OPINION
JOHNSON, Chief Judge.
In March 2009, the Public Employees Retirement Association (PERA) notified 485 active and retired employees of the City of Duluth that PERA intended to make adjustments to their defined-benefit retirement plans. PERA decided that adjustments were necessary because it determined that the city had, for more than a decade, miscalculated the amounts of contributions to its employees’ retirement plans. PERA’s adjustments would result in smaller retirement annuity payments for retired city employees.
Some of the persons who received PERA’s notices challenged the decision, which led to contested-case proceedings before an administrative law judge. At the culmination of those proceedings, the PERA Board of Trustees reaffirmed the decision to make adjustments to the affected retirement plans. We are asked ■ to review the PERA board’s decision by way of a writ of certiorari. We conclude that the PERA board’s decision is correct with respect to one form of compensation that the city paid to its employees because PERA’s interpretation of the relevant statute is consistent with the plain meaning of the statute. But with respect to the other form of compensation that the city paid to its employees, we conclude that the PERA board’s decision is erroneous because it is based on an improperly promulgated new rule that is inconsistent with the plain meaning of the relevant statute and is not a longstanding interpretation of the statute. Therefore, we affirm in part,'reverse in part, and remand to PERA for further proceedings.
FACTS
A. Overview of PERA
PERA administers several public-sector employee retirement plans. As a general rule, employees of municipalities are required to be members of PERA and to participate in one of its retirement plans. Minn.Stat. § 358.01, subd. 2a (2010). Both municipal employees and their municipal employers must contribute to an employee’s retirement plan each pay period. Minn.Stat. §§ 353.27, subds. 2, 3, .65, subds. 2, 3 (2010).
Upon retirement, a member employee is entitled to receive a defined benefit from a PERA retirement plan in the form of monthly annuity payments. Minn.Stat. §§ 353.29, subd. 1, .651, subd. 1 (2010). The amount of the annuity payment is based on the employee’s compensation before his or her retirement. Minn.Stat. §§ 353.29, subd. 3, .651, subd. 3. Both the employer and the employee must make periodic contributions to an employee’s retirement plan, which also are based on the employee’s compensation. Minn.Stat. [567]*567§§ 358.27, subds. 2, 3, 4, .65, subds. 2, 3, .29, subd. 3, .651, subd. 3.
Not all types of compensation are considered for purposes of calculating contributions. The forms of compensation that are included in or excluded from an employee’s so-called “PERA salary” are determined by statute. See Minn.Stat. § 353.01, subd. 10 (2010). If the employer makes an error in determining an employee’s PERA salary, PERA is required by statute to make refunds of erroneous contributions. Id., subd. 7(c) (2008). Furthermore, “[i]n the event that a retirement annuity ... has been computed using invalid service or salary, [PERA] must adjust the annuity or benefit and recover any overpayment....” Id., subd. 7(d) (2010).
B. The City’s Payment of Supplemental Compensation
During the past two decades, the city has compensated some of its employees with monthly payments that supplement their regular salaries. The city first agreed to pay supplemental compensation in a 1995-96 collective-bargaining agreement (CBA) with one of its unions. Beginning in 1997, the city agreed to make similar monthly payments of supplemental compensation to members of four other unions. Initially, the city agreed to make monthly payments of $25 to each represented employee’s qualified deferred-compensation plan. In subsequent CBAs, the city increased the monthly payments several times until they reached $229 in 2009. The parties refer to these monthly payments as “deferred compensation” payments, but it is more appropriate for this court, for purposes of this opinion, to refer to them as “salary supplement” payments.1
Beginning in 1997, the CBAs between the city and the five unions also provided employees with an alternative form of supplemental compensation. Specifically, the CBAs permitted city employees to elect, in lieu of salary-supplement payments, to receive monthly payments that could be applied to the employee’s purchase of group health insurance. The parties refer to these monthly payments as “insurance supplement” payments. Both salary-supplement payments and insurance-supplement payments were included in future CBAs that governed the city’s labor-management relationships until 2008 and 2009.
