Opinion for the Court filed by Senior Circuit Judge SILBERMAN.

SILBERMAN, Senior Circuit Judge:

Catholic Health Initiatives challenged a decision of the Secretary of Health and Human Services denying certain Medicare reimbursements that Catholic Health believed it was owed under the Medicare statute. The district court held that the Secretary’s decision was unlawful because the agency, in calculating reimbursements owed for a 1997 cost-reporting period, had retroactively applied a 2004 rulemaking without congressional authorization. We reverse. The policy on which the agency relied in this case was first announced in an adjudication in 2000, not in the 2004 rulemaking. We further conclude that the agency’s interpretation of the statute is permissible, and the denial of reimbursements was not arbitrary and capricious. Catholic Health has not shown that it relied to its detriment on the position the agency allegedly held before 2000.

The federal Medicare program provides health insurance for the elderly and dis *916 abled and reimburses qualifying hospitals for services provided to eligible patients. The Medicare statute has five parts, two of which are relevant in this case. Part A establishes the requirements that individuals must meet to be eligible for Medicare benefits and provides such individuals insurance for hospital and hospital-related services. See 42 U.S.C. § 1395c. These benefits include coverage for “inpatient hospital services,” id. § 1395d, which generally refers to overnight stays in a hospital. But Part A coverage for inpatient hospital services is limited to a certain number of days, after which coverage is exhausted. Specifically, Medicare beneficiaries are entitled to coverage for the first 90 days of their stay, and they may then elect to use up to 60 “lifetime reserve days” beyond the first 90 days. 42 C.F.R. § 409.61(a); see also 42 U.S.C. § 1395d.

Part E of Medicare sets out “Miscellaneous Provisions,” including a prospective payment system for reimbursing hospitals that provide inpatient hospital services covered under Part A. 42 U.S.C. § 1395ww(d). Hospitals receive reimbursement based on prospectively determined national and regional rates, not on the actual amount they spend, and they also receive payment adjustments for some hospital-specific factors. See id. § 1395ww(d)(2) & (d)(5)(F)(i)(I). The adjustment at issue in this case is the “disproportionate share hospital” (DSH) adjustment, under which the government pays more to hospitals that “serve[] a significantly disproportionate number of low-income patients.” Id. § 1395ww(d)(5)(F)(i)(I). This provision is based on Congress’s judgment that low-income patients are often in poorer health, and therefore costlier for hospitals to treat. See Adena Reg’l Med. Ctr. v. Leavitt, 527 F.3d 176, 177-78 (D.C.Cir.2008).

A hospital’s adjustment is based on its “disproportionate patient percentage” (DPP), 42 U.S.C. § 1395ww(d)(5)(F)(v) — a higher DPP means greater reimbursements because the hospital is serving more low-income patients. This figure, however, is not the actual percentage of low-income patients served; rather, it is an indirect, proxy measure for low income. The DPP is statutorily defined as the sum of two fractions, often called the “Medicare fraction” and the “Medicaid fraction.” The Medicare fraction is:

[T]he fraction (expressed as a percentage), the numerator of which is the number of such hospital’s patient days for such period which were made up of patients who (for such days) were entitled to benefits under part A of [Medicare] and were entitled to supplementary security income [SSI] benefits ..., and the denominator of which is the number of such hospital’s patient days for such fiscal year which were made up of patients who (for such days) were entitled to benefits under part A of [Medicare]....

Id. § 1395ww(d)(5)(F)(vi)(I). The Medicaid fraction is:

[T]he fraction (expressed as a percentage), the numerator of which is the number of the hospital’s patient days for such period which consist of patients who (for such days) were eligible for medical assistance under a State [Medicaid plan], but who were not entitled to benefits under part A of [Medicare], and the denominator of which is the total number of the hospital’s patient days for such period.

Id. § 1395ww(d)(5)(F)(vi)(II).

