Strategic Statutory Interpretation by Administrative Agencies

Strategic Statutory Interpretation byAdministrative Agencies

Yehonatan Givati, Harvard Law School

Many statutes are administered by administrative agencies. This paper shows that, when

interpreting an ambiguous statute, administrative agencies choose between two strate-

gies of statutory interpretation: the risky strategy, a relatively aggressive interpretation

that provokes an appeal by the firm; and the safe strategy, a relatively nonaggressive

interpretation that the firm complies with. The paper also shows that a change in the

level of judicial deference may result in a shift from the risky strategy to the safe

one, or vice versa. Therefore, contrary to the commonly held view, an increase in the

level of judicial deference may result in agencies choosing a less aggressive statutory

interpretation, and in more court decisions reversing agencies’ statutory interpretation.

(JEL D02, D73, D78, K23)

1. Introduction

Many statutes are administered by administrative agencies. These statutesare often very general, and can be interpreted in more than one way. Howdo administrative agencies choose their statutory interpretation?

I am grateful to Assaf Eilat, Louis Kaplow, Steven Shavell, Holger Spamann, MatthewStephenson, participants in the Eighteenth Annual Meeting of the American Law andEconomics Association at Columbia Law School, and the Political Economy and PublicLaw Conference at Harvard Univeristy for helpful comments on prior drafts. I am alsograteful for research support from the Terence M. Considine fellowship and the John M.Olin Center for Law, Economics, and Business at Harvard Law School.

Send correspondence to: Harvard Law School, 23 Everett Street, Rm. 313, Cambridge,MA 02138, USA; Telephone: 617-910-7026; E-mail: [email protected].

American Law and Economics Reviewdoi:10.1093/aler/ahp017

C© The Author 2009. Published by Oxford University Press on behalf of the American Law and EconomicsAssociation. All rights reserved. For permissions, please e-mail: [email protected].

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American Law and Economics Review 20 ( – )

To address this question, this paper employs a model with two strategicplayers: an administrative agency and a firm; and a nonstrategic one, thecourt. In the model, the agency, which maximizes some objective function,adopts a rule that interprets a statute that applies to the firm. The firm decideswhether to comply with the rule or to appeal it in court, claiming that theinterpretation adopted by the agency does not follow from the statute. Ifthe rule is appealed, the court has to decide whether to uphold the agency’sinterpretation, or to reverse it and adopt what the court thinks is the mostreasonable interpretation of the statute. The court’s decision is affected bythe doctrine of judicial deference, set forth in the landmark decision Chevronv. Natural Resources Defense Council (467 U.S. 837 [1984]), according towhich courts must defer to the agency’s interpretation of its own statute aslong as that interpretation is reasonable.

The model shows that, when deciding how to interpret an ambiguousstatute, administrative agencies choose between two strategies of statutoryinterpretation: the risky strategy and the safe one. In the risky strategy,the agency chooses a relatively aggressive interpretation that provokes anappeal by the firm, and consequently the agency bears the risk of having itsinterpretation reversed by the court. In the safe strategy, the agency chooses arelatively nonaggressive interpretation that, given the firm’s litigation cost,will be complied with and will not be appealed. The agency’s choice ofstrategy depends on the level of judicial deference and on the firm’s litigationcost. The model realistically predicts that, depending on these parameters,in some cases the agency’s interpretation will not be appealed, in other casesit will be appealed and upheld by the court, while in yet other cases it willbe appealed and reversed by the court.

How does a change in the level of judicial deference to administrativeagencies affect agencies’ statutory interpretation? It would appear that achange in the legal doctrine so that courts become more deferential to agen-cies would lead agencies to choose a more aggressive statutory interpreta-tion. Furthermore, one would naturally expect to observe more court deci-sions upholding agencies’ statutory interpretation following such a change.However, an analysis of the model shows that an increase in the level of judi-cial deference makes both the risky strategy and the safe one more attractive.Consequently, when the firm’s litigation cost is neither too high nor too low,such a change will result in the agency moving from the risky strategy to asafer one, or vice versa. This means that in some cases an increase in the

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level of judicial deference will result in the agency adopting a more aggres-sive interpretation, but in other cases it will result in the agency adopting aless aggressive interpretation. Moreover, since a move to the safe strategyeliminates litigation and a move to the risky strategy produces litigation, achange in the level of judicial deference results in a change in the set ofcases that are brought before the court. Thus, one cannot analyze the effectof a change in the level of judicial deference by simply comparing courtdecisions prior to such a change and following it, or by comparing courtdecisions in cases where different doctrines of judicial deference apply.1

Several papers have used formal models to address administrative agen-cies’ statutory interpretation, either directly (Spiller, 1992; Stephenson,2006) or indirectly, when analyzing the interaction between Congress, thepresident, an administrative agency, and the court (Cohen and Spitzer, 1994;Eskridge and Ferejohn, 1992; Ferejohn and Weingast, 1992). Unlike thesepapers, which assume that agencies’ interpretation will always be challengedin court, this paper incorporates the firm’s decision to appeal the agency’sinterpretation into the model. In this respect the model has the same basicstructure as the appeals model in Shavell (2006).2 Furthermore, some ofthose papers do not incorporate the judicial deference doctrine into theirmodel, while others that do so predict that the agency’s statutory interpre-tation is never appealed or reversed by the court, and that a higher levelof deference will always result in the agency choosing a more aggressivestatutory interpretation.

