420 Mass. 599 (1995)
Supreme Judicial Court of Massachusetts, Suffolk.
March 7, 1995.
June 19, 1995.
Present: LIACOS, C.J., ABRAMS, O'CONNOR, & GREANEY, JJ.
 E. Michael Sloman (Michael B. Meyer with him) for the plaintiffs.
Eric A. Smith, Assistant Attorney General, for the Commissioner of Insurance.
The decision of the Commissioner of Insurance (commissioner) establishing private passenger motor vehicle insurance rates for 1995 resulted in an over-all rate reduction of 6.1%. The Automobile Insurers Bureau of Massachusetts (AIB) and ten of its member companies filed a complaint for judicial review under G.L.c. 175, § 113B (1992 ed.), of the commissioner's decision in the Supreme Judicial Court for Suffolk County. On a joint motion of the parties, a single justice reserved and reported the case without decision for determination by the full court. We affirm the commissioner's decision.
1. The proceedings. The commissioner determined that competition was insufficient to assure that private passenger automobile insurance rates would not be excessive. See G.L.c. 175E, § 5 (1992 ed.). The commissioner therefore invoked the procedures of G.L.c. 175, § 113B, to fix and establish automobile insurance rates for calendar year 1995. Interested parties were invited to participate in the proceedings.  Four parties formally intervened: the AIB; the State Rating Bureau, pursuant to G.L.c. 26, § 8E (1992 ed.); the Attorney General, pursuant to G.L.c. 12, § 11F (1992 ed.); and the Professional Independent Insurance Agents of Massachusetts (PIIAM), a trade association.
All but four issues were resolved by stipulations accepted by the commissioner. On December 15, 1994, the commissioner issued a decision resolving the four contested issues: (1) the effect of recent law changes, particularly the 1994 mandatory seat belt law, on loss pure premiums; (2) retention of the competition adjustment factor (CAF); (3) the appropriate methodology for calculating loss development factors; and (4) the appropriate methodology for setting increased limit factors. The plaintiffs do not appeal from the methodology for calculating loss development factors or increased limit factors. The commissioner concluded that the seat belt law would produce savings to the industry and therefore reduced the bodily injury portion of rates by 4.9%, which represents an over-all rate decrease of approximately 2.2%. The commissioner concluded that other legal and regulatory changes did not warrant any rate adjustment. She continued to apply the CAF to reduce certain company expenses. Application of the CAF reduced over-all rates by approximately 1.6%. On appeal, the plaintiffs raise three issues: (1) the validity of the commissioner's rate change for the seat belt law; (2) whether rates should have been changed due to other law changes; and (3) the confiscatory effect of the CAF.
2. Seat belt law adjustment. The commissioner reduced loss pure premiums for bodily injury coverage to reflect anticipated  savings from the 1994 seat belt law, St. 1993, c. 387, which mandated the use of seat belts as of February 1, 1994. The plaintiffs argue that this reduction was not authorized, that the model used to establish the amount of the reduction was faulty, and that the inputs used in applying this model were improper.
a. Authority to reduce rates. The seat belt law provides that "[t]he commissioner of insurance shall mandate a minimum five percent reduction in bodily injury premiums if the observed seat belt use rate among all occupants equals or exceeds fifty percent one year after this law has been in effect." St. 1993, c. 387, § 7. The seat belt law had not been in effect for one year at the time the commissioner made the rate reduction. It thus was impossible to observe seat belt use one year after the law took effect. The plaintiffs assert that the commissioner erred because she was not authorized to reduce insurance rates to reflect the effect of the law. We do not agree.
