
578 F.3d 592 (2009)
CENTRA, INC. and Detroit International Bridge Co., Plaintiffs-Counterdefendants-Appellants,
v.
CENTRAL STATES, SOUTHEAST AND SOUTHWEST AREAS PENSION FUND, Defendant-Counterplaintiff-Appellee.
No. 08-4041.
United States Court of Appeals, Seventh Circuit.
Argued May 27, 2009.
Decided August 20, 2009.
*593 Richard Willard (argued), Steptoe & Johnson, Washington, DC, for Plaintiffs-Counterdefendants-Appellants.
Richard L. Fenton, Sonnenschein, Nath & Rosenthal, Chicago, IL, James P. Condon (argued), Central States, Southeast & Southwest Areas Pension Fund, Rosemont, *594 IL, for Defendant-Counterplaintiff-Appellee.
Before CUDAHY, RIPPLE and WOOD, Circuit Judges.
CUDAHY, Circuit Judge.
CenTra, Inc. is a holding company that owns subsidiaries in trucking and real estate, as well as one that operates the Ambassador bridge between Detroit and Windsor, Ontario. In 1995, CenTra was reorganized to shed its unprofitable unionized trucking operations. Two years later, CenTra's last unionized subsidiarythe Detroit International Bridge Co. (DIBC) withdrew from the Central States pension fund, and the fund assessed more than $14 million in withdrawal liability against CenTra under the Multiemployer Pension Plan Amendments Act of 1980 (MPPAA), 29 U.S.C. §§ 1381-1461. CenTra challenged the assessment in arbitration, and the arbitrator reduced the assessment to roughly $960,000. The district court vacated the arbitrator's award and reinstated the fund's assessment. We affirm.

I
The MPPAA amended Title IV of ERISA to require employers withdrawing from multiemployer pension plans to pay their proportionate share of the plans' unfunded vested benefitsthe so-called "withdrawal liability." 29 U.S.C. § 1381(b)(1). The purpose of withdrawal liability is to protect the other employers in the plan from having to pay for the benefits vested in the withdrawing employer's employees. See, e.g., Santa Fe Pacific Corp. v. Central States, Southeast and Southwest Areas Pension Fund, 22 F.3d 725, 726-27 (7th Cir.1994). The pension plan calculates a withdrawing employer's withdrawal liability based in large part on the employer's history of contributions to the fund. See Central States, Southeast and Southwest Areas Pension Fund v. Nitehawk Express, Inc., 223 F.3d 483, 486 (7th Cir.2000). Here, the "employer" withdrawing from the fund is the group made up of CenTra and its subsidiariesa "controlled group" in the argot of the MPPAA.[1] The question is whether CenTra's controlled group, which withdrew from the plan in 1997, was properly assessed withdrawal liability based on the contribution histories of two CenTra subsidiaries that disappeared in the 1995 reorganization.

A
Though the parties quibble about the details, the facts are not materially in dispute. In 1970, T.J. Moroun and his four children created CenTra as a holding company for various trucking subsidiaries the family had owned for decades. T.J. died in 1992; by 1994 his son Manuel (Matty), CenTra's first president, was also CenTra's principal owner and controlling shareholder. Matty's three sisters were minority owners.
From 1970 until 1995, two of CenTra's subsidiaries were Central Cartage Co. and Central Transport, Inc. (Old Subsidiaries or Old Subs). Central Cartage performed local pick-up and delivery services in cities across the Midwest and employed drivers and dockmen. Central Transport was an "over-the-road" line haul carrier that employed drivers who owned their own trucks. The Old Subsidiaries worked together to provide shippers door-to-door service. The dockmen, local drivers and over-the-road truckers that the Old Subs employed all belonged to local unions affiliated *595 with the Teamsters. The Old Subs each had labor agreements with those unions under which they contributed to the Central States pension fund on behalf of their employees. In 1979, Central Cartage purchased DIBC, which owns and operates the Ambassador Bridge. DIBC was also a union employer and contributed to the Central States pension fund. Also relevant here is Crown Enterprises, Inc., a real estate firm that, prior to the 1995 reorganization, was owned by Central Transport. Crown never participated in the pension plan. Rounding out the relevant employers in the pre-1995 CenTra controlled group was U.S. Truck Company, Inc., another fund contributor. Matty's sister Agnes Anne (Anne) owned U.S. Truck. It was affiliated with CenTra by virtue of an agreement between Matty and Anne giving Matty an option to purchase U.S. Truck's stock. U.S. Truck also contributed to the fund.