The appropriate scope of judicial review of agency decisions has dom-inated the administrative law scholarship, especially after the Chevron de-cision (see, for example: Breyer, 1986; Pierce, 1988; Scalia, 1989; Starr,1986; Sunstein, 1989; Sunstein, 1990). In particular, many attempts havebeen made to empirically measure the effect of the different levels of judicialdeference by observing the number of court decisions in which the court

1. For example, according to United States v. Mead Corporation (533 U.S. 218[2001]), agency interpretations of statutes in less formal guidance documents or interpre-tive statements, rather than rules or orders, should be reviewed under a less deferentialstandard than the Chevron standard, articulated in Skidmore v. Swift & Co. (323 U.S. 134[1944]).

2. The agency in the model is like the trial court in Shavell (2006). However,incorporating the judicial deference doctrine into the model yields two optimal policiesfor the agency that are not present in Shavell (2006).



upheld agencies’ statutory interpretation (Avila, 2000; Cohen and Spitzer,1994; Eskridge and Lauren, 2008; Gossett, 1997; Hickman and Krueger,2007; Kerr, 1998; Merill, 1992; Schuck and Elliott, 1990; Womack, 2002).

The paper proceeds as follows. Section 2 presents the results of the modelusing an illustrative example. Section 3 presents the model which, for con-creteness, and without restriction of generality, focuses on an environmentalagency. Section 4 analyzes the model and Section 5 analyzes comparativestatics. Section 6 presents two extensions: one analyzes the case where theagency is uncertain about the firm’s litigation cost, and the other considersthe effect of an increase in the level of judicial deference on the aggressive-ness of the risky strategy. Section 7 concludes.

2. An Illustrative Example

Suppose a statute requires an environmental agency to set the minimumlevel of air quality around a chemical plant. A higher standard of air qualityis more costly to the firm that owns the plant. Given the different scientificstudies on this issue, the court is likely to think that the right standard is inthe range between 80 and 100.

The agency, which prefers a higher standard to a lower one, would like toset a standard higher than 100. The court will not simply reverse any standardover 100, since the doctrine of judicial deference requires the court to deferto the agency’s interpretation of the statute as long as that interpretationis reasonable. The agency is uncertain about the court’s decision whenconsidering a standard higher than 100. Still, the agency knows that thehigher the standard it chooses the more likely the court is to reverse it andset the standard at 100, since a higher standard is further away from thecourt’s range of right standards. Assume, for instance, that increasing thestandard by one increases the probability of reversal by the court by 1%.Accordingly, if the agency sets the standard at 120, there is a 20% probabilityof reversal; and if it sets the standard at 160, there is a 60% probability ofreversal.

The firm bears a certain cost when appealing the agency’s standard incourt. Accordingly, the firm will not appeal every standard over 100 that isset by the agency. For example, if the agency sets the standard at 101 thefirm will comply with it, since the benefit of an appeal, given the relatively

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low standard and the 1% probability of success, does not outweigh the costof litigation. More generally, taking into account the probability of reversalby the court, the cost of complying with a higher standard, and the cost oflitigation, the firm determines its threshold standard. The firm will appeala standard set by the agency only if it is higher than its threshold standard.Suppose this threshold standard is 120.

Since any standard lower or equal to 120 will not be appealed, and sincethe agency prefers a higher standard to a lower one, the agency will neveradopt a standard lower than 120. However, the agency might consider settinga higher standard. Because the firm will appeal a standard higher than 120,claiming that the interpretation adopted by the agency does not follow fromthe statute, the agency faces a trade-off when choosing such a standard. Ifthe agency’s chosen standard is not reversed by the court, the agency prefersa higher standard to a lower one; but a higher standard also increases thelikelihood of reversal by the court. Therefore, as an alternative to settingthe standard at 120, the agency will consider the optimal standard given anappeal. Suppose that, taking into account the probability of reversal by thecourt, the agency’s optimal standard given an appeal is 150.