C. The City’s Treatment of. Supplemental Compensation as PERA Salary
As previously stated, the city is required to report salary information to PERA each pay period and to remit contributions to its employees’ retirement plans. Minn.Stat. §§ 353.27, subds. 3, 4, .65, subd. 3. From 1995 to 2007, the city included both the salary-supplement payments and the insurance-supplement payments in its calculations of so-called “PERA salary.” The city relied on PERA staff when deciding to include the supplemental payments in PERA salary. According to a former payroll employee, Jackie Morris, the city sought guidance from PERA staff when it began making salary-supplement payments in 1995 and was told to include those payments in PERA salary. The city implemented PERA staffs guidance and adopted the same approach two years later with respect to insurance-supplement payments.
[568]*568In July or August of 2007, however, the city auditor, Wayne Parson, contacted PERA staff and was told that the city should not include either salary-supplement payments or insurance-supplement payments in the city’s calculations of PERA salary. The city discontinued the practice of including supplemental payments in PERA salary in September 2007. One year later, in September 2008, the city’s chief administrative officer, Lisa Pot-swald, sent a- letter to PERA stating that the supplemental payments to employees had been erroneously included in PERA salary. After receiving Potswald’s letter, PERA staff and the city conducted a joint investigation to determine the scope of the payments that had been included in PERA salary. This investigation led to the decision by PERA staff that it was necessary to make adjustments to the contributions and benefits of the city’s employees.
In March 2009, PERA sent letters to 485 active and retired employees, advising them that “PERA staff has determined that certain amounts reported to our association as ‘salary by [the city] cannot be used for purposes of calculating retirement plan contributions or benefits.” PERA’s letters advised each employee or retiree of the total amount of contributions that had been improperly withheld during employment and, thus, would be refunded. PERA’s letters also advised each retiree of a downward adjustment to his or her monthly retirement annuity payment, as well as the amount of overpaid benefits that they would be required to repay.
D. Administrative Review
Seventy current and former city employees filed petitions for review by the PERA Board of Trustees. See Minn.Stat. § 356.96 (2010). The PERA board referred the petitions to the Office of Administrative Hearings for contested-case proceedings before an administrative law judge (ALJ). The petitions were consolidated and assigned to a single ALJ. The petitioners argued that PERA had erred by interpreting section 353.01, subdivision 10, to exclude the supplemental payments from their PERA salary.
After denying motions for summary disposition and holding an evidentiary hearing, the ALJ issued a 62-page, single-spaced order with findings of fact, conclusions of law, and a recommendation to PERA. With respect to the salary-supplement payments, the ALJ concluded that PERA’s interpretation of the statute was not properly promulgated as an interpretive rule and, thus, may not be applied to the city and petitioners. With respect to the insurance-supplement payments, the ALJ concluded that PERA’s interpretation of the statute is an interpretive rule that may be applied to the city’s supplemental payments to the petitioners because the interpretation is consistent with the plain meaning of the statute. Accordingly, the ALJ recommended that the PERA board reverse the decision of PERA staff in part by not adjusting contributions and benefits based on the salary-supplement payments.
Some petitioners and the PERA staff filed exceptions to the ALJ’s findings, conclusions, and recommendation. The PERA board issued an order that modified some of the ALJ’s findings, rejected some of the ALJ’s conclusions of law, and accepted the ALJ’s recommendation in part. Contrary to the ALJ’s recommendation, the PERA board concluded that the PERA staffs decision in March 2009 to make adjustments that would exclude salary-supplement payments from PERA salary was based on a longstanding interpretation of the statute that could be applied to the petitioners without the promulgation of a rule. But the PERA board adopted the ALJ’s recommendation that the PERA [569]*569staffs decision to make adjustments to exclude insurance-supplement payments from PERA salary was consistent with the plain meaning of the statute. Accordingly, the PERA board affirmed the PERA staffs downward adjustments of deductions and benefits and its determinations of overpaid benefits.