Pre-1995, then, the CenTra controlled group looked like this:

Deregulation of the trucking industry in the 1980s led to increased competition, and CenTra began looking for ways to cut costs. In particular, CenTra sought to alleviate the burdens imposed by the unions' standard wage rates, which were higher than non-union rates. According to CenTra, the unions stood fast, and the Old Subs suffered financially. Matty wanted to reorganize in a way that would allow CenTra to get rid of the Old Subs' trucking operations while retaining DIBC and Crown, which were profitable. He also wanted the reorganization to be tax neutral. In 1987, CenTra obtained a favorable tax ruling from the Internal Revenue Service for a proposed reorganization, but it would be another eight years before the Moroun siblings reached an agreement allowing the reorganization to go forward.[2]
In 1995 the reorganization finally did go forward. In preparation, CenTra created two new subsidiaries, Central Cartage Co. of Michigan, Inc. and Central Transport of Michigan, Inc. (New Subsidiaries or New Subs), which were intended to take on CenTra's union trucking operations, and a third subsidiary, Central Transport International, Inc. (CTII), which was to engage in non-union trucking.
*596 
Then, on December 31, 1995, the Old Subs merged into CenTra and ceased to exist as such, leaving CenTra as the surviving corporation. At the same time or shortly thereafter (as discussed below, the timing is irrelevant to the analysis), CenTra contributed certain assets and assigned certain liabilities to the New Subs, and the New Subs were renamed to take on the names of the Old Subs (i.e., the "of Michigan, Inc." was dropped).
CenTra refers to the contribution of capital and assignment of liabilities to the New Subs as a "drop down." In particular, CenTra "dropped down" Old Transport's line haul operations, which constituted a portion of Old Transport's motor carrier division, to New Transport. CenTra also contributed $266,000 in common stock and paid-in capital to New Transport. CenTra retained the remainder of Old Transport's motor carrier division, which included Crown Enterprises, the real estate business that had been a subsidiary of Old Transport and which had a book value of $44.5 million at the time of the merger. In addition, CenTra retained Old Transport's freight receivables and other receivables, as well as its other divisions, including a Mexico sales office, several terminal properties and some Canadian real estate, all of which appear to have been contributed by CenTra to CTII. CenTra Chief Financial Officer Robert Youngert testified that New Transport was to be a line haul carrier for CenTra only, and that CenTra retained Old Transport's freight receivables to avoid saddling New Transport with the risk that they would not be collectible.
The Old Transport assets and liabilities that CenTra dropped down to New Transport had a book value of about $6.8 million; those transferred to CTII or retained by CenTra were valued at roughly $104.2 million. With respect to Central Cartage, CenTra "dropped down" Old Cartage's freight division to New Cartage, and contributed $306,000 in common stock and paid-in capital. CenTra retained DIBC. The assets and liabilities dropped down to New Cartage were valued at roughly $23.5 million and those retained by CenTra were valued at approximately $29.9 million.[3]
All of the Old Subs' union trucking operations (including drivers and other employees) were transferred to the New Subs. The New Subs also assumed the Old Subs' labor agreements and their obligations to contribute to the pension fund. CenTra, *597 however, retained the Old Subs' freight contracts and transferred those contracts to CTII. After the merger of the Old Subs into CenTra and the drop down to the New Subs, the CenTra controlled group looked like this:

On February 29, 1996, CenTra sold its stock in New Transport to U.S. Truck. On August 9, 1996, CenTra sold its stock in New Cartage to U.S. Truck. Then on August 19, 1996, Matty and Anne entered a settlement agreement in which Matty gave up his option to purchase U.S. Truck stock. This agreement ended CenTra's affiliation with U.S. Truck. Following the stock sale and settlement agreement, there were two controlled groups, one headed by CenTra and one headed by U.S. Truck:

U.S. Truck's controlled group did not fare well. In 1997, New Transport shut down. In 1999 New Cartage failed, and U.S. Truck filed for bankruptcy and was ultimately liquidated. The fund assessed withdrawal liability against U.S. Truck for a partial withdrawal in 1998, 29 U.S.C. § 1385, and again for a complete withdrawal in 1999, 29 U.S.C. § 1383.