When the agency decides on its standard, it compares the thresholdstandard 120, with the optimal standard given an appeal 150. If the agencysets the standard at 150, the firm will appeal it in court. There is a 50%probability that the court will uphold the standard, and a 50% probabilitythat the court will reverse it and set the standard at 100. Thus, when settingthe standard at 150, the agency’s expected standard is 125. By contrast, ifthe agency sets the standard at 120, the firm will comply with it and will notappeal it in court. Thus, when setting the standard at 120, the agency knowswith certainty that this standard will apply. Since the expected standard whensetting the standard at 150 is 125, which is higher than 120, the agency willset the standard at 150.

More generally, choosing 150 is the risky strategy, since the firm willappeal this decision in court, and with some probability the court will reversethe agency’s decision and the agency will end up with a low standard of 100.Choosing 120 is the safe strategy, because the firm will comply with it,and although the agency might ultimately end up with a lower standard(120 instead of 150), it will not bear the risk of reversal by the court. Theagency chooses its standard by comparing its expected utility from the twostrategies.

99



Now, suppose there is a change in the legal doctrine so that courts becomemore deferential to agencies. This means that for every standard the agencychooses, there is now a lower probability of reversal by the court. Becausethe firm knows that it now has a lower probability of success in court, it willbe more reluctant to appeal the agency’s standard. Therefore, the thresholdstandard above which it will go to court will be higher than before. Supposethe new threshold standard is 125. Furthermore, given the lower probabilityof reversal by the court, the agency might want to choose a different standardthan 150 for its optimal standard given an appeal. Suppose the new optimalstandard given an appeal is 155.3

Accordingly, following the increase in the level of judicial deference, theagency has to decide on setting the standard either at 125 (the safe strategy)or at 155 (the risky strategy). Since the safe strategy is more attractive thanbefore (125 instead of 120), the agency may decide to move from the riskystrategy to the safe one, adopting a less aggressive standard. Similarly, sincethe risky strategy is also more attractive than before (because the agencyprefers 155 to 150), the agency may also move from the safe strategy tothe risky one, adopting a more aggressive standard. Thus, in some cases anincrease in the level of judicial deference will result in the agency adopting amore aggressive interpretation, but in other cases it will result in the agencyadopting a less aggressive interpretation.

Furthermore, suppose that following an increase in the level of judicialdeference, the agency moves from the safe strategy to the risky one on manydifferent environmental standards that it sets. This means that the agency’soriginal standards were not high enough for the firms to appeal them incourt, but its new standards provoke an appeal by the firms. With certainprobability the firms’ appeal will succeed, and the court will reverse some ofthe agency’s new standards. Thus, if one would compare the court’s decisionsprior to the increase in the level of judicial deference and following it, onewould note that before the change the court did not reverse any interpretationby the agency, but after it the court did. Ignoring the agency’s change ofstrategy and focusing only on court decisions could thus lead to the mistakenconclusion that following the change the court only became less deferential,

3. As Section 6.2 shows, the new optimal standard given an appeal will not neces-sarily be higher than the original optimal standard given an appeal. This depends on thefirst-order condition in expression (6).

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since the increase in the level of judicial deference only lead to more courtdecisions reversing agency’s interpretations. Therefore, one cannot analyzethe effect of a change in the level of judicial deference by simply comparingcourt decisions prior to such a change and following it.

3. The Model

Consider a model with two risk-neutral players: an environmental agencyand a firm, and a nonstrategic one—the court. A statute concerning an envi-ronmental standard that the firm has to comply with is ambiguous. Differentstatutory interpretations are possible, and every possible interpretation cor-responds to a certain standard. The possible standards are between a lowstandard, sl, and a high standard, sh, and the court’s view of their reason-ableness is described using the probability density function f (s). The higherf (s) the more reasonable the standard s is.

Given the different possible statutory interpretations and the court’s viewof their reasonableness, the most reasonable standard that the firm shouldcomply with is s∗, where

s∗ = arg maxs

f (s).

I assume that f ′(s) > 0 for s ∈ [sl, s∗), and that f ′(s) < 0 for s ∈ (s∗, sh].This means that as we move away from s∗, the reasonableness of the standarddecreases.4 Figure 1 depicts a possible density function of the standards.

The model has three stages. In the first stage the agency chooses s, thestandard that it thinks the firm should comply with. In the second stage thefirm decides whether to comply with this standard or to appeal it in court,claiming that the interpretation adopted by the agency does not follow from

4. The analysis will not change if there are several standards that are equally mostreasonable instead of a single one. Specifically, if [s ′, s ′′] = arg max f (s), which meansthat [s ′, s ′′] ⊂ (sl , sh) includes possible standards that are all equally most reasonable(and assume now that f ′(s) > 0 for s ∈ [sl , s ′) and that f ′(s) < 0 for s ∈ (s ′′, sh]), thenif we define s∗ = s ′′ or s∗ = (s ′ + s ′′)/2 (depending on which interpretation we think thecourt picks when reversing the agency’s interpretation), there will be no change in theanalysis of the model. In such a case the administrative agency will choose s ∈ [s ′′, sh]and the model explains how the agency stretches the statutory interpretation beyond themost aggressive interpretation that is also most reasonable (s ′′). In a similar setting, s∗

can be thought of as the agency’s expected interpretation upon remand.