The commissioner had the authority to effect the rate reduction under her broad rate setting powers. The commissioner has the statutory authority, and duty, under G.L.c. 175, § 113B, to establish insurance rates that are adequate, just, reasonable, and nondiscriminatory. In so doing, she can, and indeed must, consider all changes in conditions which affect rates, including changes in the law. See, e.g., Massachusetts Auto. Rating & Accident Prevention Bureau v. Commissioner of Ins., 389 Mass. 824, 842-844 (1983)  (adjustment for increased sanctions for driving under the influence); Massachusetts Auto. Rating & Accident Prevention Bureau v. Commissioner of Ins., 384 Mass. 333, 338-339 (1981) (adjustment for merit rating); Massachusetts Auto. Rating & Accident Prevention Bureau v. Commissioner of Ins., 381 Mass. 592, 599-600 (1980) (adjustment for raised drinking age).
The rate-reduction language in the 1994 seat belt law does not limit the commissioner's ability to consider seat belt use in setting rates under her powers pursuant to G.L.c. 175, § 113B. It simply sets a minimum reduction (i.e., five per cent) in the event of a certain occurrence (i.e., "the observed safety belt use rate among all occupants equals or exceeds fifty percent one year after" the law takes effect). St. 1993, c. 387, § 7. "Specific authority to act in a particular respect does not bar other action that is consistent under general statutory authority." Massachusetts Elec. Co. v. Department of Pub. Utils., 419 Mass. 239, 246 (1994). See Grocery Mfrs. of Am., Inc. v. Department of Pub. Health, 379 Mass. 70, 76 (1979). The reduction for 1995 is consistent with a further reduction for 1996 if observed seat belt use equals or exceeds fifty per cent after February 1, 1995.
b. The model. The plaintiffs also contest the model by which the commissioner determined the amount of the rate reduction. The model used by the commissioner in determining the rate reduction was previously used to take account of the effects of the 1986 seat belt law in determining insurance  rates for 1986, 1987, and 1988. The model seeks to establish the effect of changes of seat belt usage, as a result of the law, on the loss experience for bodily injuries, and, in turn, on insurance costs. It compares prelaw and postlaw seat belt usage, multiplied by the efficacy of seat belts in reducing four major classes of injury (fatal, severe, moderate and minor). These amounts are then multiplied by the distribution of injury costs for vehicle occupants for each category of injury. The resulting amounts are applied to reduce loss pure premiums.
In reviewing the commissioner's decision, under G.L.c. 175, § 113B, "our inquiry is limited to `whether the rates have reasonable support in evidence.'" Aetna Casualty & Sur. Co. v. Commissioner of Ins., 408 Mass. 363, 378 (1990), quoting Massachusetts Auto. Rating & Accident Prevention Bureau, 384 Mass. at 337. "[T]his standard is indistinguishable from the substantial evidence standard." Automobile Insurers Bureau of Mass. v. Commissioner of Ins., 415 Mass. 455, 457 (1993), quoting Aetna Casualty & Sur. Co., supra at 378 n. 14. "We will not perform a de novo weighing of the evidence, and we give due weight to the commissioner's experience, technical competence, specialized knowledge, and discretionary authority" (citations omitted). Aetna Casualty & Sur. Co., supra at 378. "If there is substantial evidence supporting the commissioner's decision, we will not substitute our own judgment for hers." Automobile Insurers Bureau of Mass., supra at 457-458. See Aetna Casualty & Sur. Co., supra at 378-379, and cases cited (deference applies especially to commissioner's choice of methodology).
There was substantial evidence supporting the commissioner's decision. It was reasonable for the commissioner to conclude that the clearly evidenced increase in seat belt use would reduce losses. See Attorney Gen. v. Commissioner of Ins., 370 Mass. 791, 819, 820-821 (1976). To determine the amount by which to reduce rates, the commissioner used an  existing, accepted model. The plaintiffs did not meet their burden of showing that the commissioner's choice of methodology was erroneous. See Massachusetts Bonding & Ins. Co. v. Commissioner of Ins., 329 Mass. 265, 280 (1952) (party challenging methodology has burden of establishing that commissioner's order is erroneous); Aetna Casualty & Sur. Co., supra at 373 (can continue to use previously used methodologies where party does not provide adequate reason not to).
