GILMAN, J., delivered the opinion of the court, in which CLAY, J. joined. McKEAGUE, J. (pp. 270-75), delivered a separate dissenting opinion.
*250OPINION
RONALD LEE GILMAN, Circuit Judge.This case involves a challenge to regulation 42 C.F.R. § 412.106(b), promulgated in 2004 by the United States Department of Health and Human Services (HHS). The regulation deals with the amount that certain hospitals are entitled to receive as enhancements to their regular reimbursement payments from the Medicare program. In connection with this program, Congress has created a statutory formula to identify hospitals that serve a disproportionate number o'f low-income patients and to calculate the increased payments due such hospitals.
Metropolitan Hospital (Metro) challenges the way that the Secretary of HHS (Secretary) interprets this statutory formula to exclude certain patients who are simultaneously eligible for benefits under both Medicare and Medicaid. According to the Complaint, the exclusion of such dual-eligible patients cost Metro more than $2.1 million in the 2005 fiscal year.
Addressing the parties’ cross-motions for summary judgment, the district court ruled that the challenged HHS regulation is invalid because it violates the statute that it purports to implement. Metro. Hosp., Inc. v. U.S. Dep’t of Health & Human Seros., 702 F.Supp.2d 808, 825-26 (W.D.Mich.2010). HHS then timely filed this appeal, and Metro timely filed a cross-appeal regarding the district court’s decision to remand the case to HHS for the calculation of damages and interest due Metro. For the reasons set forth below, we REVERSE the judgment of the district court and REMAND the case with instruction to enter judgment in favor of HHS. Metro’s cross-appeal is DISMISSED as moot.
I. BACKGROUND
A. Regulatory background
The Medicare program’s Prospective Payment System (PPS) reimburses a hospital a fixed dollar amount for each Medicare patient it discharges on the basis of the patient’s diagnosis, regardless of the actual cost of the treatment provided. Good Samaritan Hosp. v. Shalala, 508 U.S. 402, 406 n. 3, 113 S.Ct. 2151, 124 L.Ed.2d 368 (1993). Recognizing “the higher costs incurred by hospitals that serve a large number of low income patients,” Jewish Hosp., Inc. v. Sec’y of Health & Human Servs., 19 F.3d 270, 272 (6th Cir.1994), Congress in 1983 required the Secretary to make “exceptions and adjustments to the PPS program” that would account for these higher costs, id. at 280 (Batchelder, J., dissenting) (internal quotation marks omitted).
But the Secretary failed to establish “a system to estimate the number of poor patients served in such hospitals and [to] issue payments,” and again failed to act when subsequent legislation set a deadline of December 31, 1984 for the Secretary to define and identify the “disproportionate share hospitals” (DSHs) that would receive these adjusted payments. See id.; see also Deficit Reduction Act, Pub. L. 98-369, § 2315(h), 98 Stat. 494, 1080 (1984) (setting the year-end 1984 deadline). Congress in 1985 therefore established its own measure for assessing whether a hospital “serves a significantly disproportionate number of low income patients.” See 42 U.S.C. § 1395ww(d)(5)(F)(v). That measure is called the “disproportionate patient percentage” (DPP). 42 U.S.C. § 1395ww(d)(5)(F)(vi).
The DPP is the sole variable in the “disproportionate share adjustment percentage” that ultimately determines the dollar amount of any enhanced payment due to a DSH. Id. § 1395ww(d)(5)(F)(vii). *251A higher DPP produces a higher adjustment percentage, which in turn produces a larger adjustment payment. See id. In sum, the DPP is the key figure in determining whether a hospital will receive additional Medicare dollars for serving low-income patients and, if so, in what amount.
Two separate fractions are added together to produce the DPP: the Medicare fraction and the Medicaid fraction. Id. § 1395ww(d)(5)(F)(vi). The basic unit of measurement in both fractions is a hospital’s “patient days.” Id. In the numerator of the Medicare fraction is the number of patient days in a cost-reporting period that are attributable to patients who were both “entitled to benefits under [Medicare] part A” and “entitled to supplemental security income [SSI] benefits.” Id. § 1395ww(d)(5)(F)(vi)(I). The denominator is the total number of patient days in the fiscal year that are attributable to patients who were “entitled to benefits under [Medicare] part A.” Id. In other words, the Medicare fraction measures the portion of a hospital’s Medicare-entitled patient population that is also entitled to SSI, a cash benefit provided to low-income elderly, blind, or disabled individuals. See id. §§ 1381-1383Í. This fraction can be expressed visually as follows:
[[Image here]]
The Medicaid fraction has both a different numerator and a different denominator. Its numerator is the number of patient days in a cost-reporting period that are attributable to patients who were “eligible for [Medicaid] ... but who were not entitled to benefits under [Medicare] part A.” Id. § 1395ww(d)(5)(F)(vi)(II). The denominator is the total number of the hospital’s patient days in the same cost-reporting period for all patients. Id. This fraction measures the proportion of a hospital’s total patient population that is Medicaid-eligible, with the caveat of excluding patients who are also entitled to Medicare benefits. The Medicaid program, codified at 42 U.S.C. §§ 1396-1396w, is a federal-state cooperative program that “provides financial assistance to low-income individuals seeking medical care.” Markva v. Haveman, 317 F.3d 547, 550 (6th Cir.2003). This fraction can be expressed visually as follows:
[[Image here]]
The Medicare fraction and the Medicaid fraction are expressed as percentages and then added together to produce the DPP. 42 U.S.C. § 1395ww(d)(5)(F)(vi). These fractions summarize the following relevant portion of the DPP statute:
In this subparagraph, the term “disproportionate patient percentage” means, with respect to a cost reporting period of a hospital, the sum of—
(I) the 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 this subchap-ter and were entitled to supplementary *252security income benefits (excluding any State supplementation) under subchap-ter XVI of this chapter, 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 this subchapter, and
(II) the 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 plan approved under subchapter XIX of this chapter, but who were not entitled to benefits under part A of this subchapter, and the denominator of which is the total number of the hospital’s patient days for such period.
Id.
The Medicaid fraction’s numerator accounts for the fact that some Medicaid-eligible patients are also entitled to Medicare benefits (known as dual-eligible patients). Central to the dispute in the present case is which fraction, if any, is the appropriate place to count the patient days of dual-eligible patients who have exhausted their Medicare benefits for inpatient hospital care during a particular “spell of illness.” See id. § 1395d.
All Medicare beneficiaries — not just dual-eligible patients — are entitled to have Medicare pay for inpatient hospital services for up to 90 days during any spell of illness (the period from when a person enters a hospital for an injury or illness until he or she has been out of the hospital for 60 consecutive days). Id.; see also id. § 1395x(a) (defining the term “spell of illness”). They also receive an additional 60 days of such coverage that can be spread across all spells of illness during a beneficiary’s lifetime. Id. § 1395d. In other words, Medicare will cover: (1) hospital services for any spell of illness lasting up to 90 days; and (2) an additional lifetime cap of 60 days for hospital services for care in excess of 90 days per spell of illness.
This means that a Medicare patient who receives 150 days of Medicare-paid inpatient care for a single spell of illness (90 + 60) is limited to 90 days of such care for every subsequent spell of illness. The same is true of a patient who uses, for example, 110 Medicare-covered days during one spell of illness (90 + 20) and 130 such days during another spell (90 + 40). Once a patient reaches the 90th day of a spell of illness and has exhausted his or her 60-day supply of post-90th day coverage, Medicare will no longer pay for the patient’s hospital services during that same spell of illness. See id. § 1395d(b)(l).
Both parties refer to such patients as having “exhausted their Medicare Part A coverage” for inpatient hospital services. If a dual-eligible patient exhausts his or her coverage for a particular spell of illness, then the subsequent patient days are called “dual-eligible exhausted benefit days” and are generally paid by Medicaid as the payor of last resort. See 42 U.S.C. § 1396a(a)(25) (mandating that state Medicaid plans identify any third parties liable to pay for medical care available under the plan and to seek reimbursement from such parties if the Medicaid program has already paid for such care); see also State Plan Requirement and Other Provisions Relating to State Third Party Liability Programs, 55 Fed. Reg. 1423-02, 1429 (Jan. 16, 1990) (“[W]hen an individual is entitled to Medicare and eligible for Medicaid, Medicare, like any other third party, is the primary payor.”).