101



s*

Probability density

shsl

Figure 1. Reasonableness of Possible Interpretations.

the statute. The firm bears a certain cost when appealing the standard setby the agency. If the firm decides to appeal the agency’s standard then inthe third stage the court has to decide what standard the firm should complywith.

The agency’s objective function U depends on the standard s. The agencyprefers a higher standard to a lower one (an environmentalist agency).5

Assume for simplicity that U is linear in s. Thus, the agency maximizes:

U = αs, (1)

where α > 0.The firm’s objective is to minimize its cost function C, which takes into

account the cost of complying with the standard s, and its litigation cost c,if the case is litigated. The higher the standard s, the more costly it is tocomply with, and assume for simplicity that C is linear in s. Thus, the firm’scost function is:

C ={

βE[s] + c if appeal is madeβs else

, (2)

where β > 0, and E[s] is the expected standard that applies following thecourt’s ruling.

If the firm appeals the standard set by the agency, the court has to decidewhat standard the firm should comply with. Both the firm and the agencyare uncertain of the court’s decision. The court’s expected decision is afunction of the reasonableness of the standard s, represented by the function

5. One can also think of a tax agency that wants to maximize tax revenue, or inwhich there is a widespread perception among employees that promotion depends onenforcement results. See U.S. General Accounting Office (1998, pp. 28–33).

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f (s). There is a probability g( f (s)) ∈ [0, 1] that the court will reverse theagency’s interpretation of the statute and instead adopt the most reasonablestatutory interpretation s∗, and there is a probability 1 − g( f (s)) that thecourt will uphold the agency’s interpretation. I assume that g( f (s∗)) = 0,g(0) = 1, and that g′( f (s)) < 0. This is a formal expression of the judicialdeference doctrine, since it means that the less reasonable the standard s themore likely the court is to reverse it.

Let us define h(s) = g( f (s)), the probability of the court reversingthe agency’s standard s. Accordingly, h(s∗) = 0, the probability of rever-sal is zero if the agency chooses the most reasonable standard s∗, andh(sh) = h(sl) = 1, the probability of reversal is one if the agency chooses in-terpretations that are not reasonable at all. Note that h′(s) > 0 for s ∈ (s∗, sh],and that h′(s) < 0 for s ∈ [sl, s∗). This means that as we move away fromthe most reasonable standard s∗, the probability of the court reversing theagency’s standard increases.

At this point it is important to emphasize the difference between the wayjudicial deference is modeled in this paper and the way it is modeled inother papers. In other papers (Cohen and Spitzer, 1994; Stephenson, 2006;Stephenson and Vermeule, 2009) judicial deference is defined by someeffective threshold s that is decided by the court. The agency knows thatif it chooses s (or any s ≤ s) its interpretation will be upheld by the court,but if s + ε (or any s > s) is chosen, it will be reversed. By contrast, thispaper uses a framework that seems more realistic. The model assumes thatthe agency knows that there is some indisputable interpretation, representedby s∗, that will not be reversed by the court. The agency also knows thatsome flagrant interpretation is guaranteed to be reversed by the court, andthis interpretation is represented by sh (or sl). In between s∗ and sh (or sl)there are many possible interpretations that the agency may choose. Thecloser the interpretation is to the indisputable interpretation, the lower theprobability of the court reversing it.

4. Analysis

Since the agency prefers a higher standard to a lower one (see expression(1)), it will choose s ∈ [s∗, sh] in the first stage (s < s∗ will never be chosen).Let us adjust s∗, sh , and sl so that s∗ is normalized to zero.


10 American Law and Economics Review 20 ( – )

In the second stage of the model the firm appeals the standard s set by theagency if the cost of doing so, given the court’s expected ruling (based onthe probability of the court reversing the agency’s interpretation, h(s)) andits litigation cost (c), is lower than the cost of complying with the standards. Thus, based on expression (2), the firm will appeal the agency’s standardif the following condition holds:

βs > βs(1 − h(s)) + c, (3)

where the left-hand side of expression (3) is the firm’s cost of complyingwith the standard s, and the right-hand side is of expression (3) is the firm’sexpected cost when appealing the standard s. Assume that the condition inexpression (3) holds for sh, which means that the firm will always appeal theagency’s decision to adopt the highest possible standard. Since h(sh) = 1,this means that β > c

sh.

Let us define the threshold standard, above which the firm will appeal theagency’s standard. Rearranging expression (3), the threshold standard is thestandard s for which the following expression holds:

c = βh(s)s. (4)

As will be shown immediately, this standard is a corner solution, and ac-cordingly it will be denoted by scs .