The plaintiffs argue that the model should have been rejected because it proved to be erroneous in its prior application. They argue that, contrary to the model's prediction, the 1986 seat belt law did not reduce insurance costs and that, if it did, the model overstated the effect of the law. The commissioner found these arguments unpersuasive. Instead, she accepted the evidence of a relative deceleration in loss pure premiums in 1986 and evidence that the seat belt law was a cause of this drop.
The plaintiffs argue that there is no information on which to draw a direct correlation between the loss pure premium drops and the use of seat belts. The existing data reflected the result of all factors that influence loss pure premiums in either direction. Although the effect of increased seat belt use could not be isolated, there was evidence that after the 1986 law took effect, the number of motor vehicle occupant injuries declined by 20% while seat belt use increased from 20% to 35%-37% of motor vehicle occupants. After the 1986 law was repealed, seat belt use declined to 24% and the number of motor vehicle occupant injuries increased 11%.
It was reasonable for the commissioner to conclude that, because bodily injury loss pure premiums ultimately derive from injuries, the correlation between increased seat belt use and reduced loss pure premiums was shown. The commissioner should not decline to consider this correlation simply because it is difficult to quantify. See Massachusetts Auto. Rating & Accident Prevention Bureau v. Commissioner of Ins., 401 Mass. 282, 301 (1987) ("The industry argues that  there was not sufficient basis for an exact quantification of the excess, so the commissioner should not have made the reduction. Apparently, the industry believes that when an area of excess is difficult to quantify, the presumption should be that the excess will be born by the policyholders until it can be precisely measured. We cannot agree"). While the data were insufficient to prove that the degree of reduced loss pure premiums was accurately predicted by the model, the commissioner's decision was justified by the logic of the model, the available data, and the absence of evidence to the contrary. See Aetna Casualty & Sur. Co., supra at 375 ("It lies within the discretion of the commissioner to determine the weight to be given to certain evidence supporting or detracting from reliance on particular methodologies or data").
c. The inputs. The plaintiffs next dispute the use of three pieces of data by the commissioner in applying the model. The commissioner's use of these data is supported by substantial evidence.
First, the plaintiffs dispute the level of prelaw seat belt use applied by the commissioner. The commissioner used the 1993 seat belt use rate of 34.5%. The plaintiffs suggested a use rate of 39%, based on an alleged trend of increasing seat belt use over the five years prior to the law. The commissioner's use of the 1993 level, as determined by a survey by Boston University, was supported by substantial evidence. In deciding on this rate, the commissioner looked at the rates of seat belt use in 1993 and 1994. See id. at 379 (evidence supported commissioner's use of two years of historical data, rather than the six recommended by the AIB). Contrary to the plaintiffs' assertions, the data do not show a steady increase in seat belt use during the years prior to the law's effect, but rather, shows a fluctuation, with the level dropping slightly and then remaining essentially steady during the three years immediately preceding the law.
 Second, the plaintiffs dispute the accuracy of the commissioner's estimates of the effectiveness of seat belts in reducing loss costs. The commissioner used the same estimates used in testing the effect of the 1986 law. The plaintiffs argue that the estimates were erroneous because they did not account for improvements in vehicle safety which may lower the significance of seat belt use. The commissioner correctly rejected this argument because it was not supported by any quantitative evidence and because the AIB did not provide alternative estimates of effectiveness. Further, the limited data available supported the continued use of the old estimates.
Third, the plaintiffs argue that the model's distribution of injury types is outdated as a result of the trend to less severe injuries that are less affected by seat belt use. The AIB did not, however, quantify the effect of this trend or provide an alternative distribution of injury types. Further, the commissioner had before her evidence that changing the distribution weightings did not materially affect the over-all outcome of the model. Thus, the commissioner's decision was warranted.
3. Other law changes. The plaintiffs argue that the commissioner should have increased premiums to account for two law changes: a revision in regulations governing the referral shop system and the deregulation of the towing industry.  They argue that, in deciding that these changes did not warrant rate adjustments, the commissioner impermissibly placed a higher burden of proof on the AIB to show that a rate increase would be proper than it required for a decrease due to the seat belt law. See Medical Malpractice Joint Underwriting Ass'n of Mass. v. Commissioner of Ins., 395 Mass. 43, 47 (1985). The commissioner's determination that these changes did not warrant a rate increase was warranted.