Meanwhile, DIBC remained the last fund contributor in CenTra's controlled group. DIBC's labor agreement expired in November 1997, and Central States terminated DIBC's participation in the fund as of that date. DIBC, Crown and CTII are CenTra subsidiaries to the present day.

B
DIBC's withdrawal from the fund marked CenTra's "complete withdrawal" under 29 U.S.C. § 1383(a), and Central States assessed withdrawal liability. The fund calculated CenTra's withdrawal liability based on the contribution histories of the Old and New Subs up through August 1996, and based on DIBC's entire contribution history. The total amount of liability assessed was $14,761,082.66. CenTra objected that the contribution histories for the Old Subs and the New Subs should not have been used to calculate its withdrawal liability. CenTra argued that as a result of the 1995 reorganization, U.S. Truck, not CenTra, was the employer responsible for those contribution histories if and when U.S. Truck withdrew from the plan.[4] Under *598 MPPAA procedure, CenTra paid the full amount assessed and then demanded arbitration. The arbitrator ruled for CenTra, finding that its withdrawal liability should have been calculated without regard to the Old and New Subs' contribution histories, and the fund's award was reduced to $959,332, representing DIBC's history of contributions to the fund.
The arbitrator found that the merger of the Old Subs into CenTra, followed by the "drop down" to the New Subs, the stock sales to U.S. Truck and the ultimate separation of U.S. Truck from CenTra's controlled group met certain statutory safe harbors under the MPPAA, 29 U.S.C. §§ 1398, 1369(b), which prevented CenTra from incurring withdrawal liability at any point along the way. The upshot of the arbitrator's finding was that it meant the Old Subs' contribution histories traveled first to CenTra in the merger, then to the New Subs in the "drop down," and ultimately along with the New Subs in the stock sales to U.S. Truck.[5]
The district court vacated the arbitrator's award and reinstated the fund's assessment, finding that the Old Subs' contribution histories were assumed by CenTra in the merger and stayed with CenTra because none of the later steps in the reorganization met the MPPAA's statutory requirements for avoiding withdrawal liability. We agree with the district court's analysis and therefore affirm.

II

A
The MPPAA, the most extensive amendment of ERISA to date, "overhaul[ed]" ERISA's Title 4, the plan termination insurance system. John H. Langbein, Susan J. Stabile & Bruce A. Wolk, Pension and Employee Benefit Law 92 (4th ed.2006). In addition to protecting employers who remain in a plan, the MPPAA protects the Pension Benefit Guaranty Corporation (PBGC), the agency charged with implementing and interpreting the statute, from the enormous burden of insuring pension benefits, all in the interest of ensuring that employees will be able to collect their benefits upon retirement. Langbein, Stabile & Wolk, Pension and Employee Benefit Law at 69. Prior to the enactment of ERISA, an employer's liability to a multiemployer plan was governed by the terms of the collective bargaining agreement, which typically lacked any provision for contingent liability. Id. at 69-70. ERISA Title 4 imposed liability upon withdrawal by a substantial employer from a multiemployer plan, and the MPPAA imposed strict technical rules governing such withdrawals. Id.; see 29 U.S.C. §§ 1381(b)(1),1391.
With respect to this case, there are at least three steps to a pension plan's determination of withdrawal liability.[6] First, the fund determines whether an employer (here, CenTra's controlled group) has withdrawn from the plan. A complete *599 withdrawal occurs when an employer "permanently ceases to have an obligation to contribute under the plan `or' permanently ceases all covered operations under the plan." 29 U.S.C. § 1383(a)(1)-(2).
Often key to this determination are three sections of the MPPAA establishing that certain corporate level transactions do not count as a withdrawal. The first is 29 U.S.C. § 1398, which provides that a withdrawal does not occur merely because of a change in business form. In particular, and "[n]otwithstanding any other provision of this part,"
an employer shall not be considered to have withdrawn from a plan solely because
(1) an employer ceases to exist by reason of
(A) a change in corporate structure described in section 1369(b) of this title, or
(B) a change to an unincorporated form of business enterprise,
if the change causes no interruption in employer contributions or obligations to contribute under the plan . . .
