (amongst other things) and } importantly for our purposes here } does not depend upon b. Thus, Proposition 3. If Max(¸(tH(b)"b))'¸(xH ) then tax performs better than CC for !! values of b suzciently large or suzciently small. CC performs better for intermediate values. This is the case illustrated in Fig. 1. Tax is the preferred instrument for values of b less than b or greater than b . Expected social loss conditional on optimal instrument selection and calibration (the lower envelope in Fig. 1) is piecewise non-monotonic in b.
4. Endogenising the enforcement programme The analysis so far has exposed the key novelties of the paper } that social loss under the optimally calibrated tax-based regime will be non-monotonic in b and that this may imply &reversals' in instrument choice (insofar, of course, as the
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Agency has discretion over choice of instrument). The signi"cance of such results will be considered in more detail in Section 5. Until now, however, enforcement has been exogenous. In reality the intensity of the monitoring/enforcement programme is likely to be under EPA control } indeed regulatory agencies put considerable time and consideration into &optimising' their enforcement programmes (see, for some discussion, Heyes, 1998). Before taking the results too seriously, then, it is important to verify that they are robust to endogenisation of this facet of Agency activity. There are a number of ways in which monitoring or enforcement could sensibly be endogenised in a model of this sort. The approach we have taken is the one that &"ts' best in the context, whilst maintaining tractability. In Erard and Feinstein's (1994) excellent model of income tax reporting and veri"cation, the tax agency is assumed to have a "xed monitoring budget. Optimal policy involves concentrating veri"cation e!orts on low-income reports (which have a greater chance of being under-reports). An increase in the proportion of pathologically honest taxpayers reduces the fraction of low income reports and makes any such report more likely to be audited. Thus, an increase in the proportion of taxpayers who are honest has the e!ect of encouraging dishonest taxpayers to cheat by less (in our notation an increase in b would tend to decrease m). Put another way, an increase in the proportion of honest taxpayers serves to &free up' the incentive compatibility constraint for their dishonest counterparts } the honest impose a form of (negative) externality on the dishonest. We choose not to follow this approach for two reasons. Firstly, this class of interaction between taxpayer motivation and enforcement e$cacy has already been well-studied. Whilst some of Erard and Feinstein's results are not fully general (being derived from numerical simulation) it seems apparent that, in a model such as ours, the mechanism they envisage would serve to increase the social return to honesty and cause a &skewing downwards' of the right-hand end of the ¸(tH(b)"b) curve in Fig. 1. The implications of this for instrument choice and policy reversals are apparent. Second, and more importantly, whilst their sort of model is ideal for thinking about income tax monitoring } relying as it does on targeted ex post veri"cation } it is unlikely to be suited to thinking about pollution taxes. &Monitoring' in the context of an income tax return means, largely, checking the return against a paper trail (or other ex post veri"able evidence). It is an inherently responsive
As usual in models of this sort there is no really convincing story as to how that budget has been set and why its size should be "xed (why, in particular, its size should not be sensitive to the marginal social value of enforcement spending). Certainly, in the context of a large Agency such as the EPA in the US one might expect intra-agency budget allocations to adjust to re#ect (perhaps imperfectly) marginal productivity. Much of interest remains exogenous in "xed budget models of this sort.
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activity which makes it natural to model the Agency as moving second and able to condition its action upon the content of a particular return. In the pollution tax context there will not, in general, be such a paper trail. Monitoring must occur at the moment of emission (by installed or remote monitoring equipment, on-site inspections, etc.) if it is to occur at all, such that it makes sense to suppose that the Agency is obliged to choose the &intensity' of its monitoring programme (e.g. the quality of monitoring equipment it installs) ex ante. That monitoring programme is then part of the regulatory environment in which "rms make their emissions and reporting decisions. We follow Xepapadeas (1995, 1997) in endogenising the EPA's compliance programme by supposing that the Agency can erode the fraction of emissions that can be &hidden' by a dishonest "rm by increasing its monitoring e!ort. The unobserved or evadable portion of emissions, m, then, is assumed to be a decreasing function of the intensity of the EPA's monitoring e!ort, e. Thus, we can write m(e) where m(e)'0, m (e)(0. We assume further that m (e)'0; mP1 as ePR; m P!R as eP0. These are all plausible (and standard) assumptions. The former implies diminishing returns to monitoring e!ort. The latter serve to ensure that the solution to the EPA's problem will involve an interior choice of e for b'0. Under a tax-based regime, then, the EPA's problem is to choose both a tax rate and a level of monitoring intensity to minimise ¸(t, e"b) where
¸(t, e"b)"ek#b
[h c(xH(t"H))#xH(t"H)d] f (h) dh G G G
[h c(xH(t, e"D))#xH(t, e"D)d] f (h) dh, G G G where k is the unit cost of monitoring e!ort, xH(t, e"D) is de"ned by #(1!b)
(18)
!(1!m(e)).t c (xH(t, e"D))" (19) V G h G and xH(t"H) remains as de"ned by Eq. (6). The "rst-order conditions associated G with an interior solution to the EPA's problem are then
*xH(tH(b)"H) G (d!tH(b)) f (h) dh *t *xH(tH(b), e"D) G (1!b) (d!tH(b)(1!m(e))) f (h) dh *t
¸ (tH(b), e"b)"0"b R
(20)
Other authors who model enforcement e!ort as being pre-committed in this way include Nowell and Shogren (1994) and Alvenhaus (1991). See Xepapadeas (1997, pp. 138}140) for an advanced textbook discussion of some of the modelling issues involved.
