These interlocutory appeals are before us under 28 U.S.C. § 1292 (b). They arise from a group of antitrust actions brought against sixteen oil companies by the states of Arizona, California, Florida, Oregon, and Washington. The complaints, which are similar in all material respects, allege violations of the Sherman Act, 15 U.S.C. §§ 1 & 2. The portions of the complaints material to these appeals allege that the defendant oil companies combined and conspired to raise or stabilize the prices of refined petroleum products.

The cases were filed at various times between July 1973 and February 1977. In August 1976, the Judicial Panel on Multidistrict Litigation transferred the then-pending cases to the Central District of California for coordinated pretrial proceedings. In re Petroleum Products Antitrust Litigation, 419 F.Supp. 712 (Jud.Pan.Mult.Lit.1976). Subsequent cases were filed directly in the Central District.

The plaintiff States sue in their proprietary capacity and on behalf of their citizens as parens patriae pursuant to section 4C of the Clayton Act, 15 U.S.C. § 15c. They also seek to represent classes of government entities and a consumer sub-class consisting of natural persons who purchased defendants’ products prior to the September 30, 1976 effective date of the states’ parens patriae authority.

The primary goal of plaintiffs in this action is the recovery of antitrust damages for allegedly inflated retail gasoline prices paid by the plaintiffs and the classes they seek to represent. The principal difficulty plaintiffs have faced is the Supreme Court’s intervening announcement in Illinois Brick v. Illinois, 431 U.S. 720 , 97 S.Ct. 2061 , 52 L.Ed.2d 707 (1977), that indirect purchasers of price-fixed goods may not maintain an antitrust damage action for overcharges passed on to them by direct purchasers from the defendant. According to the plaintiff States, an estimated 80 percent of the retail gasoline transactions at issue here involve indirect purchases from non-defendant retail dealers.

Shortly after the decision in Illinois Brick , the defendant oil companies moved to dismiss portions of the plaintiff States’ complaints on various grounds, among them that plaintiffs are indirect purchasers barred by Illinois Brick from recovering damages. On August 26, 1980, the district court issued an order on the applicability of Illinois Brick to the instant proceedings. Portions of this order are the subject of the first interlocutory appeal.

The second interlocutory appeal is from a subsequent order of the district court denying plaintiffs’ motion for certification of the consumer sub-class. The district court made the required certification of the two appeals and the plaintiffs filed timely petitions for permission to appeal. This court granted both interlocutory appeals and the cases were calendared together for oral argument. We now affirm the district court’s orders in both cases.

The first appeal is from the district court’s certification to us of paragraphs “third” and “fourth” of its August 26, 1980 order. At paragraph “third,” the district court ruled: “[A]ll claims for damages based on purchases from firms that competed with the defendants but did not conspire with them to violate the antitrust laws are dismissed.” Paragraph “fourth” states: “[T]he plaintiffs may amend their complaints to allege that defendants conspired with retail dealers of petroleum products only if the conspiring retail dealers are joined as parties defendant.” For the reasons set forth below, we affirm these rulings.

Paragraph “Third”

Paragraph “third” dismissed plaintiffs’ claims for damages sought under an “umbrella” theory of liability. Plaintiffs contend that defendants’ successful price-fixing conspiracy created a “price umbrella” under which non-conspiring competitors of the defendants raised their gasoline prices to an artificial level at or near the fixed price. Since defendants are allegedly responsible for creating a market situation where conduct of this nature is possible, plaintiffs argue that defendants should be held responsible for damages resulting from their competitors’ higher prices.

The umbrella theory is essentially a consequential damages theory. It seeks to hold price-fixers liable for harm allegedly flowing from the illegal conduct even though the price-fixing defendants received none of the illegal gains and were uninvolved in their competitors’ pricing decisions. Since the decision in Illinois Brick , at least one district court has allowed plaintiffs to proceed under an umbrella theory. In re Bristol Bay, Alaska, Salmon Fishery Antitrust Litigation, 530 F.Supp. 36 (W.D.Wash.1981). The Third Circuit, however, has expressly rejected its use. Mid-West Paper Products Co. v. Continental Group, Inc., 596 F.2d 573 (3d Cir. 1979).