First, regulations governing the referral shop system were changed. Under this system, insurers enter into agreements with repair shops to act as referral shops. If an insured has a vehicle repaired at a referral shop, the insurer guarantees the cost and quality of the repairs. The insured need not go to a referral shop, but, if the insured has his vehicle repaired elsewhere, the insurer does not guarantee price or quality. Prior to the change, insurers were required to provide insureds with a list of at least five referral shops in a geographically convenient area. They also had to disclose that insureds could have their vehicles repaired at a nonreferral shop, but in that case, the insurer would not guarantee the quality of the repair and the insured could incur additional expense.
On May 1, 1994, a regulatory change was made, codified at 211 Code Mass. Regs. § 123.00, requiring insurers to provide insureds with a list of all registered body shops in the county where the insured resides or, on request, another county. Insurers can highlight or underline referral shops but must give the same disclosure about using nonreferral shops. The plaintiffs argue that this change will increase insurance costs because it will reduce the use of referral shops and therefore reduce the ability of insurers to negotiate reduced prices with such shops.
The commissioner properly concluded that an increase in rates was not warranted by this regulatory change. There was no evidence of a decrease or expected decrease in the use of referral shops or number of referral shops. The incentive for insureds to use referral shops remains unchanged. While the AIB did present evidence of an increase in supplemental  payments since May, 1994, it did not show the magnitude of such payments or the reason for them. There was no evidence linking the increase in such payments to the regulatory change. In short, there was no evidence supporting AIB's contention. The commissioner's decision was therefore not erroneous.
Second, police-ordered towing charges were deregulated. As of January 1, 1995, the Federal government has preempted the ability of the States to regulate rates for towing motor vehicles. 49 U.S.C. § 11501(h). Prior to this time, the Department of Public Utilities (department) had established a maximum charge for all police-ordered towing. See G.L.c. 159B, § 6B (1992 ed.); 220 Code Mass. Regs. § 272.00 (1993). The plaintiffs argue that the costs of police-ordered towing will rise and insurers will therefore incur higher claim costs. In support of this, they point to a petition to the department by the State Towing Association (STA) stating that the regulated tow rate produced a revenue deficiency of $34.61 per tow. The commissioner determined that the AIB's unqualified adoption of these unsupported data did not provide sufficient support for an adjustment to premiums. Because the actual effect of the deregulation was speculative, the commissioner deferred consideration.
There was no error. The AIB produced no evidence other than testimony about the contents of the STA's petition. It admitted that it would not have supported the petition before the department absent evidence that the proposed figures were correct and that the towers needed more revenue. Where a party admits that it does not know the basis for its  evidence, the commissioner's rejection of that evidence as speculative is amply supported. See Massachusetts Auto. Rating & Accident Prevention Bureau, 389 Mass. at 845.
4. Confiscatory effect of the CAF. The plaintiffs argue that the CAF is confiscatory. The CAF, as determined by the commissioner for the 1995 rate year, reduces the allowance for certain company expenses by fifteen per cent in order to account for a wide and unexplained variation in reported expenses and to exert a downward pressure on expenses which would be present in a competitive market. See Automobile Insurers Bureau of Mass., 415 Mass. 455, 463 (1993). The CAF has been determined by the same methodology since 1979. We have upheld the CAF on three occasions. Id. at 463-464. Massachusetts Auto. Rating & Accident Prevention Bureau, 384 Mass. at 337-338. Massachusetts Auto. Rating & Accident Prevention Bureau, 381 Mass. at 602-603. "We reasoned that `[w]here a particular item of cost varies widely from company to company and the Commissioner is fixing industry-wide rates, [she] must be allowed considerable discretion to exclude the highest costs from consideration, even though [she] cannot prove how they could be reduced.'" Automobile Insurers Bureau of Mass., supra at 463-464, quoting Massachusetts Auto. Rating & Accident Prevention Bureau, 384 Mass. at 338, quoting Massachusetts Auto. Rating & Accident Prevention Bureau, 381 Mass. at 603. These cases only addressed the commissioner's statutory authority to impose the CAF and its support in the record. They did not address the issue raised here, whether the CAF is unconstitutionally confiscatory.