The Secretary’s current regulation that implements the DPP statute interprets the *253language “entitled to benefits under [Medicare] part A” as including the patient days of all Medicare beneficiaries, regardless of whether a beneficiary has exhausted Medicare coverage for any particular patient day. See 42 C.F.R. § 412.106(b). As a result, all such days are included in the Medicare fraction— either in the denominator only, or in the numerator as well if the Medicare beneficiary is also entitled to SSI. Prior to the 2004 amendment of this regulation, however, the dual-eligible exhausted benefit days were excluded from the Medicare fraction. See 42 C.F.R. § 412.106(b) (2003) (counting only “covered” days in the Medicare fraction); see also Changes to the Hospital Inpatient PPS and FY 2005 Rates, 69 Fed. Reg. 48916-01, 49099 (Aug. 11, 2004) (codified at 42 C.F.R. pt. 412) (“[W]e are adopting 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.”).
This interpretation of the phrase “entitled to benefits under [Medicare] part A” also affects the Medicaid fraction. As noted above, the Medicaid fraction’s numerator excludes patient days attributable to individuals who are also entitled to Medicare benefits. 42 U.S.C. § 1395ww(d)(5)(F)(vi)(II). Because the Secretary views Medicare beneficiaries who have exhausted their Part A coverage for inpatient hospital services during a particular spell of illness as still being “entitled to benefits under [Medicare] part A,” HHS excludes dual-eligible exhausted benefit days from the Medicaid fraction’s numerator, even though such days are paid only by Medicaid.
Excluding such days from the Medicaid fraction’s numerator comports with the Secretary’s current interpretation of the phrase “entitled to benefits under [Medicare] part A,” but HHS contends that it had excluded these days from the fraction even before the 2004 change to the regulation. See Centers for Medicare & Medicaid Services, Ruling No. CMS-1498-R 7-8 (April 28, 2010) (noting that the Secretary’s original policy excluded dual-eligible exhausted benefit days from the Medicaid fraction’s numerator). The Secretary’s pre-2004 position on whether to count dual-eligible exhausted benefit days in the Medicaid fraction is less than clear, however, as is HHS’s explanation in this litigation for why such days were supposedly viewed as excluded.
At bottom, the current regulatory framework relevant to the present case can be summarized as follows: (1) a dual-eligible exhausted benefit day is counted in the DPP’s Medicare fraction, provided that the patient was also entitled to SSI on that day; and (2) under no circumstances may a dual-eligible exhausted benefit day be counted in the DPP’s Medicaid fraction. With that established, we turn next to the nature of Metro’s challenge to that framework.
B. Nature of the present case
Metro has operated an Assisted Breathing Center since 1985, providing care to ventilator-dependent patients that is generally unavailable in nursing homes. Virtually all of these patients are eligible for Medicaid, many are dual-eligible patients, and a few are entitled to SSI. Each Medicaid-eligible patient that the Center admits must be pre-approved by the state agency that administers Michigan’s Medicaid program. One of the agency’s “considerations for pre-admission authorization” is that a dual-eligible patient’s Medicare Part A coverage be exhausted, leaving Medicaid as the sole payor for what is typically long-term care at the Center. Because of these patients, a significant portion of Metro’s *254patient days are dual-eligible exhausted benefit days. How these days should be accounted for under the DPP is what has led to the dispute in this case.
Pursuant to the Medicare regulations, Metro submits annual cost reports to the “fiscal intermediary” between Metro and HHS. (A fiscal intermediary is a contractor, generally a private insurance company, that acts on behalf of HHS.) Consistent with previous cost reports, Metro’s report for 2005 included in the Medicaid fraction of its DPP calculation the patient days of dual-eligible patients in its Assisted Breathing Center who had exhausted their Medicare Part A coverage for a particular spell of illness. The fiscal intermediary audited the 2005 report and determined that Metro could not count these patient days in the Medicaid fraction, nor could most of these days be counted in the Medicare fraction because very few of the patients were entitled to SSI. As a result, Metro’s DPP for 2005 was reduced from 26.28% (as calculated by Metro) to 14.06% (as calculated by the fiscal intermediary). According to the fiscal intermediary, this overstatement of Metro’s DPP caused Medicare to overpay Metro by $2,179,740 in 2005, which funds were subsequently recouped by HHS.
Metro now challenges the Secretary’s interpretation of the DPP statute that led to this alleged overpayment. The district court ruled in Metro’s favor, holding that 42 C.F.R. § 412.106(b) is invalid because the regulation’s interpretation of the phrase “entitled to benefits under [Medicare] part A” is contrary to the meaning of the phrase in the DPP statute. Metro. Hosp., Inc. v. U.S. Dep’t of Health & Human Servs., 702 F.Supp.2d 808, 825-26 (W.D.Mich.2010). In reaching this conclusion, the district court relied primarily on this court’s opinion in Jewish Hospital v. Secretary of Health & Human Services, 19 F.3d 270 (6th Cir.1994), an opinion that struck down an earlier version of the same regulation because of its impermissible interpretation of the word “eligible” in the Medicaid fraction. See id. at 811-16, 825.
HHS has timely appealed the district court’s decision on the merits. Metro has timely cross-appealed to challenge the court’s remand order for the calculation of damages and interest.
II. ANALYSIS
A. Standard of review
An agency’s interpretation of a statute that is reflected in a regulation adopted through notice-and-comment rule-making (as was 42 C.F.R. § 412.106(b) in question here) is reviewed using the two-step framework outlined 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). See United States v. Mead Corp., 533 U.S. 218, 226-27, 121 S.Ct. 2164, 150 L.Ed.2d 292 (2001) (requiring analysis under the Chevron framework for regulations adopted through notice- and-comment rulemaking). “First, always, is the question whether Congress has directly spoken to the precise question at issue. If the intent of Congress is clear, that is the end of the matter; for the court, as well as the agency, must give effect to the unambiguously expressed intent of Congress.” Chevron, 467 U.S. at 842-43, 104 S.Ct. 2778. The reviewing court employs “traditional tools of statutory construction” to ascertain whether “Congress had an intention on the precise question.” Id. at 843 n. 9, 104 S.Ct. 2778. But “if the statute is silent or ambiguous with respect to the specific issue, the question for the court is whether the agency’s answer is based on a permissible construction of the statute.” Id. at 843, 104 S.Ct. 2778. The agency’s construction need not be the only possible permissible interpre*255tation of the statute, nor must it be “even the reading the court would have reached if the question initially had arisen in a judicial proceeding.” Id. at 843 n. 11, 104 S.Ct. 2778. Our review of this interpretation dispute will be de novo because the district court ruled as a matter of law in granting summary judgment to Metro. See Lefevers v. GAF Fiberglass Corp., 667 F.3d 721, 723 (6th Cir.2012).
B. Congress has not “directly spoken” to how the DPP calculation should account for dual-eligible exhausted benefit days
1. Plain-language arguments
Metro contends, and the district court agreed, that the plain language of the DPP statute unambiguously provides that a dual-eligible exhausted benefit day must be counted in the Medicaid fraction and that no exhausted benefit day (whether dual-eligible or not) may be counted in the Medicare fraction. See Metro. Hosp., Inc., 702 F.Supp.2d at 822, 825. The foundation for this argument is that Congress purposefully used the term “entitled” in reference to Medicare benefits rather than “eligible” (the term it chose for counting Medicaid patient days), and therefore the term “entitled” must signify the actual payment for hospital services rather than merely being eligible for such services. See id. at 820-22. HHS, on the other hand, argues that the phrase “entitled to benefits under [Medicare] part A” has a clear, consistent meaning throughout the Medicare statute; i.e., covering any individual who meets the statutory criteria set out in 42 U.S.C. § 426. Congress used that phrase in the DPP provision, HHS contends, to invoke this specific meaning. We conclude that the statute’s plain language does not unambiguously endorse either party’s interpretation.