Although the Court in Illinois Brick was not faced with an umbrella claim, the rationale for its decision barring indirect purchasers from seeking antitrust damages must be considered in determining the viability of an umbrella theory of liability. In Illinois Brick , plaintiffs attempted to recover damages from defendants who allegedly had overcharged the sellers from whom the plaintiffs purchased. The plaintiffs claimed that their immediate sellers passed on the overcharges to them. In rejecting the offensive use of a pass-on theory, the Court noted the possibility of duplicative recovery if both direct and indirect purchasers could claim damages resulting from a single overcharge by an antitrust defendant. 431 U.S. at 730-31 , 97 S.Ct. at 2066-67 . The Court reasoned that, by concentrating the recovery in direct purchasers rather than among a broad class of potentially affected plaintiffs, the antitrust laws would be enforced more effectively. The Court further noted the tremendous burden that would be placed on antitrust proceedings by the “massive evidence and complicated theories” necessary to measure and trace the effect of an overcharge through each step of the distribution chain, id. at 737 , 97 S.Ct. at 2070 , and the attendant complexities inherent in apportioning damages “among all potential plaintiffs that could have absorbed part of the overcharge.” Id. at 741 , 97 S.Ct. at 2072 .

In Mid-West Paper, supra, the Third Circuit found the umbrella claim before it analogous to the pass-on issue involved in Illinois Brick because “in both situations the plaintiff seeks to recover for higher prices set by, and paid by it to, parties other than the defendants.” 593 F.2d at 584. Given the fact that numerous factors influence a firm’s pricing decisions, the court concluded that an umbrella claim is necessarily conjectural and speculative in nature. Id. at 584-85. Moreover, ascertaining how and why a competitor of the defendant charged a certain price would mire the court in a complex economic proceeding of the type Illinois Brick sought to prevent. Id. at 585. The spectre of complicated, speculative proceedings combined with the potential for ruinous recoveries, well in excess of defendants’ illegally earned profits, id. at 586, led the court to hold that purchasers from competitors of price-fixing defendants may not seek damages under an umbrella theory of liability.

The decision in Mid-West Paper is not without its critics. See id. at 595-99 (Higginbotham, J., dissenting in part); In re Beef Industry Antitrust Litigation, 600 F.2d 1148 , 1166 n. 24 (5th Cir. 1979), cert. denied, 449 U.S. 905 , 101 S.Ct. 280 , 66 L.Ed.2d 137 (1980); 93 Harv.L.Rev. 598 (1980). First, since the umbrella claimant in Mid-West Paper was a direct purchaser from a competitor of the defendants, there was no danger of duplicative recovery, a major concern of the court in Illinois Brick . Second, Mid-West Paper involved only one class of plaintiffs and a single level of distribution. Therefore, the concern in Illinois Brick over the complexities involved in tracing the effects of a conspiracy through several levels of manufacture and distribution was not present. Third, proof of what the non-conspiring competitor may have charged absent the conspiracy need not involve evidence more complicated than that adduced in other antitrust proceedings. Fourth, the Court in Illinois Brick was concerned with prohibiting economically complex evidence only where it would threaten the effective enforcement of the antitrust laws by reducing the incentive of direct purchasers to sue. Allowing an umbrella claimant to sue for his injuries in no way reduces the incentive to sue of direct purchasers from the defendants. Fifth, although the possibility of ruinous recovery is not unimportant, this concern is more properly addressed to Congress. See Reiter v. Sonotone Corp., 442 U.S. 330, 345 , 99 S.Ct. 2326, 2334 , 60 L.Ed.2d 931 (1979).

The viability of an umbrella claim in the wake of Illinois Brick is an important issue of first impression in this circuit. We need not decide, however, whether, in a situation involving a single level of distribution, a single class of direct purchasers from non-conspiring competitors of the defendants can assert claims for damages against price-fixing defendants under an umbrella theory. In the case before us, the umbrella claimants purchased gasoline from independent marketers who, in turn, purchased their gasoline from independent refiners. These independent refiners manufactured a percentage of the independent marketers’ supply and brokered the remainder of the marketers’ supply from major refiners, i.e., the defendants.