Now we can define U (s), the agency’s expected utility for every choiceof standard s it makes:

U (s) ={

αs if s ≤ scs

αs(1 − h(s)) else. (5)

Expression (5) can be understood intuitively. If the agency chooses astandard s ≤ scs as its interpretation of the statute, the firm will comply withit and will not appeal it in court. If the agency chooses a standard s > scs

as its interpretation of the statute, the firm will appeal the standard in court.In that case the agency’s expected utility depends on the probability of thecourt upholding its chosen standard (1 − h(s)).

The agency chooses its standard to maximize expression (5). There is adifferent standard that maximizes each range. For s ≤ scs , scs maximizesU (s). This is the corner solution. For s > scs the standard that maximizesU (s) is defined by the first-order condition:

h′(s)s = 1 − h(s). (6)

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The standard for which expression (6) holds is the interior solution, and willbe denoted by sis .6

Intuitively, the right-hand side of expression (6) is the increase in theagency’s utility from increasing its chosen standard by one, since it is theprobability that the court will uphold the agency’s standard. The left-handside of expression (6) is the decrease in the agency’s utility from increasingits chosen standard by one, since it is the marginal change in the probabilitythat the court will reverse the agency’s standard, multiplied by the agency’sloss of utility in that case. Thus, the first-order condition means that themarginal increase in the agency’s utility from increasing its chosen standardby one is equal to a marginal decrease in its utility from such a change.

Proposition 1. The agency chooses its statutory interpretation by compar-ing its expected utility from the interior solution standard and the cornersolution standard. If U (scs) ≥ U (sis), it will choose the corner solutionstandard scs . If U (scs) < U (sis), it will choose the interior solution standardsis .

Choosing the interior solution standard sis is the risky strategy, since thefirm will appeal the agency’s decision, and consequently the agency bearsthe risk of having its interpretation reversed by the court. Choosing thecorner solution standard scs is the safe strategy, since the firm will complywith the agency’s standard and will not appeal it.

U (s) is depicted in Figure 2 for the case where U (sis) > U (scs). As onecan see, reflecting expression (5), U (s) is the linear function αs for s ≤ scs ,but, for s > scs , it is the curve αs(1 − h(s)). The corner solution standardscs and the interior solution standard sis are indicated in Figure 2.

Depending on the parameters of the model the agency will chose thesafe strategy in some cases, and the risky strategy in other cases. If thesafe strategy is chosen, the agency’s standard is not appealed. If the riskystrategy is chosen, the agency’s standard is appealed. It will be reversedby the court with probability h(sis), and upheld with probability 1 − h(sis).Thus, the model explains three types of cases: cases where the agency’s

6. The second-order condition for this s to maximize U (s) is h′′(s) > −2h′(s)/s.Since h′(s) and s are positive, the second-order condition will not be met only if h′′(s)is negative, and smaller than −2h′(s)/s. In such a case this s will minimize U (s), andthe agency will always choose the corner solution or a different s that maximize U (s).Therefore, such a case is of little interest.



U(s)

ααscs

scs sis sh

ααs(1 - h(s))

s

Figure 2. Agency’s Expected Utility from Chosen Interpretation.

statutory interpretation is not appealed; cases where the agency’s statutoryinterpretation is appealed and reversed by the court; and cases where theagency’s statutory interpretation is appealed and upheld by the court.

5. Comparative Statics

The level of judicial deference to agencies’ statutory interpretation re-flects a balance between two competing objectives: allowing agencies touse their expertise, and requiring agencies to adopt a reasonable reading ofthe statute so that they will not pursue their own independent objectives.A change in the balance between these two objectives changes the level ofjudicial deference.

An increase in the level of deference to the agency’s statutory interpre-tation means that for every statutory interpretation the agency adopts, thereis a lower probability of reversal by the court. Formally, h(s) was defined inSection 3 as a function that expresses the probability of the court reversingthe agency’s standard s and instead ruling that s∗ = 0 should be compliedwith. The function h1(s) expresses a higher level of deference if h(s) > h1(s)for any s ∈ (s∗, sh).

The increase in the level of deference affects the model. Following thechange in the court’s decision function from h(s) to h1(s), the new thresholdstandard above which the firm appeals the agency’s decision will be denotedby scs

1 , and is defined by the following condition:

c = βh1(s)s. (7)

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This standard is also the new corner solution. Comparing expressions (4) and(7), we can see that scs

1 > scs (since h1(scs) < h(scs) and h′1(s) > 0). This

result can be understood intuitively. The increase in the level of deferencemeans that for every standard that the agency chooses there is a lowerprobability of reversal by the court. Thus, the firm will be more reluctantto appeal the agency’s decision, and will appeal the decision only above ahigher threshold.