Seven petitioners now appeal to this court by way of a petition for writ of certiorari.
ISSUES
I. Did the PERA board engage in improper rulemaking by interpreting Minn. Stat. § 353.01, subd. 10 (2010), to not include the city’s salary-supplement payments in “PERA salary?”
II. Did the PERA board engage in improper rulemaking by interpreting Minn. Stat. § 353.01, subd. 10(b)(2) (2010), to exclude the city’s insurance-supplement payments from “PERA salary?”
III. Was the PERA board’s decision untimely due to a statute of limitations, barred by the doctrine of estoppel, or a violation of relators’ constitutional rights?
PV. Did the PERA board err by not awarding attorney fees to relators?
ANALYSIS
“For the purposes of appellate review, a public-retirement-fund board, like the PERA board of trustees, is analogous to an administrative agency.” In re Disability Earnings Offset of Masson, 753 N.W.2d 755, 757 (Minn.App.2008). Accordingly, this court may reverse or modify a decision by the board only if
the substantial rights of the [relators] may have been prejudiced because the administrative finding, inferences, conclusion, or decisions are:
(a)in violation of constitutional provisions; or
(b) in excess of the statutory authority or jurisdiction of the agency; or
(c) made upon unlawful procedure; or
(d) affected by other error of law; or
(e) unsupported by substantial evidence in view of the entire record as submitted; or
(f) arbitrary or capricious.
Minn.Stat. § 14.69 (2010).
As noted above, both contributions to and benefits from retirement plans managed by PERA are calculated based on an employee’s “salary.” Minn.Stat. §§ 353.27, subds. 2, 3, .65, subds. 2, 3, .29, subd. 3, .651, subd. 3. For these purposes, the term “salary” is defined by statute, in relevant part, as follows:
(a) Subject to the limitations of section 356.611, “salary” means:
(1) the periodic compensation of a public employee, before deductions for deferred compensation, supplemental retirement plans, or other voluntary salary reduction programs, and also means “wages” and includes net income from fees;....
(b) Salary does not mean:
(2) employer-paid amounts used by an employee toward the cost of insurance coverage, employer-paid fringe benefits, flexible spending accounts, cafeteria plans, health care expense accounts, day care expenses, or any payments in lieu of any employer-paid group insurance coverage, including the difference between single and family rates that may be paid to a member with single coverage and certain amounts determined by the executive director to be ineligible;....
Minn.Stat. § 353.01, subd. 10. The PERA board relied on this definitional statute when deciding that the city’s supplemental [570]*570payments should be excluded from the calculations of PERA salary and retirement annuity payments.
I.
Relators first argue that the PERA board erred by adjusting contributions and benefits and recouping overpaid benefits on the ground that the city’s salary-supplement payments were improperly included in PERA salary. Specifically, relators argue that the PERA board’s decision is based on an improperly promulgated new rule.
Administrative agencies generally formulate policy by promulgating administrative rules. See Bunge Corp. v. Commissioner of Revenue, 305 N.W.2d 779, 785 (Minn.1981). An administrative agency’s authority to adopt administrative rules is governed by the Minnesota Administrative Procedure Act (MAPA), Minn. Stat. §§ 14.01-.69 (2010), which requires that administrative rules be promulgated by giving public notice and providing all interested persons an opportunity to submit comments, Minn.Stat. §§ 14.14, .22. An administrative rule is defined to include “every agency statement of general applicability and future effect, including amendments, suspensions, and repeals of rules, adopted to implement or make specific the law enforced or administered by that agency or to govern its organization or procedure.” Minn.Stat. § 14.02, subd. 4. In light of this expansive definition of rule, an agency must promulgate legislative rules (those that are “promulgated pursuant to delegated powers to make substantive law”) as well as interpretive rules (those that “make specific the law enforced or administered by the agency”). Cable Communications Bd. v. Nor-West Cable Communications P’ship, 356 N.W.2d 658, 667 (Minn.1984) (quotations omitted).
