*612Division 1181 A.T.U.-New York Employees Pension Fund and its trustees (collectively, "the Fund") appeal from a judgment of the United States District Court for the Southern District of New York (Castel, J. ), dismissing the Fund's claims against the New York City Department of Education (the "DOE") for delinquent withdrawal liability payments under the Multiemployer Pension Plan Agreements Act ("MPPAA"), 29 U.S.C. § 1381 et seq. The Fund argued that the DOE was the "employer" of the Fund's participants under the MPPAA and is therefore subject to the withdrawal liability incurred by some of its private contractors upon their withdrawal from the Fund. The District Court held that the DOE had no obligation to contribute to the Fund and was therefore not an employer under the MPPAA. We AFFIRM .

BACKGROUND

1. Facts

The DOE operates the public schools in the City School District of the City of New York. For decades, it has contracted with private companies, including Hoyt Transportation, DAK Transportation, Canal Escorts, and the Logan Bus Company (collectively, the "Contractors"), to provide transportation services for students who attend school in the district. Each of the Contractors was, at all relevant times, party to a collective bargaining agreement ("CBA") with the Amalgamated Transit Union Local 1181-1061, AFL-CIO (the "Union"). The CBAs required the Contractors to make monthly contributions to the Fund, a multiemployer pension plan, on behalf of covered employees.

Under the terms of the transportation contracts, the DOE assigned bus routes to each Contractor and required each Contractor to display a DOE route number on its buses, to make available its financial and maintenance records to the DOE, and to report all bus accidents to the DOE. The contracts also addressed certain management issues. While generally prohibiting DOE officers and employees from serving on the board of any Contractor (unless the officer or employee was "not involved in the Contractor's business with the City," App'x 325), the contracts required each Contractor to report any change in management to the DOE and to obtain DOE approval for changes in ownership greater than five percent.

The contracts also covered the Contractors' employees. As relevant to this appeal, those employees fell within two main categories: drivers and escorts. Drivers were responsible for driving buses along the routes assigned by the DOE, while escorts were responsible for "generally supervis[ing] and aid[ing]" disabled students on their trips to and from school. N.Y.C. Admin. Code § 19-603(a). Under the contracts, both drivers and escorts had to be certified by the DOE to perform contract work and were subject to DOE inspections while on duty. If a driver or escort failed an inspection, the DOE could suspend or revoke that employee's certification.

In 1979 the DOE announced that it planned to accept new bids for transportation contracts that did not provide drivers with certain wages and benefits. In response, the Contractors' drivers went on strike. To end the strike, the DOE and the *613Union negotiated a written agreement known as the "Mollen Agreement." As part of the Mollen Agreement, the DOE agreed to insert Employee Protection Provisions ("EPPs") into all of its transportation contracts, including those with the Contractors. The EPPs required each Contractor (1) to contribute to the Fund on behalf of participating employees in amounts determined by either its DOE contract or its CBA with the Union, and (2) to certify annually that it owed no outstanding contributions. If a Contractor failed to contribute to the Fund, the DOE could "withhold the appropriate amounts from any payments due to the [C]ontractor and pay them" to the Fund on behalf of affected employees or, if the failure was willful, cancel the contract. App'x 303. If a contract expired or was canceled by the DOE, the Contractor would "remain liable for any outstanding pension ... contributions still due and owing." App'x 304.

The EPPs themselves did not materially distinguish between driver and escort employees. But the contracts contained a separate Cost Reimbursement provision that applied to escorts alone. Under that provision, a Contractor could elect to receive "full reimbursement" from the DOE for certain expenses incurred "in connection with the employment, training[,] and qualification of escorts," including those itemized in an attached "Schedule of Special Education Escort Costs." App'x 129. That Schedule, in turn, included the Contractor's "share of pension paid" to the Fund "as per [the Division] 1181 union contract." App'x 189.

Until 2012, even though the term of the Mollen Agreement had expired, the DOE voluntarily continued to extend the contracts containing the EPPs. In 2012 the DOE started to issue bids for new transportation contracts that did not include any EPPs. The Contractors, who were bound by their CBAs to contribute on behalf of their covered employees, lost their contracts to other companies that were not so bound and therefore able to bid at lower prices. Having lost their only source of revenue, at least some of the Contractors filed for bankruptcy.