Section 1369(b), in turn, provides that "[i]f a person ceases to exist by reason of a merger, consolidation, or division, the successor corporation or corporations shall be treated as the person to whom this subtitle applies." 29 U.S.C. § 1369(b)(3). Taken together, §§ 1398 and 1369(b) specify that an employer does not "withdraw" from a plan solely because it undergoes a merger, consolidation, or division (terms that are, unfortunately, undefined). Following such reorganizations, the successor corporation "or corporations" are deemed the "original employer" for purposes of determining withdrawal liability, and withdrawal liability is not incurred until such time (if any) as the successor withdraws from the plan.
The third provision relevant to the question whether an employer has withdrawn is 29 U.S.C. § 1384, which provides that asset sales meeting certain stringent requirementsthe buyer must assume an obligation to make contributions to the plan at substantially the same level as the seller's contribution, the seller must post a bond and assume secondary liability and the sale must be at arm's length to an unrelated entitywill not result in a withdrawal. See 29 U.S.C. § 1384(a); Nitehawk Express, 223 F.3d at 488.
Sections 1398, 1369(b) and 1384 are most often given effect by courts addressing whether and when a withdrawal has occurred, and they are treated as "safe harbors" exempting predecessor employers from withdrawal liability. Central States, Southeast and Southwest Areas Health and Welfare Fund v. Cullum Cos., Inc., 973 F.2d 1333, 1337 (7th Cir.1992) (discussing § 1384 and quoting I.A.M. National Pension Fund v. Clinton Engines, Corp., 825 F.2d 415, 420 (D.C.Cir.1987)); Central States, Southeast and Southwest Areas Pension Fund v. Sherwin-Williams Co., 71 F.3d 1338, 1342 (7th Cir.1995) (calling § 1398 a "savings clause"). In the present case, there is no dispute about when CenTra withdrew from the plan. The withdrawal occurred in 1997, when DIBC terminated its obligation to the fund. The parties agree that the 1995 reorganization did not cause a withdrawal. Nevertheless, as will appear, the safe harbor provisions, and §§ 1398 and 1369(b) in particular, remain crucial to determining the allocation of the assessed withdrawal liability among the Old Subs' successors.
The second step to determining withdrawal liability is the calculation of the amount owed by the withdrawing employer. The rules governing this calculation are complex, 29 U.S.C. §§ 1381, 1391,[7] but *600 the calculation is based largely on the withdrawing employer's contribution history over the five or ten years preceding the withdrawal. See 29 U.S.C. § 1391(c)(2), (c)(5)(C); Central States Southeast and Southwest Areas Pension Fund v. Safeway, Inc., 229 F.3d 605, 613 (7th Cir.2000). The parties here do not dispute the amount of withdrawal liability so much as they dispute whether and how that amount is to be allocated to CenTra. To understand the distinction between the amount of the liability and its allocation, consider how the amount of the liability was calculated in this case. CenTra's withdrawal occurred in November 1997, and the fund calculated CenTra's withdrawal liability based on that date. To do so, the fund looked at the contribution histories of CenTra's controlled group going back ten years prior to the 1997 withdrawal date. In eight of those ten years, the Old Subs belonged to the CenTra controlled group. In fact, the Old Subs' contributions made up the bulk of the group's contributions during that period. If we calculated withdrawal liability merely according to § 1391, then, arguably that calculation would not take into account or make adjustments for the 1995 reorganization: the CenTra controlled group's contribution history over the ten years preceding November 1997 included contributions by the Old Subs, and therefore those contributions would be included in the calculation under § 1391. End of story.
The statute does not comment one way or the other about whether this method of calculation is appropriate. The PBGC, however, has blessed a third and further step in the process, the allocation step. The fund looks to the safe harbor provisions discussed above to determine how to allocate the withdrawal liability calculated under § 1391 among multiple employers. The PBGC has found that where an employer avoids withdrawal liability under one of the safe harbor provisionsby undergoing a merger, division or exempted asset sale, for instancethe successor employer "inherits" the contribution history of the predecessor for purposes of calculating liability for any subsequent withdrawal. PBGC Opinion Letters 82-40 (Dec. 27, 1982), 92-1 (Mar. 30, 1992); see Nitehawk Express, 223 F.3d at 491; Park South Hotel Corp. v. New York Hotel Trades Council, 851 F.2d 578, 583-84 (2d Cir. 1988). If there is more than one successor employer, the PBGC has said that the contribution history of the predecessor should be apportioned among the successors *601 on a "reasonable" basis. PBGC Opinion Letter 92-1; see also Nitehawk Express, 223 F.3d at 491.