For two reasons, we have little hesitancy in concluding that the limitations recognized in Illinois Brick bar umbrella claims in the context of the multi-tiered distribution chain alleged here. First, to the extent that plaintiffs seek recovery for overcharges for gasoline originally purchased from defendants by independent refiners, the overcharge to plaintiffs may simply result from a pass-on of the original unlawfully inflated price. If so, it falls squarely within Illinois Brick . Even if plaintiffs were somehow able to prove that there was no pass-on, and that the inflated prices in the non-conspirators’ distribution chain were the independent result of an umbrella effect, the danger of double recovery condemned by Illinois Brick would remain. The independent refiners would still have an enforceable claim for damages against the defendants for the entire unlawful overcharge to them, without reduction for damages suffered by plaintiffs. The result, if plaintiffs were to succeed here, would be liability of the defendants twice for the effects of the same overcharge.

The second reason that plaintiffs’ claims are barred by Illinois Brick , wholly apart from the problems of pass-on and double recovery, is that they are unacceptably speculative and complex. Thus, any umbrella claims plaintiffs may assert for damages based on those purchases of gasoline not acquired originally from the defendants also must fail. A major theme in Illinois Brick is that the “feasibility and consequences of implementing particular damages theories may, in certain limited circumstances, be considered in determining who is entitled to prosecute an action brought under § 4.” Blue Shield v. McCready, - U.S. -, - n. 11, 102 S.Ct. 2540 , 2546 n. 11, 73 L.Ed.2d 149 (1982). Although we recognize that the “difficulty of ascertainment [should not be] confused with a right of recovery,” Bigelow v. RKO Radio Pictures, Inc., 327 U.S. 251, 265 , 66 S.Ct. 574, 580 , 90 L.Ed. 652 (1946), we nevertheless must consider whether “a claim rests at bottom on some abstract conception or speculative measure of harm.” McCready, supra.

Under an umbrella theory, the result of any attempt to ascertain with reasonable probability whether the non-conspirators’ prices resulted from the defendants’ purported price-fixing conspiracy or from numerous other pricing considerations would be speculative to some degree. When the fact of a multi-tiered distribution system is imposed upon the above complex set of variables, the obstacles to intelligent inquiry become nearly insurmountable. The causal effect of each pricing decision would have to be pursued through the chain of distribution. Not only would we be required to speculate that plaintiffs were injured solely as the result of umbrella pricing, but also we would be required to sanction complex judicial inquiry into the pricing decisions of sellers remote from plaintiffs. We decline to do either, and accordingly hold that under the facts of this case, application of an umbrella theory is unwarranted.

Paragraph “Fourth”

In an effort to circumvent Illinois Brick , plaintiffs suggested to the district court that they might seek to prove a resale price maintenance conspiracy between defendants and retail dealers. At paragraph “fourth,” the district court ruled that plaintiffs must join retail dealers as defendants if they pursue a conspiracy claim.

Without benefit of specific factual allegations that the future amended complaint may contain, we express no opinion on whether a vertical conspiracy claim may be appropriate in this case. Assuming such a claim may be stated, however, we find no error in the district court’s ruling.

Absent joinder of retail dealers, serious risks of duplicative recovery and inconsistent adjudications would ensue. In re Beef Industry Antitrust Litigation, supra, 600 F.2d at 1148 . If plaintiffs recovered damages for a vertical conspiracy between defendants and non-party retail dealers, any of those dealers could prove in a subsequent action that they were not conspirators and, as direct purchasers, were entitled to damages arising out of the same events. In Illinois Brick , the Court expressly found unacceptable the risk of duplicative recovery created by allowing direct and indirect purchasers to claim damages resulting from a single transaction that violated the antitrust laws. 431 U.S. at 730-31 , 97 S.Ct. at 2066-67 . McCready, - U.S. at -, 102 S.Ct. at 2546 .