The requirement that an interpretive rule be promulgated may give rise to one of three possible consequences. First, an administrative rule that is properly promulgated, whether legislative or interpretive, “shall have the force and effect of law.” Minn.Stat. § 14.38, subd. 1. Second, an interpretive rule that has not been properly promulgated may nonetheless be valid in two situations: “if the agency’s interpretation of a [statute] corresponds with its plain meaning, or if the [statute] is ambiguous and the agency interpretation is a longstanding one.” Cable Communications Bd., 356 N.W.2d at 667. In either situation, “the agency is not deemed to have promulgated a new rule,” id., and the agency’s interpretation is not invalid, “although it does not have the force and effect of law,” In re Contested Case of Good Neighbor Care Ctrs., Inc. v. Minnesota Dep’t of Human Servs., 428 N.W.2d 397, 402-03 (Minn.App.1988), review denied (Minn. Oct. 19,1988). Rather, a reviewing court proceeds to determine the degree of deference that is appropriate. See In re Contested Cases of St. Otto’s Home v. Minnesota Dep’t of Human Servs., 437 N.W.2d 35, 43-44 (Minn.1989); In re Contested Case of Mapleton Cmty. Home, Inc. v. Minnesota Dep’t of Human Servs., 391 N.W.2d 798, 801-02 (Minn.1986). Third, if an agency’s interpretation of a statute is not properly promulgated, and if it is not within either of the above-stated exceptions for a valid interpretation of a statute, the rule is “invalid and cannot be used as the basis for agency action.” Good Neighbor, 428 N.W.2d at 402.
In response to relators’ argument that PERA engaged in improper rulemak-ing, PERA concedes that the statutory definition of “salary” is ambiguous as applied to the city’s salary-supplement payments. In light of that concession, which [571]*571we agree is warranted, PERA cannot establish the first exception to the general rule, that its interpretation of section 353.01, subdivision 10, is justified by the plain meaning of the statute. See id. at 402-03. But PERA contends that the second exception to the general rule applies, i.e., that its interpretation of section 353.01, subdivision 10, is a longstanding interpretation of the statute and, thus, is not an improperly promulgated rule.
The Minnesota caselaw recognizes that an agency’s longstanding interpretation of a statute may be valid, but the caselaw does not provide extensive guidance on the circumstances in which an agency’s interpretation may be deemed longstanding. In some opinions, the appellate courts have described the exception without applying it. See White Bear Lake Care Ctr., Inc. v. Minnesota Dep’t of Pub. Welfare, 319 N.W.2d 7, 8-9 (Minn.1982); In re Contested Case of Ebenezer Soc’y v. Minnesota Dep’t of Human Servs., 433 N.W.2d 436, 439 (Minn.App.1988). In other opinions, the appellate courts simply have held that an agency’s interpretation of a recently adopted statute or rule was not longstanding. See Cable Communications, 356 N.W.2d at 667; In re Application of Crown, CoCo, Inc., 458 N.W.2d 132, 137 (Minn.App.1990), review dismissed (Minn. Sept. 14, 1990). In re Contested Case of Mapleton Cmty. Home, Inc., 373 N.W.2d 815, 819 (Minn.App.1985), aff'd sub nom, In re Contested Case of Mapleton Cmty. Home, Inc. v. Minnesota Dep’t of Human Servs., 391 N.W.2d 798 (Minn.1986):
The principle that a longstanding interpretation of a statute may be valid, even if not properly promulgated, apparently is derived from federal caselaw. Long ago, our supreme court relied on a United States Supreme Court opinion in asserting that the weight that should be given to an agency’s interpretation of a statute “is dependent upon such construction’s having been long-continued.” State v. Dancer (In re Estate of Abbott), 213 Minn. 289, 296, 6 N.W.2d 466, 469 (1942) (citing United States v. Healey, 160 U.S. 136, 16 S.Ct. 247, 40 L.Ed. 369 (1895)); see also White Bear Lake Care Ctr., 319 N.W.2d at 8 (articulating same principle, citing 2 K. Davis, Administrative Law Treatise, § 7.22 (2d ed.1979)). But the federal case-law also does not clearly describe the requirements for deeming an agency’s interpretation longstanding.