This language is downright byzantine and its meaning not easily discernible. The Medicare and Medicaid fractions represent two distinct and separate measures of low income — SSI (i.e., welfare) and Medicaid, respectively — that when summed together, provide a proxy for the total low-income patient percentage. The *917 Medicare fraction effectively asks, out of all patient days from Medicare beneficiaries, what percentage of those days came from Medicare beneficiaries who also received SSI benefits? The Medicaid fraction in turn asks, out of all patient days in total, what percentage of those days came from patients who received benefits under Medicaid, but not under Medicare? (The exclusion of Medicare beneficiaries in the Medicaid numerator is to avoid double counting such individuals in both fractions). As we provided in Northeast Hospital Corp. v. Sebelius, 657 F.3d 1, 3 (D.C.Cir.2011), a visual representation of the two fractions is given below:

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Many aspects of the DSH adjustment have been challenged over the years, but the issue in our case is how to interpret the phrase “entitled to benefits under part A” in the Medicaid fraction numerator. 42 U.S.C. § 1395ww(d)(5)(F)(vi)(II). Specifically, does this language include individuals who meet the statutory criteria for Medicare eligibility, but who have exhausted their coverage under section 1395d? The answer in turn affects the treatment of patient days for those eligible for both Medicaid and Medicare, but who have exhausted their Medicare benefits (“dual-eligible exhausted days”). If such patients are deemed “entitled to benefits under part A” (even though their Part A coverage is exhausted), then they would not be included in the Medicaid fraction, because the statute specifically excludes from this numerator those “entitled to benefits under part A.” Of course, even if dual-eligible exhausted days are excluded from the Medicaid fraction, they could still be included in the Medicare fraction, assuming the patients were also entitled to SSI benefits. The parties dispute whether the general effect of interpreting “entitled to benefits under part A” in this manner would be to increase or decrease DSH payments, but in at least some cases, including dual-eligible exhausted days in the Medicaid fraction will result in a higher DPP, and therefore in greater payments to hospitals. 1

A hospital’s adjustment is calculated in the first instance by a fiscal intermediary, which is typically a private insurance com *918 pany acting as the agent of the Secretary. See 42 C.F.R. §§ 421.1, 421.3, 421.100-.128. A hospital may appeal an intermediary’s decision to the Provider Reimbursement Review Board, an administrative body appointed by the Secretary, which may affirm, modify, or reverse the intermediary’s decision. 42 U.S.C. § 1395oo(a), (d) & (h). The Secretary in turn may affirm, modify, or reverse the decision of the Board. Id. § 1395oo(f).

Catholic Health Initiatives owns and operates Mercy Medical Center, a hospital in Des Moines. In the 1997 fiscal period, the Hospital discharged two patients who had been inpatients since 1992, and whose patient days included many dual-eligible exhausted days — -that is, for much of these patients’ stays, they were both eligible for Medicaid and enrolled in Medicare, but they had exhausted their Medicare coverage for inpatient hospital services. The Hospital filed cost reports with its fiscal intermediary, and in 1999, the intermediary issued an adjustment payment determination for the Hospital’s 1997 cost-reporting period. That determination initially included dual-eligible exhausted days in the Medicaid fraction numerator, which meant the intermediary was not counting exhausted days as days for which the patients were “entitled to benefits” under Medicare — which, of course, was beneficial to the Hospital.

But in 2000, the Department decided Edgewater Medical Center v. Blue Cross & Blue Shield Ass’n, HCFA Adm’r Dec., 2000 WL 1146601 (June 19, 2000), 2 and stated that dual-eligible exhausted days should not be included in the Medicaid fraction. Id. at *4. Then, in 2002, responding to the Edgewater decision, Catholic Health’s intermediary revised its calculations and excluded the dual-eligible exhausted days it had previously included for the Hospital’s 1997 cost-reporting period. Catholic Health appealed this decision to the Board, but before the Board could consider it, the parties reached a settlement, in which the intermediary agreed to include some, but not all, of the dual-eligible exhausted days.

But the issue was reopened in 2005, when the intermediary announced that it would again revisit the Hospital’s DSH adjustment for 1997. 3 The impetus for this second reopening was an agency rule-making in 2004 that “adopt[ed] a policy to include the days associated with dual-eligible beneficiaries in the Medicare fraction, whether or not the beneficiary has exhausted Medicare Part A hospital coverage.” Medicare Program; Changes to the Hospital Inpatient Prospective Payment Systems and Fiscal Year 2005 Rates, 69 Fed.Reg. 48,916, 49,099 (Aug. 11, 2004); see also id. (“We are revising our regulations at [42 C.F.R.] § 412.106(b)(2)(i) to include the days associated with dual-eligible beneficiaries in the Medicare fraction of the DSH calculation.”). In this rulemaking, the Department expressly declined to “include dual-eligible beneficiaries who have exhausted their Part A hospital coverage in the Medicaid fraction.” Id. The intermediary therefore excluded from the Medicaid fraction the patient days it had previously agreed to include under the settlement, *919 and the Hospital again appealed to the Board.