2. Procedural History

In 2013 the Fund's trustees determined that the Contractors had effected a "complete withdrawal" from the Fund, triggering "withdrawal liability" under the MPPAA. See 29 U.S.C. § 1381(a). The Fund pursued its withdrawal liability claims against some of the Contractors in bankruptcy court, but the Contractors lacked sufficient assets to cover the entirety of their alleged withdrawal liability.

The Fund then commenced this action, alleging that the DOE was an "employer" of the Fund's participants and therefore jointly and severally liable for the Contractors' withdrawal liability. The Fund's complaint identified four theories of liability: (1) the transportation contracts obligated the DOE to contribute to the Fund, (2) the DOE and the Contractors were a "single employer," (3) the Contractors were alter egos of DOE, and (4) the DOE and the Contractors were "joint employers."

The DOE moved to dismiss the Fund's complaint for failure to state a claim. The District Court granted the motion in part, holding that the DOE had not signed any contract obligating it to contribute to the Fund. It also held that the Fund had not plausibly alleged that the DOE and the Contractors were a single employer, such that the DOE would be bound by the CBAs signed by the Contractors. But the District Court denied the motion to dismiss as to the Fund's joint employer and alter ego claims. The DOE moved for reconsideration of the District Court's refusal to dismiss those two claims. The District *614Court granted that motion as to the Fund's claim that the DOE and the Contractors were joint employers. It observed that an "employer" under the MPPAA is any entity with an "obligation to contribute" to a pension plan, and that the MPPAA defines "obligation to contribute" to include both contractual obligations and obligations under "applicable labor-management relations law," which includes the National Labor Relations Act ("NLRA"). Sp. App'x 20-21 (quoting 29 U.S.C. § 1392(a) ). Explaining that it had overlooked a provision in the NLRA excluding "any State or political subdivision thereof" from the definition of "employer," Sp. App'x 21 (quoting 29 U.S.C. § 152(2) ), the District Court held that the DOE, a political subdivision of the State, cannot have an obligation to contribute arising from "a duty under" the NLRA (the only labor-management relations statute to which the parties pointed the District Court) that would subject it to withdrawal liability under the MPPAA. 29 U.S.C. § 1392(a)(2).

After discovery limited to the Fund's alter ego claim, the DOE moved for summary judgment. The District Court granted the motion, reasoning that no reasonable jury could conclude, based on the evidence proffered by the Fund, that the Contractors were the corporate alter egos of the DOE. Having determined that the Contractors were not alter egos of the DOE, the District Court concluded that the Fund had failed to show "that the DOE was effectively a signatory to the CBA and therefore subject to withdrawal liability." Sp. App'x 42.

The Fund timely appealed.

DISCUSSION

We review the District Court's decisions de novo, viewing the allegations in the dismissed complaint and the evidence marshaled by both parties on summary judgment in the light most favorable to the Fund. See Apotex Inc. v. Acorda Therapeutics, Inc., 823 F.3d 51, 59 (2d Cir. 2016) ; Robinson v. Concentra Health Servs., Inc., 781 F.3d 42, 44 (2d Cir. 2015).

The Fund brings its claims against the DOE under 29 U.S.C. § 1381(a), which provides: "If an employer withdraws from a multiemployer plan ..., then the employer is liable to the plan in the amount determined under this part to be the withdrawal liability."1 Only an "employer," therefore, is exposed to withdrawal liability under the MPPAA.

The MPPAA does not define "employer." In the absence of a statutory definition, we have construed the term as "a person who is obligated to contribute to a plan either as a direct employer or in the interest of an employer of the plan's participants." Korea Shipping Corp. v. N.Y. Shipping Ass'n-Int'l Longshoremen's Ass'n Pension Tr. Fund, 880 F.2d 1531, 1537 (2d Cir. 1989) (emphasis added) (quotation marks omitted). The MPPAA, in turn, refers to "an obligation to contribute arising-(1) under one or more collective bargaining (or related) agreements, or (2) as a result of a duty under applicable labor-management relations law." 29 U.S.C. § 1392(a). The parties agree on appeal that Korea Shipping incorporated the MPPAA's statutory definition of "obligation to contribute," which includes both contractual and legal obligations. See *615Laborers Health & Welfare Tr. Fund v. Advanced Lightweight Concrete Co., 484 U.S. 539, 545-46, 108 S.Ct. 830, 98 L.Ed.2d 936 (1988). We therefore evaluate the Fund's claims using the framework established by 29 U.S.C. § 1392(a).