We also cannot accept plaintiffs’ contention that no duplicative recovery can occur here because there is no intervening market between the defendants and their retail dealers. We note that fifteen defendants in this action are named as defendants in other litigation where a certified class of lessee retail dealers, who bought gasoline from defendants during the period covered by the complaints in this case, similarly allege that defendants, through exclusive supply arrangements with their dealers, have eliminated horizontal competition at the wholesale level. Bogosian v. Gulf Oil Corp., 561 F.2d 434, 447 (3rd Cir. 1977), cert. denied, 434 U.S. 1086 , 98 S.Ct. 1280 , 55 L.Ed.2d 791 (1978).

We further reject plaintiffs’ argument that an exception to a rule requiring joinder should obtain where, as here, the statute of limitations has run on direct purchasers. We note that the claims in Bogosian, supra, overlap the claims at issue here. Moreover, the record indicates that plaintiffs intend to seek damages up to the time of trial for a continuing conspiracy. Under these circumstances, dealer claims against defendants covering the last four years would not be time-barred. Plaintiffs’ suggestion, therefore, does not remove the risk of multiple liability. Furthermore, we are unwilling to countenance ad hoc case-by-case exceptions to a rule of intended general application. See Illinois Brick, 431 U.S. at 743-45 , 97 S.Ct. at 2073-74 .

We accordingly uphold the ruling of the district court that if a proper vertical conspiracy claim is alleged, joinder of retail dealers is required to prevent a serious risk of multiple liability.

II.

The second interlocutory appeal is from the district court’s order denying plaintiffs’ motion to certify classes of indirect purchaser retail consumers pursuant to Rule 23(b)(3), Fed.R.Civ.P.

A decision denying class certification is reviewable on appeal only for abuse of discretion or for application of impermissible legal criteria. Pattillo v. Schlesinger, 625 F.2d 262, 264 (9th Cir. 1980); Yamamoto v. Omiya, 564 F.2d 1319, 1325 (9th Cir.1977). Although in determining whether to certify the class, the district court is bound to take the substantive allegations of the complaint as true, Blackie v. Barrack, 524 F.2d 891 , 901 n. 7 (9th Cir. 1975), cert. denied, 429 U.S. 816 , 97 S.Ct. 57 , 50 L.Ed.2d 75 (1976), the court also is required to consider the nature and range of proof necessary to establish those allegations. Id. at 901.

The district court ruled that if plaintiffs seek to by-pass the rule in Illinois Brick , any theory on which they might rely would raise predominantly individual questions relating to the relationships between the defendants and each of their approximately 35,000 retail dealers. We agree.

The plaintiffs argue that the “control” exception to Illinois Brick, 431 U.S. at 736 n. 16, 97 S.Ct. at 2070 n. 16 , is susceptible of proof on a classwide basis without inquiry into the pricing decisions of the retail dealers. Plaintiffs propose to establish their claim by circumstantial evidence in- eluding lease and supply agreements between the defendants and their dealers, and marketwide price statistics. None of the leases or supply agreements at issue here, however, purport to allow the defendant oil companies to fix the retail dealers’ prices to the public. Moreover, marketwide price statistics are insufficient evidence upon 'which to avoid Illinois Brick . A nationwide increase in gasoline prices may reflect nothing more than the fact that wholesale prices are important factors in retail pricing. Assuming arguendo that defendants engaged in a conspiracy to fix the wholesale price of gasoline, an across-the-board increase in gasoline prices may well indicate nothing more than the dealers’ independent decisions to pass on wholesale overcharges to the consuming public.

Without giving the district court an opportunity to pass on the issue, we are unwilling at this stage of the proceedings to pronounce the precise contours of the “control” exception to Illinois Brick or to decide whether or not it may have application to the facts of the case. We do conclude, however, that if such an exception is applicable, the degree to which the individual retail dealers may have exercised independent pricing discretion is important. Accordingly, individual questions involving the pricing decisions of 35,000 retail dealers will predominate and preclude class treatment.