To confuse the issue further, the Board reversed the intermediary’s decision, holding that the dual-eligible exhausted days should have been included in the Medicaid fraction. As a matter of statutory interpretation, the Board concluded that the phrase “entitled to benefits under part A of [Medicare],” 42 U.S.C. § 1395ww(d)(5)(F)(vi)(II), meant the right to have payment made on the patient’s behalf — so for days where a patient had exhausted his right to payment, he was not “entitled to benefits,” and such days should be counted in the Medicaid fraction. The Board also pointed to previous decisions and statements by the agency in the Federal Register that it thought supported this interpretation. The Secretary reversed, however, and concluded — consistent with the Edgewater decision — that the intermediary had properly excluded the days at issue. The Department determined that the word “entitled” in the Medicare statute “is not in reference to the right of payment of a benefit, but rather the legal status of the individual as a Medicare beneficiary under the law.” The Secretary also stated that it was a “longstanding policy” to exclude dual-eligible exhausted days from the Medicaid fraction, and that any statements or decisions to the contrary were not consistent with this policy.

Catholic Health filed suit under the APA in the District Court. The Hospital moved for summary judgment on two different grounds — first, that the Secretary’s interpretation of the Medicare statute was impermissible; and second, that the Secretary’s current position, even if entitled to deference, could not be retroactively applied to the 1997 cost-reporting period. The district court passed on the statutory-interpretation issue, holding that regardless of whether the agency’s interpretation was permissible, its decision was an unauthorized retroactive application of the 2004 rulemaking. This appeal followed.

The two main issues on appeal are the validity of the agency’s interpretation of the Medicare statute and its application to the 1997 cost-reporting period. The Secretary argues that the statute clearly states that an individual is “entitled to benefits” under Medicare when he meets the basic statutory criteria (or at least, that such an interpretation is reasonable), and that there was no impermissible retro-activity in the agency’s decision because the agency never had a clear policy to the contrary. The Hospital argues that the statute forecloses the agency’s interpretation because “entitled to benefits” means the right to have payment made on one’s behalf, and that regardless of whether the agency’s interpretation is valid, its decision was impermissibly retroactive because the agency held a contrary position in 1997.

A. “Entitled to benefits ”

The Secretary argues that her interpretation of “entitled to benefits under part A of [Medicare]” is not only superior, but necessary. Section 1395ww(d)(5)(F)(vi) does not itself define the phrase, nor is the meaning of these words obvious on their face, but the Secretary legitimately points to related provisions that clarify the question. The statutory provision on which the agency primarily relies for its interpretive argument is 42 U.S.C. § 426(a), which states that “[e]very individual who ... has attained age 65, and ... is entitled to monthly [Social Security benefits] ... shall be entitled to hospital insurance benefits under part A of [Medicare].” This language, the Department argues, clearly indicates that entitlement to Medicare benefits is simply a matter of meeting the *920 statutory criteria, not a matter of receiving payment. See also 42 C.F.R. § 400.202 (“Entitled means that an individual meets all the requirements for Medicare benefits”).

In response, Catholic Health points to 42 U.S.C. § 426(c), which provides that “entitlement of an individual to hospital insurance benefits for a month shall consist of entitlement to have payment made under, and subject to the limitations in, part A of [Medicare] on his behalf for inpatient hospital services.” (emphasis added). See also 42 U.S.C. § 1395d(a) (“The benefits provided to an individual by the insurance program under [part A of Medicare] shall consist of entitlement to have payment made on his behalf ... for ... inpatient hospital services ... for up to 150 days during any spell of illness minus 1 day for each day of such services in excess of 90 received during any preceding spell of illness....”) (emphasis added). Therefore, the Hospital argues, “entitlement” is defined in terms of the right to have payment made on one’s behalf, so where an individual has exhausted that right, they are no longer entitled to Medicare benefits for the purposes of calculating a hospital’s DSH adjustment. Catholic Health also contends, somewhat weakly, that even if the statute is ambiguous, the Department’s interpretation is unreasonable.