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and
¸ (t, eH(b)"b)"0"k#(1!b) C
*xH(t, eH(b)"D) *e
;(d!t.(1!m(eH(b)))) f (h) dh
(21)
Eq. (21) is the simple analogue of 12 in the m-"xed case. Eq. (22) characterises the intensity of the EPA's monitoring programme, conditional on t and b. It dictates that monitoring e!ort is increased up to the point at which its marginal cost (k) equals the marginal social bene"t in terms of reduced emissions from dishonest "rms. (The behaviour of honest "rms is, of course, insensitive to variations in e.) Though it is the welfare analysis which is of primary interest we start by reporting (brie#y) the main positive results } the comparative static impact of changes in b upon tH and eH. Application of Cramer's Rule to the system of equations (20) and (21) implies dtH !¸ ¸ #¸ ¸ R@ CC RC C@ " "D" db
(22)
deH !¸ ¸ #¸ ¸ RR C@ CR R@ " db "D"
(23)
and
where
¸ ¸
RR
¸
CR , RC CC such that "D"'0 in the vicinity of equilibrium. ¸ and ¸ are both positive by RR CC the second-order conditions for a minimum. Further partial di!erentiation of Eqs. (20) and (21) yields expressions for ¸ , ¸ and ¸ which, after some CR C@ R@ manipulation, can be signed as negative, positive and positive, respectively. D"
¸
These also combine to imply two partial impacts of potential interest: *tH(b)/*e'0 and *eH(b)/*t'0. The "rst says that in settings where e is "xed (e.g. where the EPA's monitoring budget is exogenously "xed) an increase in that e will generate an increase in the optimal tax. This is e!ectively the m-"xed case of Section 3. The second implies that in contexts where t is "xed exogenously (e.g. by statute), an increase in that t will generate an increase in optimal monitoring intensity. Both partials are unsurprising. I am grateful to a referee for pointing out that in some contexts these partials may be of more practical interest than the equilibrium derivatives in 22 and 23.
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We can now note that substituting terms with these signs into 22 and 23 implies that both equilibrium derivatives are negative: Proposition 4. Assuming an interior solution to the EPA's problem, tH and eH are both strictly decreasing in b. As a greater portion of regulatees are inherently honest optimal policy implies not just cutting the tax rate (as in the m-"xed case } and for the same set of reasons) but also reducing the intensity of the monitoring programme. Both monitoring intensity and higher-than-Pigouvian taxes are used (at a cost) as tools to coax dishonest "rms closer to the e$cient rate of emission. As the preponderance of dishonest "rms in the population goes down the Agency gradually &eases o! ' on its use of both tools. The speci"cation of m(e) implies, more speci"cally, that from a base of eH(0)"0, eH rises continuously and monotonically in b up to some ("nite) eH(1). It is interesting to note that (as in Erard and Feinstein, 1994) the honest "rm imposes an externality upon the dishonest. In contrast to Erard and Feinstein, however, the externality here is positive. The presence of an additional honest "rm induces an incremental cut both in the tax rate and in monitoring intensity, both of which advantage the dishonest. Growth in the propensity to honesty in the population will cause the equilibrium behaviour (both in terms of volume of emissions, and proportion reported) of the dishonest to get worse. The di!erence arises from the di!erent sequencing of moves in the two models. In particular, the assumption here is that the EPA moves "rst. This, as we have argued, is justi"ed by fundamentals and constitutes an important di!erence between how we should think about the enforcement aspects of income and pollution taxes. 4.1. Honesty and welfare } still non-monotonic? The most interesting feature of the m-"xed case was the non-monotonicity of welfare in b under a tax-based regime, and the scope for &reversals' in instrument choice which that non-monotonicity implied. These features are preserved in the m-endogenous case, though the characterisation of social loss is (unsurprisingly) less &clean'. It remains apparent from the structure of the model that d¸(tH(1), eH(1)"1) ¸(tH(1), eH(1)"D)'¸(tH(1), eH(1)"H)N (0 db
(24)
Recall that in Erard and Feinstein more honest taxpayers meant a lower proportion of low-income returns and therefore a greater probability that any given low-income return (which would include a higher than proportionate fraction of dishonest (under-) reports) would be audited.