No definition of the phrases “entitled to benefits under [Medicare] part A” or “eligible for [Medicaid]” is provided in the DPP provision or elsewhere in the statutory section in which the DPP appears. See 42 U.S.C. § 1395ww. But this court has previously concluded that “eligibility” as used in the Medicaid fraction does not refer to the actual payment of benefits. Jewish Hosp., 19 F.3d at 274-75. Metro relies on the Jewish Hospital opinion in two ways: (1) as controlling precedent; and (2) alternatively, as persuasive authority for Metro’s plain-language argument that a patient is “entitled” to a Medicare benefit only when he or she has the right to the payment of an in-patient hospital service by Medicare.
i. Jewish Hospital does not foreclose the Secretary’s interpretation of the statutory phrase, “entitled to benefits under [Medicare] part A” as a matter of stare decisis
The Supreme Court recognized in National Cable & Telecommunications Association v. Brand X Internet Services, 545 U.S. 967, 125 S.Ct. 2688, 162 L.Ed.2d 820 (2005), that formal adherence to stare decisis must sometimes yield to the recognition of agency expertise in interpreting the statutes that an agency administers. See id. at 983, 125 S.Ct. 2688 (noting that an agency is “the authoritative interpreter” of a statute that it is charged with administering and that placing stare deci-sis above Chevron deference “would lead to the ossification of large portions of our statutory law” (internal quotation marks omitted)). As such, not every holding from a prior case that interprets statutory language will foreclose a subsequent agency interpretation of that language (or related language). Brand X limits the stare decisis effect of prior judicial statutory interpretations to those constructions that “follow[] from the unambiguous terms of *256the statute and thus leave[] no room for agency discretion.” 545 U.S. at 982, 125 S.Ct. 2688. This rule is a direct reference to Chevron step one. See id. (“The better rule is to hold judicial interpretations contained in precedents to the same demanding Chevron step one standard that applies if the court is reviewing the agency’s construction on a blank slate----”); see also Carpenter Family Invs., LLC, 136 T.C. 373, 400 (2011) (Halpern and Holmes, JJ., concurring) (explaining the inquiries that a court must make when “applying Brand X to find a [Chevron ] step one holding”).
Recognizing that Brand X gives stare decisis effect to a prior judicial construction of a statute only when made as a Chevron step-one holding has two important implications: First, courts often describe statutory language as “clear” or “unambiguous” without making a Chevron step-one holding. See Note, Implementing Brand X: What Counts as a Step One Holding?, 119 Harv. L. Rev. 1532, 1538 (2006) (noting that courts use these terms outside the context of Chevron and that “a later judge does not know for sure whether [prior courts] intended the terms to have the same meaning they would have had in the Chevron context”). Second, and more important to the present case, a Chevron step-one holding answers only a very specific question; i.e., “whether Congress has directly spoken to the precise question at issue.” Chevron 467 U.S. at 842, 104 S.Ct. 2778. Answers to other questions that an opinion might provide, even ones that purport to define the allegedly unambiguous terms of related statutory language, are therefore not part of the Chevron step-one holding and thus do not foreclose future agency interpretations under Brand Xs analysis.
The Brand X opinion thus requires us to determine whether Jewish Hospital made a Chevron step-one holding and, if so, to ascertain the content of that holding. We first note that the only explicit statements of a holding that appear in Jewish Hospital are expressed in terms of Chevron step two. See 19 F.3d at 275, 276 (“We hold that, even if the language of the statute can be deemed silent or ambiguous, the Secretary’s construction of the statute is not permissible.... Therefore, we hold that the Secretary’s construction of the Medicaid proxy, as represented by its promulgated regulation is impermissible.” (emphasis in the original)); see also Chevron, 467 U.S. at 843, 104 S.Ct. 2778 (describing the second step of the analysis as asking “whether the agency’s answer” to a statute’s silence or ambiguity “is based on a permissible construction of the statute”).
To be sure, the Jewish Hospital opinion suggests that the statutory language at issue in that case expresses a clear legislative mandate. 19 F.3d at 274. But rather than this clear mandate constituting “the end of the matter” as a step-one holding, see id. (citing Chevron, 467 U.S. at 843, 104 S.Ct. 2778), the opinion proceeds in the Chevron analysis to conclude that the Secretary’s interpretation was impermissible. Id. at 275-76. The opinion is thus unclear regarding whether the court’s Chevron step-one discussion is a holding. And even if that discussion amounts to a holding, we find it far from clear that the discussion constituted the “principal holding” as determined by our dissenting colleague (see Dissenting Op. at 272), given that the opinion’s only explicit expressions of a holding are in terms of Chevron step two.
But even if we were to read Jewish Hospital as making a Chevron step-one holding, we must further assess whether that holding construes the statutory language central to the present case. The “precise question at issue” for Chevron step-one purposes in Jewish Hospital was *257HHS’s interpretation of particular language from the Medicaid fraction to mean that Medicaid inpatient days included only those days for which a state’s Medicaid program rendered payment. Jewish Hospital focuses on the following phrase from that fraction at the beginning of its Chevron analysis:
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].
See 19 F.3d at 274 (quoting 42 U.S.C. § 1395ww(d)(5)(F)(vi)(II)) (emphasis added in Jewish Hosp.).
Because a Chevron step-one holding is by definition limited to the scope of the “precise question at issue,” the Chevron step-one holding in Jeivish Hospital, if any, is limited to the court’s answer to that question. And the court’s answer is that “it appears that all days for which an individual is capable of receiving Medicaid should be figured into the proxy calculation,” rather than only the days of care for which Medicaid actually paid. See Jewish Hosp. 19 F.3d at 274.
The Jewish Hospital court gave several rationales in support of this answer, starting with two aspects of the above-quoted statutory language. First, the court noted that “the word ‘eligible’ refers to whether a patient is capable of receiving [Medicaid]” and that the statute does not suggest congressional intent “to impute any special meaning to the term, eligible.” Jewish Hosp., 19 F.3d at 274. Second, the court explains that “the parenthetical ‘for such days’ serves only as the antecedent to the initial phrase ‘the number of the hospital’s patient days for such period’” and thus does not restrict or otherwise qualify the meaning of the term “eligible.” Id. Supporting this interpretation of the statutory language was the court’s recognition that “Congress sought to structure a proxy that is definable and accessible, one that would not be subject to yearly budgetary constraints of individual states that may threaten a PPS hospital’s ability to continue to provide services to low income persons.” Id. at 274-75. The court’s interpretation of “the notion of ‘eligibility’ ” was consistent with this intent, such that the court would not strain to interpret the statutory language in a manner that would allow “crucial federal legislation” to be “readily altered by state legislative fiat.” Id. at 274. This analysis strikes us as the essential rationale for the Jewish Hospital decision.
As additional support for its conclusion, the Jewish Hospital court went on to note that “eligibility” in the Medicaid proxy must mean something different than “entitlement” in the Medicare proxy, and that “[t]o be entitled to some benefit means that one possesses the right or title to that benefit.” Id. at 275 (emphases in original). Metro argues that this supporting rationale is itself part of a Chevron step-one holding and therefore forecloses the Secretary’s current interpretation of the statutory phrase “entitled to benefits under [Medicare] part A.” But a Chevron step-one holding addresses only “the precise question at issue,” Chevron 467 U.S. at 842, 104 S.Ct. 2778, and that question in Jewish Hospital was the meaning of the phrase “eligible for [Medicaid],” not the phrase “entitled to benefits under [Medicare] part A.”
