Opinion for the Court filed by Senior Circuit Judge RANDOLPH.
Opinion concurring in the judgment filed by Circuit Judge BROWN.
RANDOLPH, Senior Circuit Judge:This is an appeal from an order of the district court granting summary judgment to the Secretary of Health and Human Services. Catholic Health Initiatives, a nonprofit charitable corporation, and a group of its affiliated nonprofit hospitals brought an action under the Medicare Act to recover premiums the hospitals had paid for malpractice, workers’ compensation, and other insurance. The hospitals paid the premiums to First Initiatives Insurance Ltd. from 1997 through 2002. Catholic Health wholly owns First Initiatives, which is based in the Cayman Islands.
In general, the Secretary considers malpractice, workers’ compensation, and other liability insurance premiums to be part of a hospital’s “reasonable costs” incurred in providing services to Medicare beneficiaries. As such, the costs are reimbursable. The Medicare Act defines the “reasonable cost of any services” to be “the cost actually incurred, excluding therefrom any part of incurred cost found to be unnecessary in the efficient delivery of needed health services....” 42 U.S.C. § 1395x(v)(1)(A). The “reasonable cost” “shall be determined in accordance with regulations establishing the method or methods to be used, and the items to be included, in determining such costs for various types or classes of institutions, agencies, and services ....” Id.
The regulations describe reasonable costs as “related to the care of Medicare beneficiaries,” 42 C.F.R. § 413.9(c)(3), and “determined in accordance with regulations,” id. § 413.9(b). Reasonable costs include “all necessary and proper costs incurred in furnishing” Medicare services. Id. § 413.9(a). Necessary and proper costs are those direct and indirect costs “that are appropriate and helpful in developing and maintaining the operation of patient care facilities and activities,” and that are not “substantially out of line with” the costs of similar institutions. Id. § 413.9(b)(2), (c)(2).
The Secretary has issued a Provider Reimbursement Manual. The Manual contains “guidelines and policies to implement Medicare regulations which set forth principles for determining the reasonable cost of provider services,” but it “does not have the effect of regulations.” Centers for Medicare and Medicaid Services, Provider Reimbursement Manual, Part 1, Foreword, at I (“PRM”). The Manual does bind Medicare’s “fiscal intermediaries”—private firms under contract with the Secretary to review provider reimbursement claims and determine the amount due. See 42 U.S.C. § 1395h; Yale-New Haven Hosp. v. Leavitt, 470 F.3d 71, 80-81 (2d Cir.2006); St. Mary of Nazareth Hosp. Ctr. v. Schweiker, 718 F.2d 459, 463 (D.C.Cir.1983).1
Rather than purchasing insurance in the market, some Medicare providers have established their own insurance companies— known as “captives”—for the purpose of insuring themselves against malpractice and certain other claims. PRM § 2162.2.A. If the captive is a domestic *492corporation, and if the premiums it charges are comparable to those of other insurance companies, the Manual states that the affiliated provider is entitled to reimbursement for premiums paid to the captive. Id. But if the captive is offshore, the Manual prohibits reimbursement for premiums if the captive’s investments do not comply with the following rule:
In the case of offshore captives, investments by a related captive insurance company are limited to low risk investments in United States dollars such as bonds and notes issued by the United States Government; debt securities issued by United States corporations or governmental entities within the United States rated in the top two classifications by United States recognized securities rating organizations at the time of investment; debt securities of foreign subsidiaries of United States corporations rated in the top two classifications by United States recognized securities rating organizations at the time of investment where the parent United States corporations guaranteed (on the face of the securities) payment of the subsidiaries’ securities; and deposits (including Certificates of Deposit) in United States banks or their foreign subsidiaries, and foreign banks rated in the top two short term classifications by United States recognized securities rating organizations. Low risk investments may also include investments of non-United States issuers including foreign governments and corporations and supranational agencies rated in the top two classifications by United States recognized securities rating organizations (effective with investments made on or after 10/11/91). Effective for investments made on or after 10/06/95, the limitation on related offshore captive insurance company investments is extended to include the above described low risk investments rated in the top three classifications by United States recognized securities rating organizations. Additionally, investments may include dividend paying equity securities listed on a United States stock exchange provided that the investment in equity securities does not exceed 10 percent of the company’s admitted assets, with the investment in any specific equity issue further limited to 10 percent of the total equity security investment. (All such captives are required to annually submit to a designated intermediary a certified statement from an independent certified public accountant or actuary attesting to compliance or non-compliance with these requirements for the previous period.) These investments cannot be pledged or used as collateral for loans obtained by the captive or parties related to the captive either directly or indirectly, nor may investments be made in a related organization.