"The plaintiffs are entitled to an independent review of facts and law on the constitutional issue. However ... our scrutiny should encompass only the ultimate findings and conclusions of the ratemaker." Massachusetts Auto. Rating  & Accident Prevention Bureau, 384 Mass. at 346. See Massachusetts Auto. Rating & Accident Prevention Bureau, 389 Mass. at 846. "Consistent with traditional principles of administrative law, the Commissioner's decisions will be accorded the `presumptive validity' given to actions taken by an agency." Id.
"[T]he plaintiffs bear the burden of demonstrating that the rates fixed deprive them of the opportunity to achieve a fair return and that these insufficient returns are directly attributable to the inadequacy of the rates set and not the result of other factors." Id. See Massachusetts Auto. Rating & Accident Prevention Bureau, 384 Mass. at 346-347. "This court will not interfere with the exercise of the ratemaking power unless confiscation is clearly established on the record before us." Boston Edison Co. v. Department of Pub. Utils., 375 Mass. 1, 10-11, cert. denied, 439 U.S. 921 (1978). See St. Joseph Stock Yards Co. v. United States, 298 U.S. 38, 53 (1936). The plaintiffs did not satisfy their burden of proving that the rates are unconstitutionally confiscatory.
The plaintiffs assert two arguments. First, they argue that the CAF is inconsistent with the model the commissioner employs to fix the underwriting profit component of the rates. The model fixes underwriting profits by setting the expected value of premiums equal to the expected value of losses, expenses and taxes and then factors in a provision for compensation for risk. The plaintiffs argue that the CAF sets the expense portion of premiums at a value less than the expected value of expenses the insurers will incur. They argue that, therefore, the excess of actual expenses over the expense portion of premiums, as adjusted by the CAF, will eat into their profit margin, thus denying them the opportunity to earn a fair return. Their argument ignores the purpose of the CAF. The commissioner determined that the CAF should be employed because expenses of certain companies were unreasonable. Insurers have the opportunity to increase their returns by reducing expenses.
Second, the plaintiffs argue that the CAF double counts costs of waste and inefficiency. They argue that these costs  are already removed by operation of the profit model. By subtracting such costs again, in applying the CAF, the plaintiffs argue, they are denied the opportunity to earn a fair return. This argument is not supported in the record.
Even if the plaintiffs' assertions were correct, they still would not have satisfied their burden of proof. They show neither that the over-all rates deprive them of the opportunity to achieve a fair return nor that such insufficient returns, if they do exist, are solely attributable to the inadequacy of the rates. See Massachusetts Auto. Rating & Accident Prevention Bureau, 389 Mass. at 846. They only allege that the methodology prevents them from receiving the target underwriting profit and that certain expenses are double counted. This methodological attack is irrelevant; all that matters are the actual, over-all rates. The plaintiffs do not address these rates. Further, even if the plaintiffs are unable to achieve the  target underwriting profit, they have not shown that the lesser return they can receive is not a fair return. The plaintiffs also did not show that any deficiency in their returns is solely the result of the rate-setting and not of other factors, such as the waste and inefficiency for which the CAF is applied.