It appears that, under federal law, the duration and the consistency of an agency’s interpretation of a statute are just two of several factors that determine the level of deference to be given to an agency’s interpretation of a statute.- As the United States Supreme Court has explained, “ ‘The weight [given an administrative] judgment in a particular case will depend upon the thoroughness evident in its consideration, the validity of its reasoning, its consistency with earlier and later pronouncements, and all those factors which give it power to persuade, if lacking power to control.’ ” United States v. Mead Corp., 533 U.S. 218, 228, 121 S.Ct. 2164, 2172, 150 L.Ed.2d 292 (2001) (emphasis added) (quoting Skidmore v. Swift & Co., 323 U.S. 134, 140, 65 S.Ct. 161, 164, 89 L.Ed. 124 (1944)). Consistent with this statement, federal courts decline to recognize an agency’s interpretation of a statute if the agency has been inconsistent in its interpretation. See, e.g., Leary v. United States, 395 U.S. 6, 25, 89 S.Ct. 1532, 1542, 23 L.Ed.2d 57 (1969) (holding that interpretation was not longstanding in part because of government’s inconsistent position in previous case); Thorson v. Gemini Inc., 205 F.3d 370, 379 (8th Cir.2000) (explaining that court is “far less inclined to yield to agency opinion if the administrative agency’s interpretation of a matter appears to be inconsistent”). [572]*572These cases are in harmony with the Minnesota Supreme Court’s recognition that administrative “ ‘notice and comment procedures exist for good reason: to ensure that unelected administrators, who are not directly accountable to the populace, are forced to justify their quasi-legislative rulemaking before an informed and skeptical public.’ ” Swenson v. Emerson Elec. Co., 374 N.W.2d 690, 702 (Minn.1985) (quoting New Jersey v. Department of Health & Human Servs., 670 F.2d 1262, 1281 (3d Cir.1981)).
Given the purposes of promulgated rules and the above-described caselaw, we proceed to analyze whether PERA’s interpretation of section 353.01, subdivision 10, is longstanding. As an initial matter, however, we note that the evidence on which PERA relies concerns an employer’s matching contribution of an employee’s contribution to a deferred-compensation plan. Such payments usually are variable in amount, based on an employee’s election as to whether to make contributions to a deferred-compensation plan and, if so, the amount of the contribution. In this way, the employer’s matching contribution is similar to the various forms of fringe benefits that are expressly excluded by subdivision 10(b)(2). But the city’s salary-supplement payments are different in nature. Each represented employee is entitled to a fixed monthly payment, solely because of his or her continued employment. In that way, the salary-supplement payments are similar to payments of ordinary salary. PERA’s asserted interpretation of the statute does not account for the qualitative differences between matching contributions to deferred-compensation plans and the city’s salary-supplement payments to deferred-compensation plans. Instead, PERA’s interpretation of subdivision 10 treats alike all types of contributions to deferred-compensation plans, with an emphasis on the nature of the account to which the contribution is made. But PERA’s own Employer Manual states that the classification decision “must go beyond the name that is given to the payment and consider what the payment is for and the source of the payment.”
Even if we assume that PERA’s interpretation of subdivision 10 is applicable to the facts of this case, we cannot conclude that it is longstanding, for several reasons. First, PERA’s purported longstanding interpretation of the statute is of uncertain origin. There is no evidence in the record as to exactly when PERA adopted the interpretation of the statute that was applied to the city’s salary-supplement payments. Without knowing the date of its adoption, it is difficult to conclude that the interpretation is longstanding. Second, PERA’s interpretation of the statute is unwritten and, consequently, indefinite. The provisions of a properly promulgated rule are known or knowable based on the language of its express terms. In fact, the MAPA requires that promulgated rules adhere to certain forms and be published. See Minn.Stat. §§ 14.07, .20, .27, .47. But the precise terms of PERA’s interpretation of section 353.01, subdivision 10, are unwritten and unpublished and, thus, impossible to discern. Third, PERA’s interpretation has been inconsistent over time. The evidence presented to the ALJ demonstrates that the city received conflicting answers from PERA staff regarding whether the city’s salary-supplement payments are within the statutory definition of PERA salary.