1. Obligation Under CBAs or Related Agreements

We first consider the Fund's argument under 29 U.S.C. § 1392(a)(1) that the DOE had an obligation to contribute to the Fund arising "under one or more collective bargaining (or related) agreements" involving the Contractors' drivers and escort employees.

A. Terms of the Contracts

As an initial matter, the Fund acknowledges that the DOE was not a signatory to the CBAs. For that reason, the District Court held that the CBAs themselves could not obligate the DOE to contribute. The Fund nonetheless argues that it would "elevate[ ] form over substance" to hold that the DOE lacked an obligation to contribute arising under the CBAs where the Contractors entered into the CBAs only "because they were obligated to do so by their Contracts with DOE." Appellants' Br. 21, 23.

We agree that an entity can, under certain limited circumstances, be bound by (and therefore be obligated to contribute under) a CBA it did not sign. See, e.g., Bowers v. Transportacion Maritima Mexicana, S.A., 901 F.2d 258, 262 (2d Cir. 1990) (where defendant was bound as a member of the New York Shipping Association ("NYSA") "by the agreements negotiated [o]n its behalf" by the NYSA, it was "an employer subject to withdrawal liability"). But the Fund has failed to explain how the Contractors' CBAs here bind or create any obligations enforceable against the DOE, a non-signatory. Even if the Contractors entered into the CBAs due to their contracts with the DOE, the Union could have enforced the CBAs' contribution provisions against only the Contractors. We therefore conclude that the DOE had no obligation to contribute arising under the Contractors' CBAs.

The Fund next argues that the DOE had an obligation to contribute arising under its individual agreements with each of the Contractors.2 Although the contracts place the obligation to contribute squarely on the Contractors, not the DOE, the Fund contends that the contracts created a pass-through obligation to contribute and that the Contractors were just conduits for contribution payments that originated with the DOE. We are not persuaded. We held in Korea Shipping that two shipping carriers were "employers" under the MPPAA, and therefore subject to withdrawal liability, where they had signed a CBA obligating them to make payments to the NYSA, which in turn would transmit those payments to a pension fund. 880 F.2d at 1535, 1539. Because "[t]he contributions were received directly from the carriers under the [CBA] for the express purpose of funding the ... pension plan," we concluded that the NYSA was "merely [a] conduit[ ] for monies which the carriers were obligated to pay into the ... pension fund," and that permitting the carriers to avoid liability would "effectively undermine" the purposes of the MPPAA. Id. at 1539-40. Here, by contrast, the Fund does not allege that *616the DOE was bound by any agreement that required it to contribute, directly or through an intermediary, to the Fund. This ends our analysis for the Contractors' drivers.

The contractual landscape diverges slightly for escort employees, requiring us to further analyze the claims involving them. As noted, the contracts contained a Cost Reimbursement provision that required the DOE, upon a Contractor's election, to reimburse the Contractor for pension contributions it made on behalf of its escort employees. The Fund contends that this provision imposed on the DOE an "indirect" obligation to contribute, at least on behalf of the escorts who participated in the pension plan. We have not yet determined whether an entity that assumes a contractual obligation to reimburse an employer for the pension-related costs of its employees thereby assumes an obligation to contribute under the MPPAA. The Seventh Circuit, which considered the issue in the context of a declaratory judgment action, established a general rule that "the obligation to reimburse for contributions made by another is not the equivalent of an obligation to contribute in the first instance." Transpersonnel, Inc. v. Roadway Express, Inc., 422 F.3d 456, 461 (7th Cir. 2005) ; id. at 462 & n.4 (distinguishing Korea Shipping and rejecting the plaintiff's argument that Transpersonnel was "merely a conduit through which pension plan payments passed ... to the fund" (quotation marks omitted) ). The court explained that the distinction between reimbursement and contribution is "important for purposes of [the] definition of 'employer' under the MPPAA":

By its terms, th[e] obligation of reimbursement does not arise until after a contribution has been made, and extends only to amounts actually contributed. If Transpersonnel made pension fund contributions that were too small, or omitted contributions, the pension fund could not look to Roadway for the balance as Roadway was only contractually obligated to reimburse Transpersonnel for the actual amounts Transpersonnel contributed. Roadway would have no obligation to make up the difference because it was not contractually obligated to contribute to the pension fund in the first place.