Accordingly, we decline to hold that Jewish Hospital’s “back-up” analysis contrasting the phrase “entitled to benefits under [Medicare] part A” with the phrase “eligible for [Medicaid]” — the contrast being neither “the precise question at issue” nor essential to the court’s disposition of the case — forecloses the Secretary’s interpretation of that phrase as reflected in 42 *258C.F.R. § 412.106(b). See Northeast Hosp. Corp. v. Sebelius, 657 F.3d 1, 12 n. 7 (D.C.Cir.2011) (concluding that Jewish Hospital’s discussion of the term “entitled” was dicta). And we, for the same reasons, are no more bound by Jewish Hospital than is the Secretary in determining whether Congress unambiguously expressed what that phrase means with regard to counting dual-eligible exhausted benefit days. See Brand X, 545 U.S. at 983-84, 125 S.Ct. 2688.
Our dissenting colleague, however, concludes that Jewish Hospital requires us to invalidate the challenged HHS regulation as a matter of stare decisis. We have no quarrel with the dissent’s description of the stare decisis doctrine and its fundamental importance. Nor do we dispute that “the line between holding and dictum is not always clear” (Dissenting Op. at 274), with judges of this court and our sister circuits disagreeing with regard to where that line should be drawn. See, e.g., United States v. Stevenson, 676 F.3d 557, 562 (6th Cir.2012) (noting that language from a prior opinion was “dictum because it was. not necessary to the holding”); United States v. Hardin, 539 F.3d 404, 438-440 (6th Cir.2008) (Batchelder, J., concurring in part and dissenting in part) (invoking Black’s Law Dictionary’s definition of the term “holding,” which is “[a] court’s determination of a matter of law pivotal to its decision; a principle drawn from such a decision,” to disapprove of the majority opinion’s conclusion that a principle from a prior case was dicta); United States v. Johnson, 256 F.3d 895, 914-16 (9th Cir.2001) (opinion of Kozinski, J.) (disapproving of Judge Tashima’s characterization of Judge Kozinski’s opinion as dicta).
But we part ways with our dissenting colleague in his attempt to elevate Jewish Hospital’s brief discussion of the contrast between the terms “eligible” and “entitled” from mere “obiter dictum” to “judicial dictum,” and then to effectively a full-fledged holding. See Dissenting Op. at 274-75. The definitions he provides may be useful in drilling down to an opinion’s holding as a general matter, but Brand X and Chevron give us specific direction in the context of potential conflicts between agency interpretations and prior judicial constructions of statutory language. And that direction informs us that a prior judicial construction trumps a subsequent agency interpretation only if the court held as a result of Chevron step-one analysis that the statutory language provides a clear congressional answer to the “precise question at issue.” See Brand X, 545 U.S. at 982, 125 S.Ct. 2688; Chevron, 467 U.S. at 842, 104 S.Ct. 2778. To the extent that Jewish Hospital provided a step-one holding, it decided only that the phrase “eligible for [Medicaid]” means that “a patient is capable of receiving ... Medicaid” regardless of whether a state’s Medicaid plan actually paid for the patient’s medical care. 19 F.3d at 274. The meaning of that statutory phrase, and not the phrase “entitled to benefits under [Medicare] part A,” was the “precise question at issue” in Jewish Hospital and thus defines the scope of any Chevron step-one holding that the court could have made.
Moreover, the Brand X rule is grounded in the sound policy that the meaning of statutory language should not be judicially ossified unless it has been carefully considered by a court and held to be unambiguous under Chevron step one. See Brand X, 545 U.S. at 983, 125 S.Ct. 2688. This rule also constrains the courts to their proper institutional role, i.e., deciding only the issues presented in the case or controversy before them. See, e.g., Flast v. Cohen, 392 U.S. 83, 94-95, 88 S.Ct. 1942, 20 L.Ed.2d 947 (1968) (explaining that “limiting] the business of federal courts to *259questions presented in an adversary context ... define[s] the role assigned to the judiciary in a tripartite allocation of power”). If a court is to decide that statutory language is unambiguous and leaves no gap for an agency’s interpretation to fill, then the question of that language’s meaning must be directly before the court. For this reason, we do not believe that the Jeivish Hospital decision definitively fixed the meaning of the phrase “entitled to benefits under [Medicare] part A” when the meaning of that language was not the issue presented and, as our dissenting colleague concedes (see Dissenting Op. at 271-72, 274), was not necessary to define in order to determine the meaning of the phrase “eligible for [Medicaid].”
ii. The analysis in Jewish Hospital does not demonstrate that the portion of the DPP statute at issue in the present case conveys clear congressional intent
Even if Jewish Hospital does not resolve the present case as a matter of stare decisis, Metro alternatively argues that the opinion is persuasive in its analysis of the relevant statutory language and supports the argument that Congress used different words to convey different meanings. See Jewish Hosp., 19 F.3d at 275 (“Adjacent provisions utilizing different terms ... must connote different meanings”). Metro also notes the decisions from other federal courts of appeals that have agreed with the Jewish Hospital decision and placed even greater reliance on the “entitled v. eligible” distinction in the DPP. See Cabell Huntington Hosp., Inc. v. Shalala, 101 F.3d 984, 988 (4th Cir.1996) (agreeing with the Jewish Hospital decision); Legacy Emanuel Hosp. & Health Ctr. v. Shalala, 97 F.3d 1261, 1265 (9th Cir.1996) (agreeing with the Jewish Hospital decision and basing its conclusion “on Congress’s use of the word ‘eligible’ rather than ‘entitled’ ”); Deaconess Health Servs. Corp. v. Shalala, 83 F.3d 1041 (8th Cir.1996) (per curiam) (agreeing with the Jewish Hospital decision).
The analysis from Jewish Hospital that Metro urges us to adopt has surface plausibility, but it is overly narrow. Only by examining the language of the DPP provision in isolation does Metro’s argument appear persuasive. But “[p]lain meaning is examined by looking at the language and design of the statute as a whole,” United States v. Parrett, 530 F.3d 422, 429 (6th Cir.2008), and this court “mak[es] every effort not to interpret a provision in a manner that renders other provisions of the same statute inconsistent,” Cafarelli v. Yancy, 226 F.3d 492, 499 (6th Cir.2000). Viewing the Medicare statute as a whole, the “entitled v. eligible” dichotomy loses its persuasiveness.
The lengthy statute in which the DPP appears, 42 U.S.C. § 1395ww, governs “[pjayments to hospitals for inpatient hospital services” generally, not just the special adjustments for hospitals serving a disproportionately low-income population. Notably, the phrase “entitled to benefits under [Medicare] part A” appears seven times throughout the statute other than in the DPP provision. See 42 U.S.C. § 1395ww. But the phrase “eligible for [Medicaid],” on which Metro’s plain-language argument exclusively relies, appears only in the DPP provision and nowhere else in § 1395ww.
This leaves a statutory interpreter applying Metro’s construction of “entitled to benefits under [Medicare] part A” with two unattractive options: (1) interpret every instance of that phrase in § 1395ww consistent with Metro’s construction in the DPP provision, or (2) interpret each instance of that phrase in the context of its specific subsection. The first option is *260problematic because nothing in the language or structure of § 1395ww suggests that the use of the phrase in the DPP provision should dictate the meaning of that same phrase elsewhere in the statute. Indeed, the DPP provision is not the first place that the phrase appears, nor does the DPP provision purport to define the phrase. And applying Metro’s construction of the phrase elsewhere in § 1395ww makes little sense substantively.
For instance, part of the statute’s definition of a “sole community hospital” is that such a hospital be the only source of inpatient services reasonably available to individuals “who are entitled to benefits under [Medicare] part A.” Id. § 1395ww(d)(5)(D)(iii)(II). We can perceive of no reason why Congress would intend that a hospital’s status as a sole community hospital depend on that hospital’s accessibility only to those Medicare beneficiaries who have not exhausted their benefit days for a particular spell of illness, as opposed to all Medicare beneficiaries generally. But that is precisely what Metro argues is the import of Congress’s choice to use the phrase “entitled to benefits under [Medicare] part A.” Metro’s interpretation of this phrase as employed in the DPP provision similarly does not make sense in other § 1395ww contexts in which the phrase appears. See, e.g., id. § 1395ww(d)(5)(K)(viii) (using the phrase in reference to new services or technologies qualifying for coverage); id. § 1395ww(f)(l)(B)(ii) (using the phrase in describing hospitals for which HHS may waive the requirement of implementing a standardized electronic cost-reporting format).