We have previously relied on PBGC Opinion Letter 92-1 in determining how to allocate withdrawal liability among multiple employers, Nitehawk Express, 223 F.3d at 491, and we see no reason to depart from this practice here. We note, however, that the PBGC has not promulgated regulations on this question but has merely issued the above-cited opinion letters on the subject. Opinion letters are not entitled to Chevron deference, or even the deference we accord an agency's interpretation of its own ambiguous regulation, Auer v. Robbins, 519 U.S. 452, 461, 117 S.Ct. 905, 137 L.Ed.2d 79 (1997) (An agency's interpretation of its regulation is "controlling unless `plainly erroneous or inconsistent with the regulation.'") (quoting Robertson v. Methow Valley Citizens Council, 490 U.S. 332, 359, 109 S.Ct. 1835, 104 L.Ed.2d 351 (1989)) (further quotation marks and citation omitted), but opinion letters are "`entitled to respect' ... to the extent that [they] have the `power to persuade,'" Christensen v. Harris County, 529 U.S. 576, 587, 120 S.Ct. 1655, 146 L.Ed.2d 621 (2000) (quoting Skidmore v. Swift & Co., 323 U.S. 134, 140, 65 S.Ct. 161, 89 L.Ed. 124 (1944)).
We remain persuaded that the PBGC's method of apportioning withdrawal liability is a reasonable interpretation of the statute. It respects the statute's purpose of ensuring that the plan's benefits will be adequately funded without overly burdening employers that have undergone changes in corporate structure covered by the MPPAA's safe harbors (and, therefore, without deterring such employers from engaging in beneficial reorganizations). The safe harbor provisions give structure to the MPPAA that comports with general corporate law principles. Looking to those provisions in allocating withdrawal liability therefore should respect parties' expectations regarding the effect of a corporate transaction on the corporation's obligations.
To be concrete, §§ 1398 and 1369(b) treat mergers, consolidations and divisions one way for purposes of determining whether a withdrawal has occurred, while asset sales are generally treated another way. This distinction is common to corporate law and to Title IV of ERISA. "It is axiomatic that a stock sale, merger, or consolidation has no effect on a corporation's contractual obligations. Similar principles have always applied under Title IV of ERISA." Jayne E. Zanglein & Susan J. Stabile, ERISA Litigation 1474 (3d ed.2008). A successor corporation in a merger or stock sale inherits the predecessor's contribution history just as it assumes contractual liabilities.
In contrast to a stock sale, an asset sale generally does not result in assumption of liabilities by operation of law. Again, the result under MPPAA is congruent an asset sale generally results in a complete withdrawal if the seller's controlled group no longer has covered operations or an obligation to contribute. By the same token, the buyer generally does not inherit the contribution history.
Id. at 1476 (citing PBGC Opinion Letter 82-40).
However, § 1384, the third MPPAA safe harbor provision, creates "an elective relief rule" for buyers and sellers of assets, id., so that struggling companies will not be deterred from financially beneficial asset sales by the "daunting prospect of withdrawal liability," Nitehawk Express, 223 F.3d at 487. Section 1384's limited exemption for asset sales that meet its stringent requirements does not undercut the general distinction between mergers and divisions on the one hand (transactions that transfer contribution histories to the successor corporation) and asset sales on the *602 other (transactions that generally do not transfer contribution histories to the purchaser). Because these provisions track typical distinctions in the law of corporate transactions, it is reasonable to apply them in determining the effect such transactions have on an employer's withdrawal liability.

B
The district court reviewed the arbitrator's decision regarding the fund's assessment of withdrawal liability for clear error, and we review the district court's decision under the same standard. Nitehawk Express, 223 F.3d at 488. In assessing whether the fund reasonably allocated the Old Subs' contribution histories to CenTra, we take CenTra's reorganization one step at a time.[8] The first step was the merger of the Old Subs into CenTra, which clearly caused the Old Subs to cease to exist and left CenTra as the surviving corporation. The record contains several merger documents to this effect, and the parties do not meaningfully dispute that this is the case. Under safe harbor provisions §§ 1398 and 1369(b), CenTra inherited the Old Subs' contribution histories as a consequence of the merger. See Nitehawk Express, 223 F.3d at 491 (citing PBGC Opinion Letter 92-1).