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and d¸(tH(0), eH(0)"0) ¸(tH(0), eH(0)"H)'¸(tH(0), eH(0)"D)N '0. db
(25)
If the Agency has calibrated its tax/monitoring policy on the basis that all "rms are dishonest then the substitution (in a large population) of one dishonest by one honest "rm is welfare-reducing (in particular, that &pioneer' honest "rm will under-emit). The same applies to the substitution of one honest by one dishonest "rms if policy is geared for b"1. The continuity of ¸(tH(b), eH(b)"b) in b then implies: Proposition 5. Expected social loss under an optimally calibrated and monitored tax-based regime } ¸(tH(b), eH(b)"b) } is non-monotonic in b. In particular, there will be some range of values of b su$ciently small (but positive) where social loss is increasing in b, and some interval of values b su$ciently large (but less than one) where social loss is decreasing in b. This is captured by the left- and right-hand ends of the social loss function in Fig. 2. Given the greater generality of the current version of the model, however, we cannot tie-down the shape of the function for intermediate values of b. In particular, and unsurprisingly, it will not generally be the case that
* d¸(tH(b), eH(b)"b) *b db
is negative over the whole unit interval. In terms of instrument reversal the same comments apply as in the m-"xed case. The social loss under a CC regime does not depend upon b such that ¸(xH ) can be superimposed as a horizontal line in Fig. 2. The vertical location !! of that line relative to ¸(tH(b), eH(b)) will depend, as before, upon the distribution of h (amongst other things). In the current case it would also be pertinent to G insert any per-"rm cost associated with the implementation of the CC regime, which would imply an upward displacement of ¸(xH ). It is apparent that the !! non-monotonicity of the social loss function still generates the possibility of instrument reversals, as in the m-"xed case.
5. Implications The key advantage attributed to pollution taxation is the technological #exibility it o!ers to those regulated } empowering them with choice of technique } and its implied ability to &handle' technological heterogeneity (Baumol and Oates (1988) provide the de"nitive textbook analysis). This is captured in the model presented here } in the absence of the variation in "rms technological
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Fig. 2.
&outside options' command-and-control would invariably be the preferred method of regulation. The novelty in our analysis is to incorporate another type of heterogeneity } what we might refer to as &motivational heterogeneity' } which a tax-based regime is comparatively bad at handling. Whether or not the monitoring/enforcement programme of the EPA is modelled endogenously, it turns out that command-and-control may be preferred as a regulatory instrument for (and only for) interior values of b. The implications of the analysis depends upon the interpretation applied to b. Suppose that b evolves exogenously through time, in#uenced by broader social trends, etc., then we should expect a responsive regulatory agency to adjust to take account of such evolution. This response might involve recalibrating a given instrument or } if one of the critical thresholds is traversed } switching between instruments. A long-term upward trend in the evolution of b } driven by, for example, the spreading in#uence of ethical investors } may generate &reversals' in instrument choice, with an initial switch away from market-based instruments followed by a later switch back towards them. What of regulatory attitudes towards changes in b? This depends upon the starting point and the size and direction of the change } certainly the simple view that more honesty is always good cannot be sustained. Starting from b"0 (the &default' assumption in conventional economic analysis) marginal increases in the parameter are an impediment to the agency in its work such that &pioneer' ethical "rms might legitimately be regarded as a nuisance, &throwing a spanner' into the regulatory process. Increases in population honesty are only welfareimproving at the margin once a certain critical prevalence has been achieved.