This leaves the second option — interpreting each instance of the phrase in the context of its specific subsection. The pitfall of this method is that it would lead to inconsistent meanings of the same phrase within the same statute. See First City Bank v. Nat’l Credit Union Admin. Bd., 111 F.3d 433, 438 (6th Cir.1997) (“It is a basic canon of statutory construction that phrases within a single statutory section be accorded a consistent meaning.”). Moreover, the phrase “entitled to benefits under [Medicare] part A” appears in more than 30 other sections of the Medicare statute, indicating that the phrase has a specific, consistent meaning throughout the statutory scheme, rather than a varying, context-specific meaning in each section and subsection. See Ali v. Fed. Bureau of Prisons, 552 U.S. 214, 222, 128 S.Ct. 831, 169 L.Ed.2d 680 (2008) (noting that statutory construction “must, to the extent possible, ensure that the statutory scheme is coherent and consistent”).
And these other uses of the phrase within the Medicare statute are similarly inconsistent with Metro’s restrictive interpretation. See, e.g., 42 U.S.C. § 1395b-9(c)(2)(A) (requiring the Medicare Beneficiary Ombudsman to hear complaints from “individuals entitled to benefits under [Medicare] part A,” with no indication of an intent to exclude complaints from Medicare beneficiaries who have exhausted their benefit days for a particular spell of illness). Two of the references even more directly refute Metro’s interpretation by clearly recognizing the difference between a patient who has exhausted his or her Medicare coverage for a particular spell of illness and a patient who is not entitled to Medicare benefits at all. See id. § 1395i(t)(1)(B)(n) (providing coverage for certain outpatient-department services that are “furnished to a hospital inpatient who (I) is entitled to benefits under [Medicare] part A ... but has exhausted benefits for inpatient hospital services during a spell of illness, or (II) is not so entitled” (emphasis added)); id. § 1395Z(a)(8)(B)(i) (using the same language as *261§ 1395Z(t)(l)(B)(ii) in providing for the payment of certain outpatient services).
iii. HHS’s plain-language arguments likewise fail
In contrast to Metro’s DPP-specific argument, HHS contends that the phrase “entitled to benefits under [Medicare] part A” indeed has a specific and consistent meaning throughout the Medicare statutory scheme; i.e., that the individual meets the statutory criteria set out in 42 U.S.C. § 426. Entitlement to Medicare is established by § 426 for two populations: (1) individuals over the age of 65 who are eligible for Social Security retirement benefits, and (2) individuals under the age of 65 who have been entitled to Social Security disability benefits for at least two years. See 42 U.S.C. § 1395c.
Section 426, which is captioned “Entitlement to hospital insurance benefits,” provides that individuals who meet one of those two sets of criteria “shall be entitled to hospital insurance benefits under [Medicare] part A.” Id. § 426(a)-(b). HHS argues that the meaning of this phrase in the DPP provision is no different than its meaning in the statute that establishes and defines the phrase. And because exhaustion of benefit days during a particular spell of illness does not bear on whether a patient meets the § 426 criteria, such exhaustion likewise does not bear on whether a patient is “entitled to benefits under [Medicare] part A” on a given day for the purpose of calculating the DPP.
HHS’s appeal to the consistency of its interpretation within the Medicare statutory scheme, though persuasive, is not conclusive regarding the proper treatment of dual-eligible exhausted benefit days. In fact, an HHS regulation concerning another part of § 1395ww interpreted “entitled to benefits under [Medicare] part A” precisely as Metro construes the term in the DPP until the regulation was amended in 2010. Compare Changes to the Hospital Inpatient PPS and FY 1991 Rates, 55 Fed. Reg. 35990, 35996 (Sept. 4, 1990) (“Since patients who have exhausted their part A benefits are no longer entitled to payment under part A, we do not believe such stays should be counted.”) with Hospital Inpatient PPS for Acute Care Hospitals and FY 2011 Rates, 75 Fed. Reg. 50042, 50287 (Aug. 16, 2010) (modifying the 1990 interpretation and amending the relevant regulation to include individuals who have exhausted their Medicare coverage).
This former interpretation of the same phrase used in the same statute, which was contrary to the Secretary’s current interpretation of that language in the DPP, shows that even the Secretary has not always viewed the phrase as unambiguously encompassing Medicare patients who have exhausted their Part A benefits for a particular spell of illness. And looking back to 2003, the Secretary was interpreting this language in the DPP provision to exclude exhausted benefit days. See 42 C.F.R. § 412.106(b) (2003). To be sure, an agency may change its interpretation of a statute and still warrant deference at the second step of the Chevron analysis, see Chevron, 467 U.S. at 863-64, 104 S.Ct. 2778, but such change clearly casts doubt on the idea that Congress “unambiguously expressed [its] intent” through the statutory language. See id. at 843, 104 S.Ct. 2778.
We conclude that neither Metro nor HHS has demonstrated that the plain language of the phrase “entitled to benefits under [Medicare] part A,” as used in the DPP provision and read in light of the statute as a whole, has a plain meaning that answers “the precise question at issue.” See id. at 842, 104 S.Ct. 2778. Yet both parties argue that the overarching statutory purpose of the DPP and the *262DSH adjustment evidences a clear congressional intent regarding the contested language that favors their diametrically opposite interpretations. See, e.g., Dole v. United Steelworkers of Am,., 494 U.S. 26, 35, 110 S.Ct. 929, 108 L.Ed.2d 23 (1990) (using a statute’s “object and policy” as a “traditional tool of statutory construction” for determining congressional intent in a Chevron analysis). We address these arguments immediately below.
2. Statutory-purpose arguments
Metro argues that the purpose of the DPP provision is to supplement the Medicare reimbursement payments going to hospitals serving low-income patients. It emphasizes that Congress created the specific formulas for calculating DSH adjustments (of which the DPP is the sole variable) in response to the Secretary’s failure to comply with previous legislative mandates to develop a methodology for identifying and paying DSHs. See Part II.A. above. The purpose of the DPP’s two fractions, Metro argues, is to measure two different low-income patient populations, using Medicaid eligibility as one proxy for being a low-income patient and entitlement to Medicare and SSI as the other proxy. And the Medicaid numerator’s exclusion of days attributable to patients who ■ were “entitled to benefits under [Medicare] part A” is meant to prevent the same patient day from being counted in both fractions. Metro concludes that the statutory purpose is to count, but not double-count, low-income patient days, and argues that only its interpretation of the DPP fits that purpose.
HHS, on the other hand, does not dispute Metro’s characterization of the DPP’s overarching purpose, but focuses on Congress’s intent “that the Medicare/SSI fraction serve as a proxy for low-income Medicare patients” and that only non-Medicare patient days should be counted in the Medicaid fraction. A dual-eligible patient, HHS contends, cannot by definition be a “non-Medicare” patient. And because a Medicare beneficiary remains a Medicare beneficiary even when he or she has exhausted coverage for a particular spell of illness, HHS argues that its regulation appropriately assesses a dual-eligible patient day in the Medicare fraction. HHS thus contends that its regulation effectuates, and Metro’s proposed construction undermines, the DPP statute’s purpose.
But designating the relevant low-income patient populations as “Medicare” and “non-Medicare” is purely HHS’s description of the statute and reveals nothing about the DPP’s purpose. Indeed, Metro does not dispute that the Medicaid fraction is designated to exclude Medicare patient days. Rather, the key issue is to determine what constitutes a Medicare patient day — any day of care provided to a patient who is a Medicare beneficiary, or only those days of care actually paid for by Medicare. The statutory purpose that HHS cites is equally consistent with Metro’s proposed construction of the DPP provision. That construction would define patients who have exhausted their Medicare coverage for a particular spell of illness as “non-Medicare” patients and therefore assess their “non-Medicare” patient days in the Medicaid fraction, just as HHS suggests is intended by the statute. In short, this identified statutory purpose offers little guidance in arriving at the meaning of the statute as advocated by HHS.