The second step was the "drop down" of assets and liabilities from CenTra to the New Subs. CenTra argues that this step was a "division" under § 1369(b)(3), and therefore that the New Subs inherited the Old Subs' contribution histories along with the other assets and liabilities "dropped down" by CenTra. We cannot agree. Although "division" is not defined in the MPPAA, see Sherwin-Williams, 71 F.3d at 1339, the case law has never treated a transaction such as the "drop down" of assets and liabilities at issue here as a division under the statute. Rather, "division" generally means a sale of stock, rather than a transfer of assorted assets and liabilities. See id. ("[The] sale of a subsidiary's stock is a form of corporate `division.'") (citing PBGC Opinion Letters 82-4 (Feb. 10, 1982) and 84-7 (Dec. 20, 1984)); Nitehawk Express, 223 F.3d at 491-92 ("[U]nder the statute, the contribution history of a subsidiary whose stock is sold automatically transfers to the buyer.") (citing PBGC Opinion Letter 92-1); Bowers v. Andrew Weir Shipping Ltd., 27 F.3d 800, 805 (2d Cir.1994) ("While `division' is not a term of art with a widely established meaning, the district court relying on the scant legislative history and an opinion letter of the [PBGC]concluded that the term, `as used in the MPPAA, appears to connote a transaction whereby the stock of a contributing corporation is "divided" away from its controlled group and acquired by or distributed to new owners.'.... We agree with this analysis...") (citation omitted).
CenTra urges us to follow its holistic approach and to find that the merger of the Old Subs into CenTra and the simultaneous "drop down" of the trucking operations to the New Subs is a division under § 1369(b)(3)that the merger and drop down were not separate transactions but rather were "an integrated division of the trucking operations from the Old Subsidiaries into the New Subsidiaries." In effect, CenTra wants us to treat its reorganization as though the Old Subs' were merged into CenTra and then dropped down unchanged into the New Subs (or, perhaps, as though the Old Subs were merged directly into the New Subs). If that were what happened, we might agree *603 that the merger + drop down was a "division" under the statute. But that is not what happened. The Old Subs are not equivalent to the New Subs. The Old Subs disappeared into CenTra, and only pieces of the Old Subs were transferred to the New Subs.[9]
CenTra has derided this analysis, calling it a "substantial asset" requirement "grafted" onto the statute by the district court below, and argues that nothing in § 1398 suggests that the "successor to a covered change in corporate form" must retain "a certain level of its predecessor's assets." But this argument ignores the basic fact that a successor is not a "successor" unless it succeeds to the predecessor corporation's obligations in the first place. Here, the successor to the Old Subs is CenTra, not the New Subs. CenTra has pointed to nothing in the record, and we have found nothing, supporting the assertion that CenTra turned around and transferred the Old Subs to the New Subs, contribution histories and all. What are in the record are balance sheets and financial journal entries showing how carefully CenTra picked out specific assets and liabilities and transferred only those assets and liabilities to the New Subs. There is no reason to believe that the Old Subs' contribution histories went with those assets and liabilities by fiat.
Moreover, CenTra ignores § 1398's requirement that the predecessor employer must "cease to exist" if the transaction is to be exempt from withdrawal liability. No corporate entity ceased to exist in the "drop down," as the Old Subs did in the merger with CenTra (as evidenced by the merger documents noting that the Old Subs' stock was dissolved and CenTra was the surviving corporation). It may be more in line with CenTra's framing of the argument to say that, rather than "ignoring" the § 1398 requirement, CenTra urges that we shoehorn the merger and the "drop down" into a single transaction by which the Old Subs ceased to exist and their trucking operations and contribution histories (but not much else) were "divided" into the New Subs. But as stated above, this ignores the merger into CenTra and CenTra's retention of DIBC, Crown, and the various other valuable assets that CenTra failed to transfer to the New Subs.