PRM § 2162.2.A.4. First Initiatives Insurance did not satisfy these requirements. During the contested period it invested as much as forty to fifty percent of its assets in equity securities.
In light of First Initiatives’ noncompliance with the Manual, the hospitals disallowed their premium payments on the annual cost reports they submitted to Medicare’s fiscal intermediaries. See 42 C.F.R. § 405.1801(b)(1). The hospitals then sought to recover those premiums by challenging § 2162.2.A.4 at a hearing before the Provider Reimbursement Review Board, a five-member panel with authority to affirm, modify, or reverse an intermediary’s decision. 42 U.S.C. § 1395oo(a), (d), (h). (Here the intermediary decision was merely to accept the hospitals’ own disallowance of their premium costs.) The Board must give the Manual “great weight,” but—unlike an intermediary—is not bound by it. 42 C.F.R. § 405.1867.
*493In a three to two decision, the Board held that the investment limitations in § 2162.2.A.4 of the Manual were a “valid extension” of the statute and the regulations governing “reasonable cost.” Therefore the Board majority treated the provision as “compulsory.” Catholic Health Initiatives v. Mutual of Omaha Ins. Co., PRRB Decision No.2007-D14 (Jan. 24, 2007) (“Board Decision”). The majority explained that, unlike domestic captive insurance companies, offshore captives present an “inherent risk”: “offshore captives are under the control of foreign governments and are not subject to the same level” of regulation as domestic insurers, which are regulated by the states. In addition, the ten percent limit on equity investments “is in line with the asset allocations found among domestic insurance companies.” The two dissenting Board members believed that § 2162.2.A.4 of the Manual was not an “appropriate application of Medicare statutory reasonable cost principles,” that it was “devoid of any link to the standards expressed in the regulations,” and that it could not be justified as an interpretive rule “exempt from the notice and comment provisions of the Administrative Procedure Act.... ” The ten percent provision was, the dissenters stated, an example of “why the rulemaking process is critical to establishing standards such as those involved here.”
Catholic Health and the hospitals brought this action in the district court after the Secretary’s delegate—the Administrator of the Centers for Medicare and Medicaid Services—declined to review the Board’s decision. See 42 U.S.C. § 1395oo(f); 42 C.F.R. § 405.1877. The district court viewed the issue as “whether the Board’s ruling—which found the reimbursement standard expressed in the PRM to be consistent with both the Medicare statute and the Medicare regulations-—was lawful, not whether the PRM provision itself was lawful.” Catholic Health Initiatives v. Sebelius, 658 F.Supp.2d 113, 122 (D.D.C.2009). Granting summary judgment in favor of the Secretary, the court found that the Board’s adherence to the Manual’s interpretation was “not plainly erroneous or inconsistent with the statute or the regulation....” Id. at 123.
The Secretary defends the Manual’s investment limitations on the ground that the limitations comprise an “interpretative” rule. See 5 U.S.C. § 553(b)(A); Am. Mining Cong. v. Mine Safety & Health Admin., 995 F.2d 1106 (D.C.Cir.1993). As the Secretary puts it, “the cost of insurance premiums that Medicare is asked to reimburse can be considered ‘reasonable’ only if those premiums actually purchase reliable coverage.” Reliability depends on “the financial soundness of the insurer,” Br. of Appellee at 15, which depends on the competence of the insurer’s regulator and the pervasiveness of its regulations, id. at 29-31.2 The rule, the Secretary contends, is consistent with the statute and regulations, supported by substantial evidence, and not arbitrary or capricious. Id. at 14-17, 28.