To be sure, the DPP provision’s general purpose is relatively clear: to provide enhanced payments to hospitals based on the disproportionate share of low-income patients they serve as determined by the Medicare fraction and the Medicaid fraction. See Jewish Hosp., 19 F.3d at 272. Also clear from the statute is that these *263two fractions are exclusive of one another. As noted above, the Medicaid fraction’s numerator excludes the hospital days of patients who are entitled to Medicare Part A benefits. 42 U.S.C. § 1395ww(d)(5)(F)(vi)(II). Such days are instead counted in the Medicare fraction’s numerator if the patient is also entitled to SSI benefits. Id. § 1395ww(d)(5)(F)(vi)(I). The two fractions are then added together to arrive at the DPP, suggesting that the fractions are intended to represent different portions of a hospital’s low-income patient population. As such, HHS does not dispute Metro’s contention that patient days should not be double-counted in the DPP, and congressional intent is also sufficiently clear on this point.
But knowing the statute’s general purpose and that the two DPP fractions are mutually exclusive is insufficient to divine a clear congressional intent regarding whether a Medicare patient who has exhausted his or her days of inpatient services for a particular spell of illness is “entitled to benefits under [Medicare] part A” Even if we were to assume that Congress intended the DPP to account for all of a hospital’s low-income Medicare and Medicaid patients in one or the other of the two fractions, such intent still would not favor Metro’s proposed interpretation over that of the Secretary, or vice versa.
As we will explain below, each party’s interpretation of the statute would exclude from the DPP calculation a group of low-income patients — defined by either entitlement to SSI or by eligibility for Medicaid — that the other party’s interpretation would include. Because either interpretation would necessarily exclude certain low-income patients from the DPP calculation, we can find no support for a clear statutory mandate to account for all low-income patients between the two fractions. The inclusion or exclusion of patient days attributable to particular subsets of low-income patient populations that results from either party’s interpretation thus neither effectuates nor frustrates such a mandate.
As the present case demonstrates, the Secretary’s current regulation excludes one subset of low-income patient days from both numerators: the dual-eligible exhausted benefit days of patients who were not entitled to SSI on those days. Yet dual-eligible patients are not only Medicaid-e%i6ie on such days; Medicaid actually pays for their hospital services. Eligibility for Medicaid is a proxy for being a low-income patient that the DPP statute employs, and the Secretary does not dispute that these patients are, in fact, low-income. Nor does she suggest any reason why Congress would intend for the patient days of this particular low-income patient population to be excluded from the DPP calculation.
But Metro’s proposed interpretation fares no better. It proposes that any Medicare patient who has exhausted his or her days of inpatient hospital services for a particular spell of illness is no longer “entitled to benefits under [Medicare] part A.” This interpretation has two consequences: (1) such a Medicare patient cannot be counted in the Medicare fraction; and (2) such a Medicare patient can be counted in the Medicaid fraction only if he or she is also eligible for Medicaid (that is, he or she is a dual-eligible patient). As the regulation now stands, patient days of Medicare beneficiaries who are entitled to SSI are counted in the Medicare fraction whether or not they have exhausted their benefits for a particular spell of illness. See 42 C.F.R. 412.106(b). But if the statute were to be read as Metro proposes, then the exhausted benefit days of Medicare patients who are not dual-eligible would be totally excluded from the DPP calculation. These are low-income patients as evi*264denced by their entitlement to SSI, a proxy .(like eligibility for Medicaid) that the DPP provision employs. Metro offers no reason why Congress would intend for the patient days of this particular low-income patient population to be excluded from the DPP calculation. In sum, Metro’s interpretation of the DPP provision is no more consistent with the alleged statutory purpose of including all low-income patient days than is HHS’s current regulatory interpretation.
We do note, however, that Metro’s proposed interpretation would not exclude this subset of low-income patient days if patients entitled to SSI were automatically eligible for Medicaid. This is because every such patient day that Metro’s interpretation would exclude from the Medicare fraction would necessarily be a dual-eligible exhausted benefit day and therefore included in the Medicaid fraction. But an individual entitled to SSI, though generally eligible for Medicaid, see 42 U.S.C. § 1396a(a)(10)(A), is by no means guaranteed such eligibility. See Schweiker v. Gray Panthers, 453 U.S. 34, 38, 101 S.Ct. 2633, 69 L.Ed.2d 460 (1981) (explaining the general requirement that SSI-recipients be entitled to Medicaid). But since the SSI program’s inception in 1972, states have had the option to make Medicaid eligibility more restrictive than the qualifications for receiving SSI benefits. See Social Security Amendments of 1972, Pub. L. No. 92-603, § 209(b), 86 Stat. 1329, 1381 (codified at 42 U.S.C. § 1396a(f) (2011)). Eleven states currently employ this so-called “§ 209(b)” option, see Medicaid and the SSI Program, Social Security Program Operations Manual System SI 01715.010, available at https://secure.ssa.gov/poms. nsf/lnx/0501715010 (last visited Mar. 26, 2013), but more have done so in the past. See Gray Panthers, 453 U.S. at 39 n. 6,101 S.Ct. 2633 (listing 15 states using the § 209(b) option). Because not all SSI recipients are eligible for Medicaid due to the § 209(b) option, Metro’s proposed interpretation would indeed exclude patient days from the DPP calculation that the current regulation includes.
This analysis also shows how the present case differs substantially from the circumstances in Jewish Hospital. The contested regulation in that case counted patient days in the Medicaid fraction only if a state Medicaid program actually paid for the hospital care provided on that day. See Jewish Hosp., 19 F.3d at 272. This interpretation of “eligible for [Medicaid]” was unquestionably more restrictive than the alternative interpretation of that statutory language, which would count a Medicaid-eligible patient’s day of hospital care in the Medicaid fraction regardless of whether the state Medicaid program actually paid for such care. Id. at 276. The regulation in Jewish Hospital thus “unnecessarily restricted] the available subsidy” to hospitals across the board, whereas the regulation that Metro contests does not uniformly restrict DSH adjustments. Rather, the regulation’s interpretation of the DPP provision counts patient days that will presumably increase some hospitals’ DSH adjustments while excluding other patient days that decrease the DSH adjustments of hospitals like Metro.
The reason, by the way, that Metro is so adversely affected by HHS’s regulation is because most of Metro’s dual-eligible patients are not entitled to SSI benefits. This means that the patient days of these non-SSI recipients cannot be counted alternatively in the Medicare fraction. The exclusion of these same patient days from the Medicaid fraction (because the patients are dual-eligible) thus means exclusion from the DPP calculation altogether, thereby significantly decreasing Metro’s DSH adjustment.
*265In sum, the current regulation’s practical effect of excluding some low-income patient days from the DPP calculation does not demonstrate that it is contrary to Congress’s clear intent because Metro’s alternative interpretation of the phrase “entitled to benefits under [Medicare] part A” would have the same exclusionary effect on a different set of low-income patient days. Metro has thus failed to show why the Secretary’s interpretation of the DPP calculation is any more of an “absurd result” than the one proposed by Metro. We therefore conclude that Congress has not directly spoken to the question of how exhausted benefit days should be counted in the DPP, leading us to analyze the second step of the Chevron analysis.
C. The Secretary’s interpretation of the DPP provision is a permissible construction of 42 U.S.C. § 1395ww
Having determined that § 1395ww is, at best, ambiguous with respect to the treatment of dual-eligible exhausted benefit days, our analysis proceeds to Chevron's second step. If the Secretary’s interpretation of the DPP provision is based on a permissible construction of the statute, then we must defer to that interpretation and uphold the regulation. See Chevron, 467 U.S. at 843, 104 S.Ct. 2778. A permissible construction is one that is not “arbitrary, capricious, or manifestly contrary to the statute.” Id. at 844, 104 S.Ct. 2778.