We think it unnecessary to parse all the other provisions of the statute the parties cite in support of their respective positions. We conclude that, although the Department’s interpretation is the better one, it is not quite inevitable. Either interpretation seems permissible, a conclusion that is reinforced by our recent decision in Northeast Hospital Corp. v. Sebelius, 657 F.3d 1 (D.C.Cir.2011). That case also involved a hospital challenging the amount of reimbursement it was due, and the specific statutory dispute was whether individuals enrolled in Medicare Part C were still considered “entitled to benefits under part A” for the purposes of computing the Medicaid fraction. Id. at 5. The basic arguments made by the parties in Northeast Hospital track those made here, and after a lengthy analysis, in which we noted “the Medicare statute’s inconsistent and specialized use of the phrase ‘entitled to benefits under Part A,’ ” id. at 13, we found the statute ambiguous on this question. Therefore, under Chevron U.S.A., Inc. v. Natural Res. Def. Council, Inc., 467 U.S. 837, 842-43, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984), we of course defer to the Department’s construction. See Metro. Hosp. v. U.S. Dep’t of Health & Human Servs., 712 F.3d 248, 270 (6th Cir.2013) (reaching the same conclusion regarding the construction of the same provision).

B. Retroactivity

The main dispute presented before the district court and before us is rather puzzling; the arguments have turned on whether the regulation was impermissibly retroactive. 4 We certainly understand why Catholic Health would embrace that framing of the issue — as we stated in Northeast Hospital, “[i]t is well settled that an agency may not promulgate a retroactive rule absent express congressional authorization.” 657 F.3d at 13 (citing Bowen v. Georgetown Univ. Hosp., 488 U.S. 204, 208, 109 S.Ct. 468, 102 L.Ed.2d 493 (1988)). But while the 2004 rulemaking was phrased as a matter of revised *921 statutory interpretation, it is clear that the regulation — at least as it bears on the issue in this case — simply reiterated the pri- or rule of decision first announced in the Edgewater adjudication and reaffirmed two years later in Castle Medical Center v. Blue Cross & Blue Shield Ass’n, HCFA Adm’r Dec., 2003 WL 22490097, at *10-11 (Sept. 12, 2003). And of course, it is black-letter administrative law that adjudications are inherently retroactive. NLRB v. Wyman-Gordon Co., 394 U.S. 759, 763-66, 89 S.Ct. 1426, 22 L.Ed.2d 709 (1969) (plurality opinion); SEC v. Chenery Corp., 332 U.S. 194, 203, 67 S.Ct. 1575, 91 L.Ed. 1995 (1947); Qwest Servs. Corp. v. FCC, 509 F.3d 531, 539 (D.C.Cir.2007) see also Bowen, 488 U.S. at 221, 109 S.Ct. 468 (“[SEC v..] Chenery [Corp., 332 U.S. 194, 67 S.Ct. 1575, 91 L.Ed. 1995 (1947) ] involved that form of administrative action where retro-activity is not only permissible but standard. Adjudication deals with what the law was; rulemaking deals with what the law will be.”) (Scalia, J., concurring).

In short, the premise of the primary argument before the district court was fallacious — but given the government’s confusing presentation, we certainly do not fault the district judge. Indeed, not only has the agency’s briefing on appeal seemed to accept the rulemaking framework (relying only tangentially on the Edgewater decision), but the Administrator’s decision in this very case relied on the 2004 rule-making, rather than the Edgewater decision, as supplying the dispositive rule.

Nevertheless, the Secretary’s reliance on the 2004 rulemaking does not necessarily render “retroactive” the application of that rule. When a rule is challenged, the first question is always whether the rule is substantively valid on its face, and as we have already explained, the Secretary’s interpretation in this case is permissible under Chevron. The next question is whether it is retroactive, meaning that the rule itself effected a clear change in the legal landscape and attached new legal consequences to past actions. See Arkema Inc. v. EPA 618 F.3d 1, 7 (D.C.Cir.2010). But the policy of excluding dual-eligible exhausted days from the Medicaid fraction was announced four years earlier in Edge-water, and the rulemaking was simply a reiteration of this position. 5

To be sure, as Catholic Health argues, the Edgewater decision contained problems that might have rendered it arbitrary and capricious if challenged on direct appeal (which perhaps explains why the Secretary has been reluctant to rely on it heavily). First, it did not forthrightly discuss prior statements and administrative decisions that could be thought inconsistent with the interpretation given in that case, and second, it erroneously claimed that the agency’s policy at that time was to include Medicare-exhausted days in the Medicare fraction (in fact, the agency did not follow this practice until the 2004 rule-making). 2000 WL 1146601, at *4. But the issue for retroactivity purposes is not whether a prior adjudication is substantively sound; it is only whether a prior *922 adjudication does, in fact, establish the policy at issue. There is no doubt that the Edgewater adjudication set forth the interpretation that governs this case prior to the 2004 rulemaking, so the alleged retro-activity problem is not one of retroactive rulemaking.