The hospitals dispute each of these assertions. They claim that the rule regulates insurance investment decisions and therefore lies outside the scope of the Secretary’s “reasonable cost” authority under the Medicare Act. In addition, the hospitals believe that an important premise of the rule is wrong. The Board majority believed that offshore captives “are not subject to the same level of industry regulations applied to onshore agencies by State insurance companies.” Board Deei*494sion at 6. But the evidence submitted at the hearing before the Board showed “that the level of state regulation of equity investments by domestically domiciled captives is essentially zero.” Br. of Appellants at 39. In fact, “only a minority of states—twenty-three—regulate captive insurers at all.” Id. at 40. The hospitals argue that to the extent that the Manual’s limitations were intended to promote the financial strength and solvency of the offshore insurer, the limitations are arbitrary because they are both overbroad and underinclusive. The limitations are over-broad, for instance, because they permit equity investments only in securities that pay dividends. Yet the hospitals point out that many companies that appear to be financially sound—such as Microsoft during the years at issue and Google—do not pay dividends. The Manual’s investment limitations are underinclusive, the hospitals claim, because there is no requirement that a captive diversify its investments. Although no one equity investment may make up more than ten percent of a captive’s equity holdings (and thus one percent of its total assets), nothing in the Manual prevents a captive from having all of its assets in, for instance, one corporation’s bonds. See PRM § 2162.2.A.4.
We do not decide whether the Medicare Act’s reasonable cost provision would authorize the ten percent rule, or whether the reasoning and evidence in support of the Board’s decision enforcing the Manual provision are sufficient. There is an antecedent question, discussed by the dissenting Board members and raised— although without much elaboration—by the hospitals. The question is whether the Manual’s investment limitations for offshore captives is, as the Secretary contends, an “interpretive rule.”
To fall within the category of interpretive, the rule must “derive a proposition from an existing document whose meaning compels or logically justifies the proposition. The substance of the derived proposition must flow fairly from the substance of the existing document.” Robert A. Anthony, “Interpretive” Rules, “Legislative” Rules, and “Spurious” Rules: Lifting the Smog, 8 Admin. L.J. Am. U. 1, 6 n. 21 (1994). If the rule cannot fairly be seen as interpreting a statute or a regulation, and if (as here) it is enforced, “the rule is not an interpretive rule exempt from notice-and-comment rulemaking.”3 Central Tex. Tel. Coop. v. FCC, 402 F.3d 205, 212 (D.C.Cir.2005) (citing Syncor Int’l Corp. v. Shalala, 127 F.3d 90, 95 (D.C.Cir.1997)); United States v. Picciotto, 875 F.2d 345, 347-49 (D.C.Cir.1989); Hoctor v. USDA, 82 F.3d 165, 170 (7th Cir.1996).4
Although § 2162.2.A.4 of the Manual does not identify what it is purporting to interpret, the Manual’s Foreword claims that every Manual provision rests on the “reasonable cost” language in the statute and the regulations. But as Professor An*495thony has written, if the relevant statute or regulation “consists of vague or vacuous terms—such as ‘fair and equitable,’ ‘just and reasonable,’ ‘in the public interest,’ and the like—the process of announcing propositions that specify applications of those terms is not ordinarily one of interpretation, because those terms in themselves do not supply substance from which the propositions can be derived.” Lifting the Smog, 8 Admin. L.J. Am. U. at 6 n. 21. This court’s opinion in Paralyzed Veterans of America v. D.C. Arena L.P., stated much the same. 117 F.3d 579, 588 (D.C.Cir.1997). In support, Paralyzed Veterans cited United States v. Picciotto, a case in which the Park Service issued a detailed rule specifying types of property that “may not be stored” in Lafayette Park. 875 F.2d at 346. The rule supposedly interpreted a regulation allowing “additional reasonable conditions” to be added to demonstration permits. The court held that the rule did not interpret this “open-ended” regulation and therefore could not be enforced because it was not issued after notice and comment. Id. at 346, 349.