Metro argues that the Secretary’s interpretation of the phrase “entitled to benefits under [Medicare] part A” is contrary to the statute, inconsistent with prior agency interpretations of the same language in the DPP provision and elsewhere in § 1395ww, and is the result of an arbitrary rulemaking process. Each of these arguments is analyzed in turn below.
1. Sections 426(c) and 1395d do not preclude the Secretary’s interpretation
Metro first takes aim at HHS’s argument that 42 U.S.C. § 426 supports interpreting the phrase “entitled to benefits under [Medicare] part A” as describing individuals who meet § 426’s old-age or disability-based criteria. Subsection 426(c) instead “fully negatefs]” HHS’s reliance on § 426(a)-(b), Metro argues, because § 426(c) explains that entitlement to a benefit consists of the right to have payment made for a service. The relevant portion of that subsection provides that “entitlement of an individual to hospital benefits for a month shall consist of entitlement to have payment made under, and subject to the limitations in, part A of title XVIII on his behalf for inpatient hospital services ... during such month.”
Metro further argues that the following language from another Medicare statute, 42 U.S.C. § 1395d, confirms that “entitlement” to Medicare benefits is synonymous with the right to have payment made for such benefits: “The benefits provided to an individual by the insurance program under this part shall consist of entitlement to have payment made on his behalf ... for [inpatient hospital services and other specified benefits].” 42 U.S.C. § 1395d(a). In addition, the statute sets forth the limitation on days of coverage for a spell of illness that is at the heart of this case. See id. § 1395d(a)(l).
But neither § 426(c) nor § 1395d(a), properly analyzed, are inconsistent with the Secretary’s interpretation of the DPP provision. Metro wrongly conflates what are limitations on the scope of a benefit with the qualifications that an individual must possess to be entitled to the benefit in the first place. In other words, where the Medicare statute explains what is and is not part of a benefit, Metro implicitly *266argues that the statute is actually providing criteria for the initial entitlement to that benefit. But the statute does no such thing.
Subsections 426(a) and (b) define who is entitled to hospital insurance benefits under Medicare. The next subsection, titled “Conditions,” then explains that “hospital insurance benefits” means the right to have payment made for certain hospital services, subject to the limitations in Medicare Part A. See id. § 426(c). An individual who meets the § 426 criteria is obviously not entitled to have unlimited payments made for unlimited hospital services. Medicaid Part A describes the substance and limitations of hospital insurance benefits and § 426(c) clarifies that an individual who is entitled to Medicare will receive only those benefits as described in Part A. The limitations that appear in Medicare Part A are thus limitations on the substance of a Medicare beneficiary’s hospital insurance benefits, not on who is entitled to those benefits.
One such limitation that appears in Medicare Part A is § 1395d’s limitation on the days of inpatient hospital services during a spell of illness, explained above in Part II.A. Section 1395d’s title, “Scope of benefits,” confirms that its limitations apply to benefits, not to beneficiaries. An exhausted benefit day, like purely cosmetic surgery, is therefore a service to which no Medicare beneficiary is entitled. See id. § 1395y(a)(10) (excluding coverage for cosmetic surgery). And just as a Medicare beneficiary who receives no Medicare coverage for cosmetic surgery is nonetheless “entitled to benefits under [Medicare] part A” as defined in § 426, so too is a Medicare beneficiary who receives no Medicare coverage for inpatient services rendered on an exhausted benefit day. Moreover, § 1395d’s limitations apply only to enumerated services such as inpatient and critical access hospital care, see id. § 1395d(a)(l), and not to other care that Medicare might cover, such as certain physician or skilled nursing services. See CMS Ruling No. CMS-1498-R at 10 (Apr. 28, 2010) (noting that other Medicare-covered services are still available to a beneficiary after exhausting inpatient hospital benefits). So contrary to Metro’s argument, nothing in § 1395d provides that individuals who exhaust their benefit days for a particular spell of illness lose their entitlement to all Medicare benefits.
2. Changes in the Secretary’s interpretation of the relevant statutory language do not preclude judicial deference
Metro next contends that the Secretary’s current interpretation of the DPP provision conflicts with earlier interpretations, thus warranting “considerably less deference than a consistently held agency view.” See INS v. Cardoza-Fonseca, 480 U.S. 421, 448 n. 30, 107 S.Ct. 1207, 94 L.Ed.2d 434 (1987) (internal quotation marks omitted). But Metro overstates these conflicts and inconsistencies. Moreover, “an initial agency interpretation is not instantly carved in stone,” and “informed rulemaking” requires consideration of “the wisdom of its policy on a continuing basis.” Chevron, 467 U.S. at 863-64, 104 S.Ct. 2778.
In support of its argument on this issue of deference, Metro contends that the current regulation’s exclusion of dual-eligible exhausted benefit days from the Medicaid fraction is a complete reversal of the Secretary’s prior position. See Catholic Health Initiatives-Iowa, Corp. v. Sebelius, 841 F.Supp.2d 270, 278 (D.D.C.2012) (“[T]he Secretary was for including dual-eligible exhausted benefit days in the Medicaid fraction before she was against it.”). The administrative materials that Metro *267relies on for this conclusion are a 1995 HHS rulemaking decision and a 1996 decision by HHS’s administrator of the Centers for Medicare and Medicaid Services (CMS) that are cited in Catholic Health Initiatives. See id. at 279-80 (citing Changes to the Hospital Inpatient PPS and FY 1996 Rates, 60 Fed. Reg. 45778, 45811 (Sept. 1, 1995); Presbyterian Med. Ctr. of Phila. v. Aetna Life Ins. Co., CMS Adm’r Dec., 1996 WL 887683, reprinted in Medicare & Medicaid Guide (CCH) ¶45,-032 (Nov. 29,1996)).
But the propriety of including dual-eligible exhausted benefit days in the Medicaid fraction was not the subject of either proceeding. The issue in the cited portion of the 1995 rulemaking was the use of a hospital’s “cost reporting year” versus the “Federal fiscal year.” 60 Fed. Reg. at 45811. And the issue in the Presbyterian Medical Center of Philadelphia decision was the same issue decided in Jewish Hospital; i.e., whether days of care provided to Medicaid-eligible patients should be counted in the Medicaid fraction only if the state Medicaid program paid for the care. See 1996 WL 887683, at * 1. Moreover, a CMS Administrator’s decision that squarely addressed the issue concluded that dual-eligible exhausted benefit days did not belong in the Medicaid fraction. See Edgewater Med. Ctr. v. Blue Cross & Blue Shield Ass’n, CMS Adm’r Dec., 2000 WL 1146601, at *4 (June 19, 2000). In the absence of a definitive agency rule or regulation, and in light of these conflicting CMS Administrator decisions, the Secretary’s position on this issue was, at worst, ambiguous. The 2004 amendment to 42 C.F.R. § 412.106(b) cleared up this ambiguity. It did not squarely contradict a former interpretation.
Metro next points to HHS’s former regulation that allowed only “covered” days (unexhausted benefit days) to be counted in the Medicare fraction. See 42 C.F.R. § 412.106(b) (2003). While acknowledging the change in policy that the 2004 amendment to this regulation brought, HHS contends the change was not a result of a new interpretation of the phrase “entitled to benefits under [Medicare] part A.” The agency instead argues that it has always understood that phrase to refer to an individual’s meeting the § 426 criteria. What changed was its understanding, in light of this court’s decision in Jewish Hospital and the decisions of other courts of appeal that followed, of the phrase “for such days” in the following language that describes the Medicare fraction’s numerator: “the number of the hospital’s patient days for such period which were made up of patients who (for such days) were entitled to benefits under part A.” See 42 U.S.C. § 1395ww(d)(5)(F)(vi)(I).