Thus, the only remaining question, which might be thought to have been raised implicitly, is whether applying the Edgewater interpretation “retroactively” to Catholic Health is improper. Even though adjudication is by its nature retroactive, we have recognized that “denying] retroactive effect to a rule announced in an agency adjudication” may be proper where the adjudication “substituyes] ... new law for old law that was reasonably clear” and where doing so is “necessary ... to protect the settled expectations of those who had relied on the preexisting rule.” Williams Natural Gas Co. v. FERC, 3 F.3d 1544, 1554 (D.C.Cir.1993) (quoting Al-iceville Hydro Assocs. v. FERC, 800 F.2d 1147, 1152 (D.C.Cir.1986)). By “retroactive effect,” of course, we typically refer to an order or penalty with economic consequences, not retroactive application of the rule itself — after all, under Wyman-Gor-don, an adjudication must have retroactive effect, or else it would be considered a rulemaking. 394 U.S. at 763-66, 89 S.Ct. 1426.

The parties have extensively argued whether the Edgewater interpretation constituted a legal volte face — that is, whether pre-jEdgewater agency statements and decisions did, in fact, establish a contrary policy. But it is unnecessary for us to decide that question in this case because Catholic Health has presented no explanation as to how it relied to its detriment on the alleged prior policy — neither in its brief, nor when asked directly at oral argument. 6 So even assuming the Edgewater rule was “retroactively” applied to the 1997 cost-reporting period, it would not constitute the sort of unfair retroactivity that may render an agency decision arbitrary and capricious. The judgment of the district court is therefore reversed.

So ordered.

. The mathematical cause of this tendency is that the two fractions use different denominators — one that is affected by how this issue is resolved, and one that is not. The Medicaid denominator is simply the total patient days, but the Medicare denominator is only patient days for those entitled to benefits under Medicare. So if "entitled to benefits” is construed broadly to include exhausted benefits, then dual-eligible exhausted days are excluded from the Medicaid numerator, causing that fraction to go down. But even if such days are added to the Medicare numerator (for those patients also receiving SSI benefits), they are added to the Medicare denominator as well, which dilutes the effect of counting such days in this fraction. So while the Medicare fraction itself might go up, the magnitude of this increase will often be less than the corresponding decrease in the Medicaid fraction (though the exact result will depend on the relative number of days hospitals spend treating Medicare patients, dual-eligible patients, Medicare/SSI patients, and other patients).

. The administrative decisions referred to in this case are those made by the Centers for Medicare & Medicaid Services (CMS), formerly the Health Care Financing Administration (HCFA). The Secretary has authorized the CMS Administrator to act on her behalf in reviewing the Board's decisions, and the Administrator's review of a Board ruling is considered the final decision of the Secretary. See 42 C.F.R. § 405.1875.

. Intermediary determinations may be reopened within three years of a decision or final settlement. 42 C.F.R. § 405.1885(b).

. The agency also relies on the alternative— and much more difficult — claim that even if the regulation was retroactive, the existence of a prior inconsistent policy is irrelevant because the Secretary's present interpretation of the statute is the only permissible reading. We need not consider that question because, as we have already concluded, the statute can reasonably be interpreted either way.

. The 2004 rulemaking did effect a change with respect to whether Medicare-exhausted days could be included in the Medicare fraction. Prior to 2004, the Secretary interpreted the phrase “entitled to benefits under part A of [Medicare]” in the Medicare fraction to include only “covered Medicare Part A inpatient days.” Medicare Program; Fiscal Year 1986 Changes to the Inpatient Hospital Prospective Payment System, 51 Fed.Reg. 16,-772, 16,777 (May 6, 1986). Only after the rule went into effect did the agency include in the Medicare fraction all days for which patients were eligible for Medicare, regardless of whether Medicare actually paid for those days. But the dispute in this case turns on whether to include dual-eligible exhausted days in the Medicaid fraction, so Edgewater clearly established the relevant rule prior to the 2004 rulemaking.

. The parties' briefing does not touch at all on detrimental reliance, but this issue — along with the broader rulemaking vs. adjudication framework discussed above — was explored in some detail at oral argument. Had Catholic Health argued that the Secretary waived the right to argue a lack of reliance, then the agency might well have been foreclosed from prevailing on this point so late in these proceedings. But counsel never made any such suggestion — in briefing or at oral argument— so we construe Catholic Health as having itself waived any waiver argument.