Another general principle cuts against the Secretary. Among other things, § 2162.2.A.4 of the Manual provides that an offshore captive insurer’s “investments may include dividend paying equity securities listed on a United States stock exchange provided that the investment in equity securities does not exceed 10 percent of the company’s admitted assets, with the investment in any specific equity issue further limited to 10 percent of the total equity security investment.” Judge Friendly wrote that when an agency wants to state a principle “in numerical terms,” terms that cannot be derived from a particular record, the agency is legislating and should act through rulemaking. Henry J. Friendly, Watchman, What of the Night?, in Benchmarks 144-45 (1967). We too have recognized that “numerical limits cannot readily be derived by judicial reasoning,” although courts occasionally draw such limits.5 Mo. Pub. Serv. Comm’n v. FERC, 215 F.3d 1, 4 (D.C.Cir.2000). Our statement in Missouri Public Service relied on Hoctor v. USDA, 82 F.3d 165, 170 (7th Cir.1996). Hoctor held that an agency performs a legislative function when it makes “reasonable but arbitrary (not in the ‘arbitrary or capricious’ sense) rules that are consistent with the statute or regulation under which the rules are promulgated but not derived from it, because they represent an arbitrary choice among methods of implementation. A rule that turns on a number is likely to be arbitrary in this sense.” Hoctor cautioned that the court did not mean “that an interpretive rule can never have a numerical component.” 82 F.3d at 171. Examples in this circuit include American Mining Congress v. Mine Safety & Health Administration, 995 F.2d 1106 (D.C.Cir.1993), and Chippewa Dialysis Services v. Leavitt, 511 F.3d 172, 176-77 (D.C.Cir.2007) (dicta). “Especially in scientific and other technical areas, where quantitative criteria are common, a rule that translates a general norm into a number may be justifiable as interpretation.” Hoctor, 82 F.3d at 171.
The Hoctor court concluded that “[w]hen agencies base rules on arbitrary choices they are legislating, and so these rules are legislative or substantive and require notice and comment rulemaking.” Id. at 170-71. Section 2162.2.A.4 falls within that *496category. With respect to the ten percent limits “it is impossible to give a reasoned distinction between numbers just a hair on the OK side of the line and ones just a hair on the not-OK side.” Mo. Pub. Serv. Comm’n, 215 F.3d at 4. Here the Secretary has not even made the attempt.
The short of the matter is that there is no way an interpretation of “reasonable costs” can produce the sort of detailed— and rigid—investment code set forth in § 2162.2.A.4.6 This is essentially the point of the dissenting Board members. The statute gives the Secretary authority to promulgate regulations defining “the method or methods to be used, and the items to be included, in determining” what constitutes a provider’s “reasonable costs.” 42 U.S.C. § 1395x(v)(1)(A). We may assume, without deciding, that the Manual’s investment • limitations are an “extension” of the reasonable cost provisions in this section and the corresponding regulation, as the Board majority thought, and we may assume that the limitations are “consistent” with those provisions, as the Secretary has argued. But neither assumption leads to the conclusion that the Manual’s limitations represent an interpretation of the Medicare Act or of the regulations. See Hoctor, 82 F.3d at 170.7 Consistency with the statute may be enough to sustain a rule duly promulgated after notice and comment, just as consistency with the Commerce Clause, Art. I, § 8, cl. 3, may be enough to sustain the constitutionality of a statute. But no one would say, for instance, that the detailed provisions of the Clean Air Act were interpretations of the language of the Constitution. The same is true here. The connection between § 2162.2.A.4 of the Manual and “reasonable costs” is simply too attenuated to represent an interpretation of those terms as used in the statute and the regulations.