Finally, the plaintiffs have not shown that the Massachusetts automobile insurance industry is an efficient industry. "[T]he protection against confiscatory rates applies only to those who conduct their operations in a reasonably efficient manner." Zussman v. Rent Control Bd. of Brookline, 371 Mass. 632, 639 (1976). "Rates ... made on the basis of the combined experience of all companies doing business in the Commonwealth ... are not confiscatory merely because aggregate collections are not sufficient to yield a reasonable profit to all companies unless it is shown that the business is so well and economically organized and carried on as to entitle the plaintiffs, as a matter of constitutional right, to have premiums amounting in the aggregate to enough to yield a reasonable return to all companies." Massachusetts Auto. Rating & Accident Prevention Bureau, 381 Mass. at 597. See Greenleaf Finance Co. v. Small Loans Regulatory Bd., 377 Mass. 282, 301-302 (1979), quoting Aetna Ins. Co. v. Hyde, 275 U.S. 440, 448 (1928). See also New England Tel. & Tel. Co. v. Department of Pub. Utils., 360 Mass. 443, 494 (1971), quoting New England Tel. & Tel. Co. v. New Hampshire, 95 N.H. 353, 363 (1949) ("mere actuality of expense  does not establish its `reasonableness ... propriety or necessity'").
5. Disposition. We remand this case to the county court for entry of a judgment affirming the decision of the commissioner fixing and establishing private passenger automobile insurance rates for 1995.
 Ten insurance companies duly authorized to write motor vehicle insurance in Massachusetts.
 The plaintiffs assert that 1995 insurance rates are 6.1% lower than the rates for 1994. The commissioner does not dispute this. The components of the commissioner's decision at issue in this appeal account for a rate reduction of approximately 3.8%.
 "The Automobile Insurers Bureau of Massachusetts is an unincorporated voluntary association of insurance companies licensed to write automobile insurance in Massachusetts." Automobile Insurers Bureau of Mass. v. Commissioner of Ins., 415 Mass. 455, 456 n. 1 (1993).
 The case was reserved and reported on: (1) the complaint for judicial review and the answer of the commissioner; (2) the commissioner's "Opinion, Findings and Decision on 1995 Automobile Insurance Rates"; and (3) the commissioner's certification of the portion of the record of the 1995 rate proceedings which pertained to the matters on appeal, including prior automobile insurance rate decisions and other material of which the commissioner took official notice.
 The hearings were conducted under five separate administrative dockets: territories, docket no. R94-2; cost containment and fraudulent claims, docket no. R94-3; underwriting profits, docket no. R94-4; main rate hearing, docket no. R94-5; and safe driver insurance plan, docket no. 94-11.
 The PIIAM intervened in the main rate hearing. The other interveners intervened in all the hearings.
 The plaintiffs, in their brief, waived the claim of error in these components of the commissioner's decision.
 "Loss pure premiums" are the portion of premiums allocated to losses or claims. See Massachusetts Auto. Rating & Accident Prevention Bureau v. Commissioner of Ins., 401 Mass. 282, 293 (1987); Massachusetts Auto. Rating & Accident Prevention Bureau v. Commissioner of Ins., 384 Mass. 333, 345 (1981); Massachusetts Bonding & Ins. Co. v. Commissioner of Ins., 329 Mass. 265, 267 (1952).
 This statute inserted a new section, § 13A, in G.L.c. 90, which requires operators and passengers of most motor vehicles to wear seat belts, subject to a fine of twenty-five dollars for noncompliance. St. 1993, c. 387, § 1. The section is to be enforced "only when an operator of a motor vehicle has been stopped for a violation of the motor vehicle laws or some other offense." Id.
 This statute also provides that, "[i]f at any time the safety belt use rate in the commonwealth exceeds the national average, additional reductions in bodily injury premiums shall take effect." St. 1993, c. 387, § 7. The commissioner did not base the rate reduction on this provision.
 The commissioner's rate reduction furthers the seat belt law's intent of reducing rates to reflect seat belt usage. Not only does the law provide for the aforementioned minimum rate reduction, but it also provides that "[a]nnual safety belt survey results shall be a criterion in all future regulatory actions regarding bodily injury premiums." St. 1993, c. 387, § 7. In reducing the rates, the commissioner considered safety belt survey results. Disallowing the reduction, as suggested by the plaintiffs, would conflict with both the purpose of this law and the purpose of G.L.c. 175, § 113B, to set rates that are "just" in light of known factors. See Hadley v. Amherst, 372 Mass. 46, 51 (1977) ("a statute is to be interpreted in harmony with prior enactments to give rise to a consistent body of law").