To the extent that plaintiffs’ proposed vertical conspiracy claim may differ from its allegations of the “control” exception to Illinois Brick , we reach a similar conclusion. Vertical price fixing, of course, is per se illegal. Continental T.V., Inc. v. GTE Sylvania, Inc., 433 U.S. 36 , 51 n. 18, 97 S.Ct. 2549 , 2558 n. 18, 53 L.Ed.2d 568 (1977). Supplier actions that might influence resale prices but which do not sufficiently induce avoidance of price competition, however, do not constitute vertical price fixing. General Cinema Corp. v. Buena Vista Distribution, 681 F.2d 594 at 597 (9th Cir. 1982); Knutson v. Daily Review, Inc., 548 F.2d 795, 806 (9th Cir. 1976), cert. denied, 433 U.S. 910 , 97 S.Ct. 2977 , 53 L.Ed.2d 1094 (1977). To prevail on a vertical price fixing claim, plaintiffs must show “affirmative action” on the part of the oil companies which induced their dealers to charge certain prices. General Cinema, supra. They also must show that the dealers succumbed to such pressure. Hanson v. Shell Oil Co., 541 F.2d 1352 , 1355-57 & n. 3 (9th Cir. 1976), cert. denied, 429 U.S. 1074 , 97 S.Ct. 813 , 50 L.Ed.2d 792 (1977).

Proof of a close conformity between wholesale and retail prices is insufficient to establish a vertical conspiracy claim on a class-wide basis. Absent common evidence of standard contracts that demonstrate control over the retail dealers’ pricing decisions or some other readily demonstrable and equally convincing evidence, individual issues will predominate and render class treatment inappropriate. See Chicken Delight, Inc. v. Harris, 412 F.2d 830, 831 (9th Cir. 1969).

Because plaintiffs have failed to suggest any acceptable method of demonstrating on a class basis that the individual retail dealers lacked pricing discretion, they have not met their burden of showing that the proposed classes satisfy the requirements of Rule 23, Fed.R.Civ.P. In re Hotel Telephone Charges, 500 F.2d 86, 88 (9th Cir. 1974).

AFFIRMED.