PERA’s most specific argument as to why its interpretation of section 353.01, subdivision 10, is longstanding is based on advice that PERA staff provided to another municipal employer in 2004. The record of the contested-case proceeding includes a letter that a PERA staff member sent to the City of St. Paul, which the ALJ [573]*573stated was the “only ... written expression” of PERA’s interpretation of the statute relevant to the city’s salary-supplement payments. The letter states, “After reviewing the information that you provided concerning the deferred compensation match established in the labor agreement ..., we find that our decision is the same as a previous response dated May 19, 1992 (copy enclosed).” This letter fails to establish the existence of a longstanding interpretation of the statute. As an initial matter, the letter does not describe the PERA staff member’s interpretation of the statute but, rather, simply states a conclu-sory answer to the City of St. Paul’s situation-specific question. The letter states that “PERA considers employer-paid amounts to deferred compensation plans as payments ineligible for PERA withhold-ings,” but this conclusory statement does not reveal the reasons for that policy, which might allow this court to infer an interpretive rule. In addition, the information provided by the City of St. Paul, which also was in evidence, describes matching contributions to employees’ deferred-compensation plans in amounts that depended only on an employee’s years of service. As explained above, this form of compensation is not the same as the salary-supplement payments in this case, which means that the correspondence between the PERA staff member and the City of St. Paul is of only limited relevance to the City of Duluth. Thus, the letter from a PERA staff member to the City of St. Paul in 2004 does not establish a longstanding interpretation of the statute that supports PERA’s decision to exclude the city’s salary-supplement payments from PERA salary.
In light of the circumstances and all the evidence in the agency record, we conclude that PERA’s interpretation of section 353.01, subdivision 10, as it concerns the city’s salary-supplement payments, is not a longstanding interpretation of the statute. If we are to accept an improperly promulgated rule as valid on the ground that it is “longstanding,” we must insist on a greater level of formality and consistency than is evident in the agency interpretation in this case. Thus, PERA’s interpretative rule excluding the city’s salary-supplement payments from relators’ PERA salary is an invalid rule, which “cannot be used as the basis for agency action.” Good Neighbor, 428 N.W.2d at 402. Accordingly, we reverse the decision of the PERA board that was taken in reliance on PERA’s un-promulgated interpretive rule. See St. Otto’s Home, 437 N.W.2d at 45 (reversing agency decision based on unpromulgated interpretive rule); Crown CoCo, 458 N.W.2d at 139 (same).
II.
Relators next argue that the PERA board erred by adjusting contributions and benefits and recouping overpaid benefits on the ground that the city’s insurance-supplement payments were improperly included in PERA salary. The ALJ and the PERA board concluded that the decision of PERA staff to exclude the city’s insurance-supplement payments from PERA salary is consistent with the plain meaning of the statute and, thus, is not based on an improperly promulgated rule. On appeal, relators do not challenge this conclusion, and we agree that PERA’s decision is consistent with the plain meaning of the statute insofar as it concerns the city’s insurance-supplement payments. This is so because the statutory definition of “salary” does not include “employer-paid amounts used by an employee toward the cost of insurance coverage.” Minn. Stat. § 353.01, subd. 10(b)(2).
Having conceded that the PERA board’s interpretation of the statute is consistent with its plain meaning, relators argue only [574]*574that the PERA board erred because its decision is arbitrary, unreasonable, and not supported by substantial evidence. Specifically, relators contend that the city’s treatment of the insurance-supplement payments is inconsistent with federal tax law. Relators do not establish that federal tax law is relevant to the application of section 353.01, subdivision 10(b)(2), or to the city’s insurance-supplement payments. The PERA board can apply the pertinent language of subdivision 10(b)(2) to the city’s insurance-supplement payments without encountering any issue of federal tax law.