 This law was in effect for only ten months as it was repealed by voter referendum.
 The factor does not include losses attributable to injury to pedestrians.
 The validity of this survey was not contested.
 The survey showed that seat belt use was 27% in December, 1986, dropped to 26% in December, 1987, increased gradually to 36% in May, 1991, dropped to 34% by June, 1992, and remained at that level until June, 1993.
 The Boston University survey showed a 20% reduction in fatalities as a result of increased seat belt use. This is the same as the estimate used by the model. We note, however, that the survey recognized that other factors may have contributed to the reduction.
 The trend to less severe injuries may be the result of increased seat belt use.
 The plaintiffs point out that many insurance claims are fraudulent or inflated, see Automobile Insurers Bureau of Mass. v. Commissioner of Ins., 415 Mass. 455, 461 (1993), and therefore unaffected by the use of seat belts. They do not, however, show that such claims have become more prevalent, thus making the earlier model outdated. Again, they provide no quantitative evidence or alternative.
 "A supplemental payment [occurs] after a claimant disputes the initial appraisal as underestimating the actual cost of repairs.... This may occur when, for instance, damage is discovered during the repair process which was not visible at the time of the initial appraisal." Massachusetts Auto Body Ass'n v. Commissioner of Ins., 409 Mass. 770, 776 (1991).
 "Police-ordered towing charges," in this context, refers to the costs of towing following collisions.
 Due to the change in Federal law, the department never considered the petition.
 The adjustment was performed by multiplying by a factor of 0.85 three components of company expenses: acquisition expenses other than commissions; general expenses; and taxes, licenses, and fees. It does not apply to loss adjustment expense, investment expense, or commission expense.
 "[I]t is not theory but the impact of the rate order which counts. If the total effect of the rate order cannot be said to be unreasonable, judicial inquiry ... is at an end. The fact that the method employed to reach that result may contain infirmities is not then important." Duquesne Light Co. v. Barasch, 488 U.S. 299, 310 (1989), quoting Federal Power Comm'n v. Hope Natural Gas Co., 320 U.S. 591, 602 (1944). "The economic judgments required in rate proceedings are often hopelessly complex and do not admit of a single correct result. The Constitution is not designed to arbitrate these economic niceties. errors to the detriment of one party may well be canceled out by countervailing errors or allowances in another part of the rate proceeding. The Constitution protects the [companies] from the net effect of the rate order on [their] property. Inconsistencies in one aspect of the methodology have no constitutional effect on the [companies'] property if they are compensated by countervailing factors in some other respect." Duquesne Light Co., supra at 314. See Fitchburg Gas & Elec. Light Co. v. Department of Pub. Utils., 371 Mass. 881, 884 n. 5 (1977) ("the Massachusetts Constitution does not require use of any specific economic theory or method of return computation ... except to the extent that improper [and insupportable] exclusion of an investment from valuation of a rate base denies a return on that investment"); Boston Gas Co. v. Department of Pub. Utils., 367 Mass. 92, 98 (1975) ("If an item were improperly excluded from the rate base, the rates set pursuant to that improper reduction of the rate base would deny a return on that item and, to that extent, could be confiscatory and unlawful.... [Our] law[, however,] requires no particular theory or method to be used in determining a rate base, provided the resulting rates are not confiscatory"). The plaintiffs argue that they should prevail because the commissioner has not shown such countervailing factors. The burden, however, is on the plaintiffs to show that no such factors exist.
 The target underwriting return was stipulated in the rate-setting proceedings. The plaintiffs have not indicated its relationship to the minimal constitutional rate of return.
 The commissioner found that the industry was not efficient. The statutory premise of the rate proceeding, under G.L.c. 175, § 113B, is a determination, under G.L.c. 175E, § 5, that the market is not sufficiently competitive to assure that rates are not excessive. See Metropolitan Property & Liab. Ins. Co. v. Commissioner of Ins., 382 Mass. 514, 522-523 (1981).