Previously, the Secretary read the parenthetical phrase “for such days” to “act[ ] as a restrictive qualifier,” which meant that the formula applied only to the days actually paid by the program referenced. See Jewish Hosp., 19 F.3d at 274. Such was HHS’s rationale for previously counting only paid Medicaid days in the Medicaid fraction. That policy was not based solely on an interpretation of the phrase “eligible for [Medicaid],” but rather on that term’s interaction with the phrase “for such days.” Id. After this court and others determined that this interpretation was contrary to the statute, HHS contends that it reconsidered and reversed its interpretation of the Medicare fraction because the prior interpretation likewise depended on reading the phrase “for such days” restrictively. It now interprets the phrase, consistent with Jewish Hospital, as merely a reference back to a preceding phrase in the Medicare fraction; i.e., “the number of such hospital’s patient days for such period.” See 42 U.S.C. § 1395ww(d)(5)(F)(vi)(I).
*268HHS’s response to Metro’s argument, though internally consistent, has little support in the administrative materials. No mention, for example, is made of the phrase “for such days” in the 2004 final rule that amended 42 C.F.R. § 412.106(b). See Changes to the Hospital Inpatient PPS and FY 2005 Rates, 69 Fed. Reg. 48916-01, 49099 (Aug. 11, 2004). But even if HHS’s amendment to the regulation was in fact based on a changed interpretation of the phrase “entitled to benefits under [Medicare] part A” as Metro contends, Metro has not shown that such change renders the current interpretation arbitrary or manifestly contrary to the DPP provision. See Chevron, 467 U.S. at 863-64, 104 S.Ct. 2778. The change instead appears to be the result of a reasoned deliberative process, reflecting HHS’s experience in case-by-case administrative adjudications and in federal-court litigation, and its benefiting from stakeholder input through notice-and-comment rulemaking.
3. The Secretary consistently interprets the phrase “entitled to benefits” elsewhere in the DPP provision and other parts of § 1395
Metro further claims that alleged inconsistencies exist between the Secretary’s interpretation of the phrase “entitled to benefits under [Medicare] part A” in the DPP provision and (1) a similar phrase, “entitled to [SSI] benefits,” in that same provision; and (2) the “entitled to benefits” phrase in another part of § 1395ww. Neither argument, however, provides a basis for concluding that 42 C.F.R. § 412.106(b) is an impermissible construction of the DPP provision under Chevron.
HHS has determined that the patient days of an individual who is eligible for SSI, but not receiving SSI benefit payments, should be excluded from the Medicare fraction’s numerator. See Hospital Inpatient PPS for Acute Care Hospitals and FY 2011 Rates, 75 Fed. Reg. 50042, 50280-81 (Aug. 16, 2010). Although seemingly in tension with the interpretation of the similar phrase “entitled to benefits under [Medicare] part A,” the differences in the language used in the SSI and Medicare statutory schemes explain this apparent inconsistency.
The Secretary reasonably views the Medicare statute’s consistent use of the phrase “entitled to benefits under [Medicare] part A” as giving that phrase a specialized, statute-specific meaning, which is set forth in § 426. In contrast, the SSI statute refers to both eligibility and entitlement, with the two terms being used interchangeably. See, e.g., 42 U.S.C. § 1381a (titled “Basic entitlement to benefits,” but describing persons determined “to be eligible on the basis of [] income and resources”). And whereas individuals meeting the § 426 criteria for Medicare “shall be entitled to hospital insurance benefits,” id. § 426 (emphasis added), individuals meeting the § 1382 criteria for SSI “shall be an eligible individual,” id. § 1382(a) (emphasis added).
This comparison reflects a key distinction between the two programs. An individual who meets the § 426 criteria is automatically entitled to Medicare Part A benefits; filing an application is not a prerequisite to entitlement. See 42 C.F.R. § 406.6(b) (using the § 426 criteria to describe “[individuals who need not file an application for hospital insurance” under Medicare Part A). In contrast, an “eligible individual” under the SSI program must file an application before that individual’s benefits are “effective.” See 42 U.S.C. § 1382(c)(7) (providing that an application for benefits is not effective until the later of (1) the individual becoming eligible for benefits, and (2) “the first day of the month following the date such appli*269cation is filed”). Such an individual is thus eligible for, but not entitled to, SSI benefits during any period in which he or she meets the criteria set forth in § 1382(a) but has no application on file. See Hospital Inpatient PPS for Acute Care Hospitals and FY 2011 Rates, 75 Fed. Reg. 50042, 50280 (Aug. 16, 2010) (discussing this distinction between SSI entitlement and Medicare entitlement). The Secretary’s nuanced interpretation of the Medicare fraction’s numerator appropriately reflects this difference between the two benefit programs.
Metro’s potentially stronger point is that, as explained above in Part V.B.I., the Secretary previously interpreted the phrase “entitled to benefits under [Medicare] part A” elsewhere in § 1395ww as excluding exhausted benefit days. See 42 U.S.C. § 1395ww(d)(5)(G)(iv) (using the phrase as part of the definition for the term “medicare-dependent, small rural hospital”); see also Changes to the Hospital Inpatient PPS and FY 1991 Rates, 55 Fed. Reg. 35990, 35996 (Sept. 4, 1990) (explaining HHS’s view that “entitlement to payment under part A ceases” upon exhaustion of benefit days). But the Secretary recognized this inconsistency and, rather than change her interpretation of that phrase in the DPP provision and everywhere else in the Medicaid statutes, instead amended her interpretation of the phrase as used in § 1395ww(d)(5)(G)(iv). This correction further demonstrates that the Secretary’s interpretation of this statutory phrase is the product of a reasoned analysis of its terms, not an ad hoc determination meant to unduly restrict DSH adjustments.
4. The 2004 amendment to HHS’s regulation was not the product of arbitrary rulemaking
Finally, Metro argues that the 2004 rulemaking that amended 42 C.F.R. § 412.106(b) was arbitrary because (1) HHS did not explain why its interpretation of the DPP formula to not account for all dual-eligible patient days was permissible, and (2) HHS followed the lead of commen-ters who raised irrelevant issues. We find Metro’s arguments unpersuasive.
The first argument presumes that 42 U.S.C. § 1395ww(d)(5)(F)(vi) has a clear purpose of accounting for all dual-eligible patient days in the DPP calculation. But as explained in our discussion with regard to the first step of the Chevron analysis, no such statutory purpose is apparent. See Part II.B.2. above. Furthermore, Metro’s proposed interpretation of the phrase “entitled to benefits under [Medicare] part A” likewise fails to account for all such days. See id. The exclusion of at least some dual-eligible patient days thus appears to be inevitable based on how Congress has structured the DPP. Because of this inevitability, no explanation was necessary for why the HHS regulation fails to account for all such days, and the lack of such explanation does not render the rulemak-ing process arbitrary.
Metro’s second argument is also unavailing because the issues raised by the com-menters had at least some relevancy to the proper interpretation of the DPP, and there is no suggestion that HHS placed undue weight on any of these comments. See Changes to the Hospital Inpatient PPS and FY 2005 Rates, 69 Fed. Reg. 48916-01, 49098 (Aug. 11, 2004). “One eommen-ter observed that a patient who exhausts coverage for inpatient hospital services still remains entitled to other Medicare Part A benefits.” Id. Others noted that the construction of the DPP provision in HHS’s 2003 proposed rule (which is the construction that Metro advocates) would increase the administrative burden on hos-*270pitáis and would reduce some hospitals’ DSH adjustments.
HHS appropriately considered these comments, but there is no evidence that it blindly accepted them as true. See id. (“[W]e note that we disagree with the commenter’s assertion that including days in the Medicaid fraction instead of the Medicare fraction always results in a reduction in DSH payments.”). In sum, we conclude that the rulemaking process was not arbitrary and that the resulting regulation is a permissible construction of the DPP provision that warrants judicial deference under Chevron.
III. CONCLUSION
For all of the reasons set forth above, we REVERSE the judgment of the district court and REMAND the case with instruction to enter judgment in favor of HHS. Metro’s cross-appeal is DISMISSED as moot.