A construction analogous to CenTra's was rejected in Penn Central Corp. v. Western Conference of Teamsters Pension Trust Fund, 75 F.3d 529 (9th Cir.1996). In that case, the Ninth Circuit held that a successor corporation that purchased one of the companies in a controlled group became the "original employer" under §§ 1398 and 1369(b) of that company only, and did not inherit the contribution histories of other subsidiaries in the controlled group that had previously ceased operations. Id. at 534. "It would be unreasonable to interpret the last sentence in 29 U.S.C. § 1398 as requiring the successor corporation to assume additional withdrawal liability for each of the parent's subsidiaries, where, as here, only one of the subsidiaries is purchased by the successor and the other subsidiaries ceased operations long before the successor's purchase." Id. Here, U.S. Truck purchased the New Subs, not the Old Subs, which ceased operations prior to U.S. Truck's purchase. We can see no reason why U.S. Truck would have incurred withdrawal liability based on the Old Subs' contribution histories, even if the merger was simultaneous with the "drop down" and the New Subs continued making contributions to the fund on behalf of employees who formerly worked for the Old Subs. The drop down was not a division, nor did it meet *604 the stringent requirements governing asset sales under § 1384. Therefore the Old Subs' contribution histories were not inherited by the New Subs but remained with CenTra after the merger.
Because the Old Subs' contribution histories remained with CenTra, we need not consider whether the sale of the New Subs' stock to U.S. Truck constituted a "division." Even if it did, the Old Subs' contribution histories were not a part of the stock sale because they never made it into the New Subs in the first place. Likewise, we need not consider whether the settlement agreement ending the affiliation between CenTra and U.S. Truck constituted a statutory division.
That leaves one final matter to put to rest: CenTra's argument that this conclusion rests on a theory that withdrawal liability "accrues over time," a theory that CenTra correctly points out has been rejected by various courts. Our holding is not based on this theory, which takes as its premise the idea that a parent cannot shed a subsidiary's contribution histories by engaging in a transaction covered by one of the safe harbor provisions discussed above. As should be clear from what we have said thus far, we agree entirely with CenTra and the courts that have considered this argument that it lacks merit. See Teamsters Pension Trust Fund of Philadelphia v. Central Michigan Trucking, Inc., 857 F.2d 1107, 1109 (6th Cir.1988) (rejecting the fund's argument that a change in corporate structure under § 1398 did not relieve the predecessor parent company from withdrawal liability that had "accrued" during its ownership of the former subsidiary); Godchaux v. Conveying Techniques, Inc., 846 F.2d 306, 310-11 & n. 12 (5th Cir.1988). A parent can shed its subs' contribution histories (or, more correctly, a parent can avoid having those contributions used in the calculation of the parent's withdrawal liability) by engaging in such a transaction. CenTra simply failed to engage in the necessary transaction here.
CenTra ignores this thrust of the argument, as did the arbitrator below, both focusing instead on the notion of liability growing in a contributing employer with the passage of time. The arbitrator found that "Central States' case is premised on the theory that, at all times prior to the reorganization, the Old Subs were accruing withdrawal liabilities, and that these accruals never left the CenTra controlled group.... The evidence and arguments in this case, however, fail to persuade one that contribution histories are, or should be, treated as liabilities."
Setting aside the question whether contribution histories are appropriately treated as liabilities,[10] it is not quite right to characterize contribution histories as "accruing" until the occurrence of a reorganization covered by a safe harbor. They do not "accrue" so much as they form the basis for any eventual calculation of the employer's withdrawal liability. That means that if the employer never withdraws (i.e., if the employer engages in a transaction covered by one of the safe harbor provisions, or if the employer simply continues in operation indefinitely and continues contributing to the fund), that employer will never be assessed withdrawal liability. Therefore, no contribution histories have "accrued"; any liability is contingent on withdrawal.
Again, where an employer engages in a transaction covered by one of the statute's *605 safe harbors, the successor employer is treated as the original employer for purposes of calculating the successor's subsequent withdrawal liability, and no liability is assessed against the predecessor. In the present case, the Old Subs are the predecessor and CenTra is the successor. When the fund calculated CenTra's withdrawal liability, it was therefore appropriate to consider the Old Subs' contribution histories; the fund did not assess any liability against the Old Subs. Likewise, when the fund initially calculated U.S. Truck's withdrawal liability, it excluded the Old Subs' contribution histories on grounds elaborated here: CenTra's drop down of assets to the New Subs did not transfer the Old Subs' contribution histories to the New Subs, so those contribution histories stayed with CenTra instead of transferring to U.S. Truck in the sale of the New Subs' stock.