The agency’s new expected utility function will be denoted by U1(s), andis defined by the following:

U1(s) ={

αs if s ≤ scs1

αs(1 − h1(s)) else. (8)

The new interior solution, sis1 , is defined by the following first-order

condition:

h′1(s)s = 1 − h1(s). (9)

Following the increase in the level of deference, if U1(sis1 ) > U1(scs

1 ), theagency will choose the risky strategy and the interior solution standard sis

1

as its statutory interpretation. Otherwise, the safe strategy will be chosen,and the corner solution standard scs

1 will be the agency’s chosen statutoryinterpretation.

To analyze more precisely the effect of an increase in the level of judicialdeference, let us scale the model by sh. We can define an adjusted litigationcost c = c

shand an adjusted upper bound sh = 1. Now, the relevant range of

standards is [s∗, sh], or simply [0, 1], and the firm’s effective litigation costis the adjusted cost c. Note that, as shown in Section 4, β > c. To simplifynotation, we keep using c instead of c when referring to the firm’s effectivelitigation cost.

Let us also assume a certain functional form for the functions that expressthe probability of the court reversing the agency’s standard s. Specifically,assume that h(s) = sx and h1(s) = sγx , where x > 0 and γ > 1. Note thath1(s) expresses a higher level of judicial deference, since h(s) > h1(s) forany s ∈ (0, 1). In other words, the probability of the court reversing anystandard chosen by the agency is lower under h1(s) than under h(s). Figure 3shows an example of an increase in the level of judicial deference, from sx

to sγx , where x = 1 and γ = 2.



1

0 1 s

h(s) = s

h1(s) = s2

Probability of reversal

Figure 3. Increase in Level of Judicial Deference.

Based on expressions (4) and (7), we get scs = ( cβ)

11+x and scs

1 = ( cβ)

11+γx .

Since β > c and γ > 1, scs1 > scs , which means that the safe strategy standard

becomes more aggressive following the increase in the level of judicialdeference (the farther a standard is from the most reasonable interpretations∗ = 0, the more aggressive it is). Using expressions (6) and (9), we getsis = ( 1

1+x )1x and sis

1 = ( 11+γx )

1γx . Because x > 0 and γ > 1, sis

1 > sis , whichmeans that the risky strategy standard becomes more aggressive followingthe increase in the level of judicial deference.

As noted, the agency chooses the safe strategy over the risky one beforethe increase in the level of judicial deference if U (scs) ≥ U (sis). Pluggingin the expressions for scs and sis , and defining m(x) = ( x

(1+x)1+x

x)1+x , we get

that this condition holds when c ≥ βm(x). Similarly, following the increasein the level of judicial deference, the agency chooses the safe strategyover the risky one if U1(scs

1 ) ≥ U1(sis1 ). Plugging in the expressions for

scs1 and sis

1 , we get that this condition holds when c ≥ βm(γx). Definec = max(m(x), m(γx)) and c = min(m(x), m(γx)).

Proposition 2. When the level of judicial deference increases, and thecourt’s decision function changes from h(s) to h1(s), then

(1) If c > βc, the agency chooses the safe strategy before the change andafter it.

(2) If c < βc, the agency chooses the risky strategy before the change andafter it.

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(3) If c ∈ [βc, βc] then the agency changes its strategy following the in-crease in the level of judicial deference. If m(x) ≥ m(γx) (whichis always true when x ≥ 1), the agency chooses the risky strategybefore the change, and the safe one after it. If m(x) < m(γx), theagency chooses the safe strategy before the change and the risky oneafter it.

Proposition 2 can be understood intuitively. If the firm’s litigation costis sufficiently high, the firm’s threshold for appealing the agency’s standardis relatively high. Therefore, the safe strategy is very attractive, since whenchoosing it the agency can set a relatively high standard without takingthe risk of reversal by the court. Accordingly, the agency will choose thesafe strategy both before the increase in the level of judicial deference andafter it.

If the firm’s litigation cost is sufficiently low, the firm’s threshold forappealing the agency’s standard is relatively low. Therefore, the safe strategyis not attractive, since in order to eliminate the risk of reversal by the court,the agency has to adopt a very low standard. Accordingly, the agency willprefer to take the risk of reversal by the court in order to set a higher standard,and will thus choose the risky strategy both before the increase in the levelof judicial deference and after it.