. We note at the outset what is not before us. At paragraph “second” of the district court’s order, the court ruled that plaintiffs may seek damages from the defendants “only as to direct purchases from the defendants, their co-conspirators, sellers with whom plaintiff had fixed-quantity, cost-plus contracts pre-dating the alleged violations, or entities owned or controlled by the defendants or their co-conspirators.” The “cost-plus” and “control” situations referred to by the district court in its ruling are possible exceptions to the bar against indirect purchaser claims. Illinois Brick, 431 U.S. at 736 and n. 16, 97 S.Ct. at 2069 and n. 16. Although much of the appellate briefing in this case is concerned with the correctness of the district court’s ruling in paragraph “second,” the district court did not certify this paragraph to us. We trust we will not surprise counsel by expressing no opinion on the issues raised by this ruling. . Plaintiffs claim standing to assert an umbrella claim under § 4 of the Clayton Act, 15 U.S.C. § 15 , which provides: Any person who shall be injured in his business or property by reason of anything forbidden in the antitrust laws may sue therefor in any district court of the United States in the district in which the defendant resides or is found or has an agent, without respect to the amount in controversy, and shall recover threefold the damages by him sustained, and the cost of suit, including a reasonable attorney’s fee. . The Court had previously held that in a suit by a direct purchaser, an antitrust violator may not defend on the ground that the direct purchaser has not been injured because it had passed on the illegal overcharge to its own customers. Hanover Shoe, Inc. v. United Shoe Machinery Corp., 392 U.S. 481 , 88 S.Ct. 2224 , 20 L.Ed.2d 1231 (1968). In Illinois Brick , the Court expressed a desire to maintain symmetry with its previous decision. . In Blue Shield v. McCready, - U.S. -, -, 102 S.Ct. 2540, 2546 , 73 L.Ed.2d 149 (1982), the Court reiterated that in Illinois Brick it had concluded that “direct purchasers rather than indirect purchasers were the injured parties who as a group were most likely to press their claims with the vigor that the § 4 treble-damages remedy was intended to promote.” (citation omitted). . Prior to Illinois Brick , one court in this circuit allowed an umbrella claim. Washington v. American Pipe & Construction Co., 280 F.Supp. 802 (W.D.Wash.1968). . In Blue Shield v. McCready, - U.S. -, -, 102 S.Ct. 2540, 2547 , 73 L.Ed.2d 149 (1982), the Court noted that two analytically distinct types of limitations have been imposed on the § 4 remedy: 1) those arising out of Illinois Brick and Hawaii v. Standard Oil Co., 405 U.S. 251 , 92 S.Ct. 885 , 31 L.Ed.2d 184 (1972), involving considerations of duplicative recovery and unwarranted evidentiary complexities engendered by speculative damage claims and 2) those arising out of claims that a particular injury is too remote from the alleged violation to accord a plaintiff standing under § 4. Because we decide this case on the basis of Illinois Brick , we need not decide whether plaintiffs meet the test of standing traditionally employed by this Circuit to determine remoteness under § 4. See, e.g., In re Multidistrict Vehicle Air Pollution M.D.L. No. 31, 481 F.2d 122 (9th Cir.), cert. denied 414 U.S. 1045 , 94 S.Ct. 551 , 38 L.Ed.2d 336 (1973). Cf. Ostrofe v. H.S. Crocker Co., 670 F.2d 1378 (9th Cir. 1982) (collecting cases and suggesting a balancing analysis). . To recover treble damages, plaintiffs must prove actual causation — “injury in fact.” Flintkote v. Lysfjord, 246 F.2d 368, 392 (9th Cir.), cert. denied, 355 U.S. 835 , 78 S.Ct. 54 , 2 L.Ed.2d 46 (1957). Although the trier of fact may reasonably estimate the amount of damages, Bigelow v. RKO Radio Pictures, 327 U.S. 251, 264-65 , 66 S.Ct. 574, 579-80 , 90 L.Ed. 652 (1946), a higher quantum of proof is required to establish “injury in fact.” Flintkote supra; see Story Parchment Co. v. Paterson, 282 U.S. 555, 562 , 51 S.Ct. 248, 250 , 75 L.Ed. 544 (1931). Plaintiff is required to establish with “reasonable probability” the existence of the latter. Flintkote, supra. . In Midwest Paper, 596 F.2d at 584 , the court listed complex pricing variables that exist when only one level of distribution is involved, including cost of production, marketing strategy, elasticity of demand, and price of comparable items. . Because plaintiffs have not amended their complaints to allege a vertical conspiracy, there is a question whether this issue should be held ripe for decision. See Nickert v. Puget Sound Tug & Barge Co., 480 F.2d 1039 (9th Cir. 1973). Because the district court has indicated its intent to allow an amendment subject to the disputed condition, and because there is little possibility of an intervening event rendering decision unnecessary, cf. id. (certified question might be rendered moot by jury verdict), we exercise our discretion to decide the joinder issue in the interest of judicial economy. In so doing, however, we expressly leave unresolved issues involving the viability of vertical conspiracy claims in situations arguably put to rest by Illinois Brick . Nor do we express an opinion on any alleged distinctions between the “control” exception alluded to in Illinois Brick, 431 U.S. at 736 n. 16, 97 S.Ct. at 2070 n. 16 and conspiracy claims based on vertical coercion, Hanson v. Shell Oil Co., 541 F.2d 1352, 1356 (9th Cir. 1976), cert. denied, 429 U.S. 1074 , 97 S.Ct. 813 , 50 L.Ed .2d 792 (1977). . At footnote 16, the Court in Illinois Brick implied that an exception to its rule barring indirect purchaser claims might exist “where the direct purchaser is owned or controlled by its customer.” . Rule 23(b)(3), Fed.R.Civ.P. requires that common questions of law or fact predominate over any individual question. . In each instance, plaintiffs allege that defendants coerced their retail dealers into charging fixed prices. . In Chicken Delight the trial court initially certified a class with respect to claims of illegal “tying.” When the time came to send class notices, plaintiffs sought to include in their description of the case a pricing issue relating to defendant’s alleged coercive, extracontractual control over its franchisees’ retail prices. We found the latter issue inappropriate for class treatment because, unlike the tying claim, it could not be tried upon the common evidence of the standard franchise contracts. We issued a writ of mandamus to correct the error.