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Such a recognition has particularly interesting implications in contexts where b } rather than being exogenous } is something that the regulatory agency might have scope to in#uence, e.g. through &good citizenship' campaigns. A policy aimed at encouraging increased honesty from a low base is only welfareimproving if it can work on a big enough scale to get over the hill and far enough down the other side of the inverted-" in Fig. 1. The analysis provides a possible e$ciency-interpretation for the USEPA's apparent willingness to tolerate widespread misreporting of environmental performance by those in its charge (as evidenced by Yaeger, 1991, and others). This is alternative to the standard view that any such tolerance must necessarily indicate incompetence, sloth or regulatory capture on the part of the agency. The analysis could, of course, be extended in a variety of ways. Perhaps most importantly: E &Honesty' could be modelled in a non-binary way (di!erent agents could, for example, be assumed to get di!erent marginal disutilities per unit of underreporting). E The EPA's monitoring and enforcement programme could be modelled in a variety of alternative ways (including, for example, speci"cation and optimisation of speci"c expected penalty functions). E The possibility of &social norm' in#uences on behaviour } for instance that a "rm may be more willing to comply if it believes that others are going to (honesty may be &infectious') or if it believes that non-compliance by other "rms will be adequately punished (as suggested by Scholtz, 1984) } could be incorporated. E There may also be interdependence in compliance decisions when "rms face each other as rivals in a product market. The only way "rms in a very competitive industry could &a!ord' honesty would be if dishonest rivals faced a signi"cant probability of being caught and punished. E Perhaps most interesting would be to model repetition } under which the EPA might have the ability to target its enforcement e!ort according to the previous performance of individual "rms (as in, for example, Harrington, 1988). Such extensions, however, could be expected to enrich rather than to negate the sorts of insights presented here. I am grateful to a referee for highlighting these possibilities. The former type of &motivational externality' has been explored by Haltiwanger and Waldman (1991, 1993). They suppose that some fraction g of a population of agents are &responders' who choose to behave opportunistically (anti-socially) if (and only if ) they observe opportunistic (anti-social) behaviour by others. Frey (1994) has explored the (he asserts negative) interaction between the intensity of regulatory compulsion and the propensity for voluntarism. Such e!ects could be added to the model here.
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Acknowledgements I am grateful to two referees and seminar participants at Tilburg University for helpful comments. Errors are mine.
Appendix Di!erentiating (9) and applying the envelope theorem yields d¸(tH(b), b) "¸(tH(b)"H)!¸(tH(b)"D). db
(A.1)
Di!erentiating yields
* d¸(tH(b), b) *tH *¸(tH(b)"H) *¸(tH(b)"D) " ! . *b *b *t db *t
(A.2)
Let the expression in brackets on the right-hand side of (A.2) be denoted X. The left-hand side of (A.4) will be opposite in sign to X (since *tH/*b(0). Now, *¸(tH(b)"D) *xH(t"D) "! (t(1!m)!d), *t *t
(A.3)
whilst (11) implies *¸(tH(b)"H) (1!b) *¸(tH(b)"D) "! *t b *t
(A.4)
such that
(1!b) *xH(t"D) X"! (t(1!m)!d) ! !1 . *t b
(A.5)
Note from the planner's "rst-order condition that (t(1!m)!d)(0 such that X'0. The inequality in (13) follows directly.
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Dimento, J., 1986. They Treated Me Like a Criminal.. University of Pittsburgh Press, Pittsburgh. Erard, B., Feinstein, J.S., 1994. Honesty and evasion in the tax compliance game. RAND Journal of Economics 25 (1), 1}19. Frey, B.S., 1994. Pricing and regulating a!ect environmental ethics. Environmental and Resource Economics 2, 399}414. Graetz, M.J., Reinganum, J.F., Wilde, L.L., 1986. The tax compliance game: Towards an interactive theory of law enforcement. Journal of Law, Economics & Organisation 2, 1}32. Gray, W.B., Deily, M.E., 1996. Compliance and enforcement: Air pollution regulation in the US steel industry. Journal of Environmental Economics and Management 31, 96}111. Haltiwanger, J., Waldman, M., 1991. Responders versus nonresponders: A new perspective on heterogeneity. Economic Journal 101, 1085}1102. Haltiwanger, J., Waldman, M., 1993. The role of altruism in economic interaction. Journal of Economic Behavior and Organization 21, 1}15. Harford, J.D., 1987. Self-reporting of pollution under imperfectly enforceable pollution standards and taxes. Journal of Environmental Economics and Management 14, 26}43. Harrington, W., 1988. Enforcement leverage when penalties are restricted. Journal of Public Economics 37, 29}53. Heyes, A.G., 1996. Cutting environmental penalties to protect the environment. Journal of Public Economics 60 (2), 251}265. Heyes, A.G., 1998. Making things stick: The economics of enforcement and compliance. Oxford Review of Economic Policy 14 (4), 50}63. Levi, M., 1988. Of Rule and Revenue. University of California Press, Berkeley, CA. Magat, W., Viscusi, W.K., 1990. The e!ectiveness of EPA's regulatory enforcement: The case of industrial e%uent standards. Journal of Law and Economics 33, 331}360. Nowell, C., Shogren, J., 1994. Challenging the enforcement of environmental regulation. Journal of Regulatory Economics 6, 265}282. Scholtz, J.T., 1984. Cooperation, deterrence, and the ecology of regulatory enforcement. Law and Society Review 18 (2). Xepapadeas, A., 1995. Observability and choise of instrument mix in the control of externalities. Journal of Public Economics 56, 485}498. Xepapadeas, A., 1997. Advanced Principles in Environmental Policy. Edward Elgar, Cheltenham, England. Yaeger, P.E., 1991. The Limits of the Law: Public Regulation of Private Pollution. Cambridge University Press, New York, NY.