If the firm’s litigation cost is somewhere in the middle, the agency willchange its strategy following the increase in the level of judicial deference.This is a result of the fact that the increase in the level of judicial deferencemakes both the risky strategy and safe one more attractive. On the onehand, the firm’s threshold for appealing the agency’s standard increases,since the firm is more reluctant to appeal the agency’s standard given thelower probability of success in court, and this makes the safe strategy moreattractive. On the other hand, the probability of the court reversing theagency standard when it chooses the risky strategy decreases, which makesthis strategy also more attractive. The type of change will depend on theshape of the court’s decision functions h(s) and h1(s). If these functionsare both convex (x ≥ 1), the agency will choose the risky strategy beforethe change and the safe strategy after it. If they are both concave (x < 1and γx ≤ 1), the agency will choose the safe strategy before the change andthe risky strategy after it. If h(s) is concave but h1(s) is convex, the twosituations are possible.



Proposition 2 shows that an increase in the level of judicial deferencemay result in a shift from the risky strategy to safe one, but may also resultin a shift from the safe strategy to risky one. Therefore, contrary to thecommonly held view (Cohen and Spitzer, 1994; Elliott, 2005; Stephenson,2006), an increase in the level of judicial deference may result in the agencybeing less aggressive in its statutory interpretation. Furthermore, when theagency moves from the risky strategy to the safe one, litigation disappears,while a change in the other direction produces litigation. Thus, a changein the level of judicial deference results in a change in the set of casesthat are brought before the court. This means that the consequences of achange in the level of judicial deference cannot be measured by observingthe number of cases in which the court upheld agencies’ interpretations, amethod that was employed in many papers (Avila, 2000; Cohen and Spitzer,1994; Eskridge and Lauren, 2008; Gossett, 1997; Hickman and Krueger,2007; Kerr, 1998; Merill, 1992; Schuck and Elliott, 1990; Womack, 2002).

6. Extensions

In this section two extensions are analyzed. First, the case where theagency is uncertain about the firm’s litigation cost is considered, showingthat the basic trade-off between a relatively aggressive interpretation anda relatively nonaggressive interpretation holds when such uncertainty isintroduced. Second, the effect of an increase in the level of judicial deferenceon the aggressiveness of the risky strategy is considered, showing that anincrease in the level of judicial deference may lead to a risky strategy that isless aggressive.

6.1. Uncertainty Regarding The Firm’s Litigation Cost

The model in Section 3 assumes that the agency knows c, the firm’slitigation cost. Suppose now that the agency does not know c with certainty,but only knows its distribution. Formally, the firm’s possible litigation costsare distributed between 0 and ch based on a strictly increasing distributionfunction J (c), which the agency knows.

Using expression (4), we know that the firm will appeal the agency’schosen standard s only if c ≤ βh(s)s. Therefore, for every standard s thatthe agency chooses, the probability of an appeal by the firm is J (βh(s)s).

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If we define s as the standard for which ch = βh(s)s, that is, the thresholdstandard that corresponds to the highest possible litigation cost ch , we candefine U2(s), the agency’s expected utility for every choice of standard s itmakes:

U2(s) ={

αs[1 − J (βh(s)s)h(s)] if s ≤ sαs(1 − h(s)) else

, (10)

Expression (10) can be understood intuitively. If the agency chooses astandard s ≤ s as its interpretation of the statute, the firm will appeal thestandard with probability J (βh(s)s), in which case the court will reverse theagency’s decision with probability h(s). If the agency chooses a standards > s as its interpretation of the statute, the firm will always appeal thestandard in court, and the court will reverse the agency’s decision withprobability h(s).

The agency chooses its standard to maximize expression (10). There isa different standard that maximizes each range. For s > s, the standard thatmaximizes U (s) is defined by the first-order condition:

h ′(s)s = 1 − h(s), (11)

which is the same condition as the one we derived in Section 4.For s ≤ s the standard that maximizes U2(s) is defined by the first-order

condition (to simplify notation J (βh(s)s) = J and h(s) = h):

[J h′ + βJ ′h(h + h′s)]s = 1 − J h. (12)

Intuitively, the right-hand side of expression (12) is the increase in theagency’s utility from increasing its chosen standard by one, since J h is theprobability of the firm appealing the agency’s chosen standard and the courtreversing it, and therefore 1 − J h is the probability that the agency’s chosenstandard will stand. The left-hand side of expression (12) is the decreasein the agency’s utility from increasing its chosen standard by one, since anincrease in the standard increases the probability of an appeal (the secondterm in the brackets) and also the probability of the court reversing theagency’s standard (the first term in the brackets). This is multiplied by theagency’s loss of utility when its interpretation is reversed. Thus, the first-order condition means that the marginal increase in the agency’s utility fromincreasing its chosen standard by one is equal to the marginal decrease inits utility from this change.

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Expressions (11) and (12) define two local optima. Choosing the optimalstandard defined by expression (11) is the relatively risky strategy, sincealthough this standard is relatively high, it will always be appealed. Choosingthe optimal standard defined by expression (12) is the relatively safe strategy,since although this standard is relatively low, with certain probability the firmwill comply with it and will not appeal it in court. The agency compares itsexpected utility from both strategies and chooses accordingly which strategyto adopt.