Relators also contend that the PERA board erred because it relied on evidence of supplemental payments that is inaccurate, according to an affidavit provided by a former payroll employee of the city. But another city employee testified that the payroll records provided by the city are official city records obtained from back-up tapes for 1997-2004 and from its present accounting system for 2005-2007. This testimony shows that PERA’s recalculation of contributions and benefits is based on substantial evidence. See In re Excelsior Energy Inc., 782 N.W.2d 282, 290 (Minn.App.2010) (stating that relator has burden to prove that agency findings are not supported by substantial evidence).
Thus, the PERA board did not err by adjusting contributions and benefits and recouping overpaid benefits with respect to the city’s insurance-supplement payments.
III.
Relators next argue that the PERA board erred for three additional reasons. Because we already have concluded that the PERA board’s decision concerning the city’s salary-supplement contributions is erroneous, we limit our consideration of these three arguments to the city’s insurance-supplement payments.
A. Statute of Limitations
Relators argue that the PERA board cannot adjust retirement plan contributions and benefits and recoup overpaid benefits after the lapse of a three-year statute of limitations. The ALJ rejected this argument on the ground that no limitations period applied at the time of the PERA board’s action. The PERA board adopted the AL J’s recommendation.
The statute governing adjustments for erroneous deductions and contributions has been amended several times. Before 1990, a three-year limitations period applied. Minn.Stat. § 353.27, subd. 7 (1988). The statute later was amended to provide that adjustments could be made “at any time.” Minn.Stat. § 353.27, subd. 7(c) (1994). In 2006, the statute was amended again to make adjustments mandatory; in the process, the “at any time” language was removed. 2006 Minn. Laws ch. 271, art. 3, § 16, at 952. The resulting statute permitted and required the PERA board to make adjustments to retirement-plan contributions upon discovery of an error, without regard for when the error occurred:
Employer contributions and employee deductions taken in error from amounts which are not salary under section 353.01, subdivision 10, are invalid upon discovery by the association and must be refunded as specified in paragraph (d).
Minn.Stat. § 353.27, subd. 7(c) (2008). This version of the statute was in effect in March 2009, when the PERA board took action to adjust contributions and benefits and to recoup overpaid benefits.2 Thus, [575]*575PERA’s action was not subject to a statute of limitations.
Relators also contend ' that the PERA board’s action is barred by statutes of limitations that are codified outside chapter 353 of the Minnesota Statutes. See Minn.Stat. §§ 541.05, subd. 1(1, 2, 4); .07(2), (5) (2010). Each of these statutes of limitations, however, governs “actions,” which refers “to judicial proceedings.” Har-Mar, Inc. v. Thorsen & Thorshov, Inc., 300 Minn. 149, 152, 218 N.W.2d 751, 754 (1974). These provisions of chapter 541 do not apply to the PERA board’s ability to adjust contributions and benefits or to recoup overpaid benefits.
Thus, at the time the PERA board took action to adjust relators’ contributions and benefits, there was no limitation on the timing of its action.
B. Estoppel
Relators argue that the PERA board should be estopped from adjusting retirement plan contributions and benefits and from recouping overpaid benefits. The ALJ rejected this argument, and the PERA board adopted the ALJ’s recommendation.
The doctrine of estoppel “cannot be applied when doing so would cause an agency to act outside the bounds of its authority.” In re Application for PERA Ret. Benefits of McGuire, 756 N.W.2d 517, 519 (Minn.App.2008), review denied (Minn. Dec. 16, 2008); see also Axelson v. Minneapolis Teachers’ Ret. Fund Ass’n, 544 N.W.2d 297, 299-300 (Minn.1996). The PERA board is required by law to adjust contributions and benefits and to recoup overpaid benefits if it discovers an erroneous calculation of PERA salary. Minn. Stat. § 353.27, subd. 7(c)-(e). This rationale is sufficient to dispose of relators’ arguments on this issue. The PERA board cannot be estopped from making an adjustment that is required by law.