The district court's decision vacating the arbitration award and reinstating the fund's assessment of withdrawal liability is therefore
AFFIRMED.
NOTES
[1]  Under the statute, all trades or businesses under common control are treated as a single employer or "controlled group." 29 U.S.C. § 1301(b)(1); see Central States, Southeast and Southwest Areas Pension Fund v. Nitehawk Express, Inc., 223 F.3d 483, 486 (7th Cir.2000).
[2]  Throughout the 1980s and 1990s there was acrimony and litigation among the Moroun siblings regarding control of the family business. For the most part, that family dispute is irrelevant to the matters at issue here.
[3]  The numbers vary depending on which balance sheet or journal entry is consulted in the record. Robert Youngert, CenTra's chief financial officer, testified that this might be because some of the financial documents in the record were audited and some were not.
[4]  The fund filed an unsecured claim for withdrawal liability in U.S. Truck's bankruptcy proceeding, and noted that the amount of liability had been calculated on the assumption that the contribution histories for the Old and New Subs prior to September 1996 would be attributable to CenTra. The fund reserved the right to increase its claim against U.S. Truck, however, if that assumption proved to be incorrect.
[5]  The arbitrator also found that the evidence was insufficient for a conclusion that a principal purpose of the reorganization was to evade or avoid withdrawal liability under 29 U.S.C. § 1392(c). Like the district court, we resolve the case under §§ 1398 and 1369(b), and therefore we need not reach this question.
[6]  Under 29 U.S.C. § 1382, the plan sponsor determines the amount of withdrawal liability, notifies the employer of that amount and collects it from the employer.
[7]  The amount of withdrawal liability is determined first by calculating the plan's unfunded vested benefits at the time of the withdrawal, defined by subtracting the value of the plan's assets from the present value of its nonforfeitable benefits. Jayne E. Zanglein & Susan J. Stabile, ERISA Litigation 1478 (3d ed.2008). In the absence of regulations governing these valuations, pension plans may use actuarial assumptions so long as they are "reasonable." Id. Second, the withdrawing employer's share of the unfunded vested benefits is determined according to one of the methods listed in 29 U.S.C. § 1391, or by an alternative method adopted by an amendment to the pension plan, subject to approval of the Pension Benefit Guaranty Corporation. 29 U.S.C. § 1391; Central States, Southeast and Southwest Areas Pension Fund v. 888 Corp., 813 F.2d 760, 762 n.2 (6th Cir. 1987) (citation omitted); see also Zanglein & Stabile, ERISA Litigation at 1481; 60A Am. Jr.2d Pensions § 728 (2009).

Unless otherwise provided for in the plan, the amount of unfunded vested benefits allocable to an employer is calculated by the "presumptive method" described in 29 U.S.C. § 1391(b) . . . Under this method, withdrawal liability is calculated by multiplying the plan's aggregate unfunded benefit liability from all employers by the fraction made up of the sum of all contributions required to have been made by the withdrawing employer, divided by the sum of all contributions by all employers in the plan during the same time period.
888 Corp., 813 F.2d at 762 n. 2 (citing Peick v. Pension Benefit Guaranty Corp., 724 F.2d 1247, 1256 (7th Cir.1983)); see also Borden, Inc. v. Bakery & Confectionery Union & Industry Int'l Pension, 974 F.2d 528, 530 n. 2 (4th Cir. 1992); Park South Hotel Corp. v. New York Hotel Trades Council, 851 F.2d 578, 580 (2d Cir. 1988).
[8]  CenTra appears to object to this approach, preferring to view the reorganization "holistically." But even were we to emphasize the whole over its partsa position for which CenTra offers no authoritywe know of no other way to talk about the reorganization than to discuss its constituent transactions.
[9]  Less than half of Old Cartage's book value transferred to New Cartage, and only about 7 percent of Old Transport's book value made its way to New Transport.
[10]  As discussed, the PBGC reasonably allows the fund to look to the statute's safe harbor provisions to determine whether a successor employer or purchaser of assets has "inherited" contribution histories. This inheritance is similar to the means whereby an employer would assume other contractual liabilities, but we do not address whether the similarity extends further.