Id. at 461. We agree with the Seventh Circuit that reimbursement and contribution are distinct concepts under the MPPAA. The Fund, like the pension plan in Transpersonnel, could not have "look[ed] to" the DOE under the escort cost reimbursement provision to cover any shortfall in the Contractors' contributions.3 Id. Had the parties intended to place such an obligation to contribute on the DOE, they could have clearly laid out that obligation in the transportation contracts. To be sure, differences exist between the reimbursement provision in Transpersonnel and the reimbursement provision in this case. Under the provision here, for example, the DOE advanced escort costs based on an initial estimate by the Contractor and, if the actual costs incurred were less than the estimated amount, the DOE would deduct the difference from the next monthly payment due to the Contractor. But we do not think these differences exempt this case from the general rule announced in Transpersonnel.4

*617We therefore hold that the DOE had no obligation to contribute arising under its transportation contracts, even on behalf of escort employees.

B. Single Employer Status

Although we conclude that the CBAs and transportation contracts did not, by their terms, obligate the DOE to contribute to the Fund, that does not end our analysis under 29 U.S.C. § 1392(a)(1). Because a finding of "single employer" status would bind the DOE to the CBAs signed by the Contractors, we consider whether the Fund adequately alleged that the DOE and each of the Contractors were a single employer.

A CBA that binds one entity also binds a non-signatory entity if (1) the two entities are a "single employer" and (2) the employees of the entities "constitute a single appropriate bargaining unit." Brown v. Sandimo Materials, 250 F.3d 120, 128 n.2 (2d Cir. 2001). Ultimately, single employer status is "characterized by [the] absence of an arms[-]length relationship found among unintegrated" entities. Id. (quotation marks omitted). To determine whether two entities are a single employer, we review several non-dispositive factors: "interrelation of operations, common management, centralized control of labor relations[,] and common ownership." Lihli Fashions Corp. v. NLRB, 80 F.3d 743, 747 (2d Cir. 1996) (per curiam) (quotation marks omitted). The entities' "use of common office facilities and equipment and family connections" are also relevant. Id.

Turning to the allegations in this case, we conclude that the Fund did not adequately plead that the DOE and each of the Contractors were a single employer. The Fund concedes that the DOE and the Contractors were not commonly owned, and it made no argument based on centralized control of labor relations. As to the interrelation-of-operations factor, the Fund points to allegations that the DOE determined the routes assigned to each Contractor and dictated maintenance and cleaning requirements for the buses, and the complaint alleges, furthermore, that the DOE required each Contractor to maintain a "website connection" with the DOE. We agree with the District Court, however, that these allegations are equally consistent with an arm's-length contractual relationship. As to the common management factor, the Fund cites contractual provisions prohibiting the Contractors from replacing their Chief Executive Officers or effecting a significant change in ownership without DOE approval. But these contractual provisions, typical in commercial contracts, do not plausibly suggest that the DOE and the Contractors had a common management structure, especially where, as here, the contracts also contained an express conflict-of-interest clause that prohibited DOE officers and employees from serving on the board of any Contractor.

Accepting, as we must, all of the Fund's nonconclusory allegations as true, we conclude that it has not pleaded DOE involvement to a degree that would suggest that the DOE and the Contractors were "a single integrated enterprise."5 Lihli Fashions, 80 F.3d at 747 (quotation marks omitted). We therefore agree with the District *618Court that the DOE is not bound by the Contractors' CBAs as a single employer.

C. Alter Ego Status

As noted, the Fund's last argument under 29 U.S.C. § 1392(a)(1) is that the Contractors were alter egos of the DOE. Alter ego status "provides an[other] analytical hook to bind a non-signatory to a [ CBA]." Truck Drivers Local Union No. 807 v. Reg'l Imp. & Exp. Trucking Co., 944 F.2d 1037, 1046 (2d Cir. 1991) ; see Local Union No. 38, Sheet Metal Workers' Int'l Ass'n v. Custom Air Sys., Inc., 357 F.3d 266, 268 (2d Cir. 2004) (per curiam). The alter ego doctrine, like the single employer doctrine, involves a flexible test that considers whether "two enterprises have substantially identical management, business purpose[s], operation[s], equipment, customers, supervision, and ownership." Ret. Plan of UNITE HERE Nat'l Ret. Fund v. Kombassan Holding A.S., 629 F.3d 282, 288 (2d Cir. 2010) (quotation marks omitted). "The focus of the alter ego doctrine ... is on the existence of a disguised continuance or an attempt to avoid the obligations of a [CBA] through a sham transaction or technical change in operations." Lihli Fashions, 80 F.3d at 748 (quotation marks omitted). "[A]nti-union animus or an intent to evade union obligations" is "germane" to the analysis, but not necessary. UNITE HERE, 629 F.3d at 288 (quotation marks omitted).