Thus, the basic trade-off between a relatively aggressive statutory in-terpretation and a relatively nonaggressive statutory interpretation that wasshown in Section 4 holds when uncertainty regarding the firm’s litigationcost is introduced.7

6.2. Aggressiveness of Risky Strategy

As shown in Proposition 2, if the firm’s litigation cost is sufficiently low,the agency will choose the risky strategy both before the increase in thelevel of judicial deference and after it. This seems particularly plausiblein high profile cases, where litigation costs are low relative to the issue atstake, and therefore the agency always expects its chosen interpretation tobe appealed. In such a case, how will the aggressiveness of the agency’sstandard be affected by an increase in the level of judicial deference?

In the functional form used in Section 5, the risky strategy standardalways becomes more aggressive following an increase in the level of judicialdeference (sis

1 > sis). This means that if the agency chooses the risky strategyboth before the increase in the level of judicial deference and after it, itschosen standard becomes more aggressive. However, analyzing this case ina more general setting shows that this is not always the case.

When the agency chooses the risky strategy both before the increase inthe level of judicial deference and after it, its chosen standard is sis before thechange and sis

1 after it. Is the new standard sis1 higher or lower than the original

standard sis? This is determined by comparing the first-order conditions in

7. To illustrate this result, let us use the scaled model from Section 5, where therelevant range of standards is [0, 1]. Suppose α = β = 1, and that h(s) = s. Supposealso that c is distributed uniformly between 0 and 0.16, and therefore s = 0.4. In thiscase the relatively risky strategy is s = 0.5, and the relatively safe strategy is s = 0.34.The agency’s expected utility from choosing the relatively risky strategy is 0.25, andits expected utility from choosing the relatively safe strategy is 0.256. Therefore, therelatively safe strategy will be chosen by the agency.

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1

sis0

sh s

h(s)h1(s)

s*

Probability of reversal

Figure 4. Increase in Marginal Probability of Reversal.

expressions (6) and (9). Define h′1(·) for which h′

1(sis)sis = 1 − h1(sis). Thismeans that for h′

1(·) the agency’s new first-order condition in expression (9)holds for sis , the agency’s original standard. Now, if h′

1(sis) < h′1(sis) then

sis1 > sis , which means that the increase in the level of judicial deference

results in the agency choosing a more aggressive standard.However, if h′

1(sis) > h′1(sis) then sis

1 < sis , which means that despitethe increase in the level of judicial deference, the agency will choose a lessaggressive standard. This occurs in the realistic case where, following theincrease in judicial deference, the court gives the agency more leeway arounds∗, the most reasonable standard, but is not significantly more tolerant formore distant standards, as depicted in Figure 4.

The latter result can be understood intuitively, focusing on the first-ordercondition in expression (6). As noted in Section 4, this condition means thatthe increase in the agency’s utility from increasing its standard by one is equalto the decrease in its utility from this change. The increase in the agency’sutility from increasing its standard depends on the probability of the courtupholding the agency’s chosen standard (the right-hand side of expression(6)). An increase in the level of deference increases the probability of thecourt upholding the agency’s standard, and thus the agency’s expected utilityfrom choosing a more aggressive standard increases. However, the decreasein the agency’s utility from increasing its standard depends on the marginalincrease in the probability of the court reversing the agency’s standard (theleft-hand side of expression (6)). Even if the level of judicial deferenceincreases, it is still possible that, in the vicinity of sis , the marginal increasein the probability of the court reversing the agency’s standard is higher



than before, and consequently, the agency’s utility from choosing a moreaggressive standard decreases. If the latter effect is sufficiently strong, theagency will choose a less aggressive standard in spite of the increase in thelevel of judicial deference.

7. Conclusion

This paper explains how administrative agencies strategically choosetheir statutory interpretation. The model shows that administrative agencieschoose between the risky strategy: a relatively aggressive interpretation thatprovokes an appeal by the firm, and the safe strategy—a relatively nonag-gressive interpretation that the firm complies with. This choice depends onthe level of judicial deference, and on the firm’s litigation cost.

After characterizing the agency’s choice of statutory interpretation,the paper analyzes how changes in the level of judicial deference affectthe agency’s choice of statutory interpretation. It shows that an increasein the level of judicial deference makes both the risky strategy and the safeone more attractive. Therefore, an increase in the level of judicial deferencemay result in the agency choosing a less aggressive statutory interpreta-tion. Furthermore, one cannot simply use the number of cases in which thecourt upheld the agency’s interpretation to measure the effect of a changein the level of judicial deference. Such a method assumes that the sameset of cases is brought before the court under different levels of judicialdeference, and ignores possible adjustments in the agency’s interpretativestrategy following a change in the level of judicial deference.

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