C. Constitutional Rights
Relators argue that the PERA board’s adjustment of contributions and benefits and its recoupment of overpaid benefits violate the constitutional prohibitions against impairment of contracts and takings of private property without just compensation. Although relators presented these arguments to the ALJ, neither the ALJ nor the PERA board addressed them. Nonetheless, they are properly addressed for the first time on appeal. See Neeland v. Clearwater Mem’l Hosp., 257 N.W.2d 366, 368 (Minn.1977) (stating that administrative agencies lack subject-matter jurisdiction to decide constitutional issues, which are within exclusive province of judicial branch).
1. Impairment of Contracts
Both the United States Constitution and the Minnesota Constitution prohibit the [576]*576impairment of contracts. U.S. Const, art. I, § 10, cl. 1; Minn. Const, art. I § 11. Relators’ argument, however, focuses on the enforceability of their statutory right to benefits. They do not argue that they had a contractual right under the CBAs to have the salary-supplement and insurance-supplement payments treated as PERA salary. In Christensen v. Minneapolis Municipal Employees Retirement Board, 381 N.W.2d 740 (Minn.1983), the supreme court held that the legislature’s amendment of a statute concerning public employees’ retirement benefits was an unconstitutional impairment of the employment contracts of employees who already had retired. Id. at 750-52. But in this case, there has been no change to the statutory benefits to which relators are entitled, and relators have not identified a contractual right to have their insurance-supplement payments included in PERA salary. Thus, their impairment-of-contracts claim fails.
2. Takings
Both the United States Constitution and the Minnesota Constitution prohibit the taking of private property for public use without just compensation. U.S. Const, amend. V; Minn. Const, art. I, § 13. To establish a taking, relators must show that they had a right to have the insurance-supplement payments included in PERA salary. See State ex rel. Humphrey v. Philip Morris Inc., 606 N.W.2d 676, 697 (Minn.App.2000) (explaining that “where there is no right, there can be no taking” (quotation and alteration omitted)), review denied (Minn. Apr. 25, 2000). Relators have not established a right to have the city’s insurance-supplement payments included in their calculation of PERA salary. Thus, relators’ takings claim also fails.
IY.
Relators last argue that the ALJ and the PERA board erred by not granting their requests for attorney fees. Relators requested attorney fees in their post-hearing submission to the ALJ and again in their exceptions to the ALJ’s findings, but neither the ALJ nor the PERA board addressed the requests.
In a contested-case proceeding, if the prevailing party shows “that the position of the state was not substantially justified, the court or administrative law judge shall award fees and other expenses to the party unless special circumstances make an award unjust.” Minn.Stat. § 15.472(a) (2010). Relators were not the prevailing parties in the administrative review proceedings that led to the PERA board’s decision. But relators have prevailed, in part, in this court. In light of relators’ partial success on appeal, the PERA board on remand should reconsider whether rela-tors are entitled to attorney fees pursuant to section 15.472(a).3
[577]*577DECISION
The PERA board erred by adjusting relators’ contributions and benefits and by recouping overpayments of benefits based on the city’s salary-supplement payments. The PERA board may not rely on its purported longstanding interpretation of the statute and, thus, may not make adjustments to contributions and benefits based on the salary-supplement payments. The PERA board did not err by adjusting relators’ contributions and benefits and in recouping overpayments of benefits based on the city’s insurance-supplement payments. On remand, the PERA board shall modify its adjustments to relators’ contributions and benefits and shall modify its recoupment of overpayments of benefits so as to ensure that the city’s salary-supplement payments to relators are included in the calculation of relators’ so-called “PERA salary.” The PERA board also shall reconsider whether relators are entitled to attorney fees.
Affirmed in part, reversed in part, and remanded.