The District Court did not err in its evaluation of the alter ego factors. It is undisputed that the Contractors managed their own budgeting and finances, made their own salary decisions, retained legal and accounting firms of their own choosing, and elected officers who were unaffiliated with the DOE. It is also undisputed that the Contractors operated out of their own offices and had sole ownership of (or leasing rights to) the buses they used to perform contract work. The Fund failed to proffer any evidence that the DOE and the Contractors were commonly owned or that the DOE harbored anti-union animus. Although the Fund adduced evidence that the DOE extensively monitored the Contractors' compliance with the contracts and that Contractor managers felt obligated to meet the DOE's demands, that evidence, viewed in context, shows little more than the existence of a long-term vendor-vendee relationship in a highly regulated commercial setting. We see nothing in the record supporting the conclusion that the Contractors were "disguised continuance[s]" of the DOE or that the DOE's transportation contracts were "sham transaction[s]" designed to avoid obligations under the CBAs. Lihli Fashions, 80 F.3d at 748 (quotation marks omitted). We therefore hold that the District Court properly granted summary judgment in favor of the DOE on the Fund's alter ego claim.6

Because the Fund has not shown that the DOE signed or was otherwise bound by any contract obligating it to make contributions, we affirm the District Court's orders to the extent they conclude that the DOE had no obligation to contribute under 29 U.S.C. § 1392(a)(1).

*6192. Obligation Under Applicable Labor-Management Relations Law

We now turn to the Fund's argument under 29 U.S.C. § 1392(a)(2). The Fund contends that, even if the DOE had no obligation to contribute arising under the CBAs or its transportation contracts, it nonetheless had such an obligation arising under an "applicable labor-management relations law." In advancing this argument, the Fund relies on the common law joint employer doctrine. That doctrine imposes liability for violations of labor or employment laws not only on the nominal employer but also on entities that, although legally separate from the nominal employer, "handle certain aspects of the[ ] employer-employee relationship jointly." Arculeo v. On-Site Sales & Mktg., LLC, 425 F.3d 193, 198 (2d Cir. 2005) (quotation marks omitted) (Title VII); see Barfield v. N.Y.C. Health & Hosps. Corp., 537 F.3d 132, 141, 149 (2d Cir. 2008) (FLSA).

In urging a contrary conclusion, the DOE argues that the phrase "applicable labor-management relations law" in 29 U.S.C. § 1392(a)(2) refers only to the NLRA and the Labor Management Relations Act ("LMRA"). Because those statutes exempt government entities from liability, it argues, neither statute obligates the DOE to contribute under 29 U.S.C. § 1392(a)(2). The DOE's initial premise is flawed. Although the Supreme Court appears to have equated "labor-management relations law" at least with the NLRA, see Laborers Health, 484 U.S. at 545-46, 108 S.Ct. 830, it has never held that the phrase is limited to the NLRA or LMRA, see Bd. of Trs. of IBT Local 863 Pension Fund v. C & S Wholesale Grocers, Inc., 802 F.3d 534, 544 n.13 (3d Cir. 2015) ; see also Bay Area Laundry & Dry Cleaning Pension Tr. Fund v. Ferbar Corp. of Calif., 522 U.S. 192, 196 n.1, 118 S.Ct. 542, 139 L.Ed.2d 553 (1997) ("An 'obligation to contribute' arises from either a collective-bargaining agreement or more general labor-law prescriptions." (emphasis added) ). The DOE acknowledged as much during oral argument. Oral Arg. Tr. at 15.

But even assuming that "labor-management relations law" includes more than the NLRA and LMRA, the Fund's argument fails. Under 29 U.S.C. § 1392(a)(2), an obligation to contribute must arise "as a result of a duty under applicable labor-management relations law." The Fund has not persuasively explained how the joint employer doctrine, untethered to any particular statute beside the MPPAA,7 creates such a "duty."

Because the joint employer doctrine does not independently create a duty to contribute under 29 U.S.C. § 1392(a)(2), we affirm the District Court's dismissal of the Fund's joint employer claim.

CONCLUSION

We have considered the Fund's remaining arguments and conclude that they are without merit. For the foregoing reasons, the judgment of the District Court is AFFIRMED .