Our concurring colleague agrees with us that § 2162.2.A.4 of the Manual cannot be sustained as a valid interpretation of “reasonable cost.”8 Based on her reading of Shalala v. Guernsey Memorial Hospital, 514 U.S. 87, 115 S.Ct. 1232, 131 L.Ed.2d 106 (1995), our colleague does not put her conclusion in those terms and then criticizes us for determining that the Manual provision is not a proper interpretive rule. Our colleague’s approach rests on what we perceive as a misreading of Guernsey. At no point did the Supreme Court suggest that interpretive rules do not have to interpret. The issue was not presented. Guernsey simply recognized that a partic*497ular provision in the Manual constituted “a prototypical example of an interpretive rule,” id. at 99, 115 S.Ct. 1232, something that cannot be said about the provision we have in front of us.
For the reasons given, the judgment of the district court is reversed. We remand the case to the district court with instructions to set aside the decision of the Provider Reimbursement Review Board and for such other relief as the district court deems appropriate in view of this decision.
So Ordered.
. In 2005, fiscal intermediaries were replaced by "medicare administrative contractors.” See 42 U.S.C. 1395h; 42 C.F.R. § 413.24(f).
. The Secretary’s argument assumes that the less heavily regulated an insurance company is, the more likely it will fail. There may be reason to doubt the assumption at least as applied to captive insurers, but we will make nothing of this.
. The Medicare Act, 42 U.S.C. § 1395x(v)(1)(A), requires “reasonable cost” to "be determined in accordance with regulations establishing the method or methods to be used, and the items to be included....” This necessarily allows the Secretary to construe her regulations, but it does not appear to allow "reasonable cost” to be based on a rule that is neither part of a regulation nor an interpretation of a regulation.
. In Central Texas, 402 F.3d at 212, we acknowledged that the "APA's definition of 'rule' contemplates that ... [both] legislative and interpretive [rules] may interpret 'law.' The EPA regulations at issue in Chevron U.S.A., Inc. v. Natural Resources Defense Council, Inc., 467 U.S. 837, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984), for instance, interpreted the term 'stationary source' in the Clean Air Act (and did a good deal more). Nor may one say there is a clear 'line between interpretation and policymaking.' John F. Manning, Nonlegislative Rules, 72 Geo. Wash. L.Rev. 893, 924 (2004).”
. See, e.g., United States v. Thirty-Seven Photographs, 402 U.S. 363, 91 S.Ct. 1400, 28 L.Ed.2d 822 (1971), which construed a federal statute authorizing the seizure and forfeiture of imported obscene materials to mean that judicial forfeiture proceedings had to be instituted within 14 days and completed within 60 days. The Court held that reading these time limits into the statute was necessary to save it from being declared unconstitutional in violation of the First Amendment.
. It might have been a closer case if the Secretary’s Manual had indicated that premiums paid to financially unstable captive offshore (or domestic) insurance companies do not represent “reasonable costs.’’ But § 2162.2.A.4 of the Manual embodies a "flat’’ rule, and the “ 'flatter' a rule is, the harder it is to conceive of it as merely spelling out what is in some sense latent in a statute or regulation. ...” Hoctor, 82 F.3d at 171.
. Hoctor analyzed whether a U.S. Department of Agriculture rule requiring a fence of at least eight feet to enclose lions, tigers, and leopards was an interpretation of a regulation providing that the enclosure had to be of “such material and of such strength as appropriate for the animals involved.” 82 F.3d at 167-68. Writing for the court, Judge Posner held that “[e]ven if ... the eight-foot rule is consistent with, even in some sense authorized by, the structural-strength regulation, it would not necessarily follow that it is an interpretive rule. It is that only if it can be derived from the regulation by a process reasonably described as interpretation.” Id. at 170.
.Thus we are told that the “investment restrictions in the Manual are clearly outside [the] scope” of the Secretary's authority “to define the 'reasonable cost',” Concurring Op. at 501; that there is no "nexus” between the Manual provision and “reasonable cost,” id.; that the “rigid” rule in the Manual lacks “any rational connection” to the statute's “ 'reasonable cost’ principle,” id. at 498; and so forth.