13 F. Supp. 2d 1308 | N.D. Fla. | 1998
PHILLIPS & JORDAN, INC., Plaintiff,
v.
Ben G. WATTS, in his official capacity as Secretary of the Florida Department of Transportation, Defendant.
United States District Court, N.D. Florida, Tallahassee Division.
*1309 W. Douglas Hall, Carlton Fields Ward Etc., Tallahassee, FL, Donald Edward Hemke, Carlton Fields Ward Etc., Tampa, FL, for Plaintiff.
Roger Blain Wood, Department of Transportation, Tallahassee, FL, for Defendant.
ORDER GRANTING PLAINTIFF'S MOTION FOR SUMMARY JUDGMENT
STAFFORD, Senior District Judge.
In this case, Phillips & Jordan, Inc. ("P & J"), challenges an affirmative action program administered by the Florida Department of Transportation ("FDOT"). Specifically, P & J contends that FDOT's practice of setting aside certain highway maintenance contracts for black and Hispanic-owned businesses violates the Equal Protection Clause of the Fourteenth Amendment to the United States Constitution. The parties have stipulated that P & J a non-minority business has been excluded in the past, and may be excluded in the future, from competing for certain highway maintenance contracts set aside for business enterprises owned by Hispanic and African American individuals.
Before the court at this time is P & J's motion for summary judgment (doc. 46). The defendant, Ben G. Watts ("Watts"), in his official capacity as Secretary of FDOT, has responded (doc. 56) in opposition to the motion; the court has heard the oral arguments of counsel; and the parties have been advised (doc. 60) that the motion would be taken under advisement as of a date certain.
I.
Under Florida law, upon a showing of past and/or continuing discrimination in statefunded highway projects, FDOT is authorized to implement programs designed to remedy disparities based upon race, national origin, or gender. Fla. Stat. § 339.0805(1)(b). FDOT may establish annual goals for expending a percentage of state-administered highway funds with small businesses owned and controlled by socially and economically disadvantaged individuals and to that end may set aside contracts for competition only among disadvantaged business enterprises. Id. FDOT's authority to utilize goals and set-asides is limited, however, to those situations where "significant disparity" has been documented at least in part through the findings of a disparity study conducted or updated by FDOT or its designee at a minimum of every five years. Id. A "significant disparity" means "a disparity index (the ratio of the percentage utilization to the percentage availability times 100) below 80." Fla. Admin. Code r. 14-78.004(3)(c).
In 1991, pursuant to section 339.0805, FDOT hired MGT of America, Inc. ("MGT"), to conduct a disparity study, one *1310 purpose of which was to document the existence of any past and/or continuing discrimination involving contracts for state-funded road maintenance projects. MGT collected both statistical data regarding the availability and utilization of minority-owned business enterprises for FDOT highway projects as well as anecdotal evidence regarding the perceptions and experiences of both minority and non-minority businesses in bidding and working on such projects. For purposes of data collection, MGT established a two-year study period covering fiscal years 1989/90 and 1990/91. The relevant market area was defined as all counties within the State of Florida plus all counties outside the State of Florida whose firms were awarded contract dollars totaling 0.5% or more of overall contract dollars over the study period.
MGT's estimate of total firms available to perform road maintenance work was based on the Census Bureau's County Business Patterns, an annual publication that reports the total number of business establishments by state, by county, and by standard industrial classification. MGT's estimate of available black and Hispanic-owned businesses in the relevant market area was based on the Census Bureau's 1982 and 1987 Surveys of Minority Owned Business Enterprises ("SMOBE"). Produced every five years, the SMOBE identifies numbers of minority-owned business enterprises ("MBEs") by county, ethnic classification, gender, and standard industrial classification.
Business establishments are assigned standard industrial classification ("SIC") codes based on business activity. Two, three, and four-digit SIC codes are used to identify related business groups. As the codes go from two to three to four digits, the groups become progressively more specific. For example, SIC Code 07 represents the major group, "Agricultural Services." SIC Code 078 represents the sub-group, "Landscaping and Horticulture Services." SIC Code 0782, "Lawn and Garden Services," represents a sub-set of sub-group 078.
MGT estimated available road maintenance firms by adding census figures from the following seven SIC codes:
078 Landscaping and Horticulture Services
0782 Lawn and Garden Services
0783 Ornamental Shrub and Tree Services
47 Transportation Services
49 Electric, Gas and Sanitary Services
16 Heavy Construction
17 Special Trade Construction.
MGT did not identify what different subgroups were encompassed within the selected two and three-digit codes. It also did not explain why it selected a combination of two, three, and four-digit codes or how it determined that all businesses included in the codes particularly the two and three-digit codeswere "available" to bid on road maintenance contracts.
Using census figures, MGT determined that, in calendar year 1989, there were 61,098 firms in the relevant market area that listed themselves as being in businesses classified in one or more of MGT's seven selected SIC groups.[1] Of those 61,098 firms, 2,605 were owned by blacks and 5,015 were owned by Hispanics. For the calendar year 1990, the census revealed a total of 65,665 firms in the seven SIC groups in the relevant market area. Blacks and Hispanics respectively owned 2,838 and 5,517 of those 65,665 firms.
MGT assumed that a much higher percentage of local, or Florida-based firms, would be ready, willing, and able to bid on FDOT projects than would firms from counties outside of Florida. To account for this assumed difference between in and out-of-state firms, MGT weighted the number of Florida-based and non-Florida-based firms by their respective proportion of the total firms that were awarded FDOT contracts during the study period. The weighted number of firms in Florida and in counties outside Florida were totaled, and the percentage for each minority classification was calculated to determine the weighted availability for each year. MGT thus determined that black-owned firms accounted for 4.05% of the total number of weighted available maintenance firms for fiscal year ("FY") 1989/90 and 4.10% of the *1311 total in FY 1990/91. Hispanic-owned firms accounted for 8.90% of the total number of weighted available maintenance firms for FY 1989/90 and 9.08% of the total in FY 1990/91.
The operations of FDOT are organized into eight districts, including a turnpike district, each headed by a district secretary. For the time period covered by this study, district offices were authorized to award construction and maintenance contracts up to a limit of $250,000. Contracts for projects in excess of $250,000 were awarded by the Central Office.
To calculate utilization rates, MGT collected data regarding the contract dollars awarded to minority firms by FDOT's district and central offices during the two fiscal years selected as the study period. During FY 1989/90, FDOT's central office awarded two maintenance contracts to firms in the relevant market area. Neither of the two centrally-let contracts was awarded to a black or Hispanic-owned business. During FY 1990/91, no maintenance contracts were let by the central office. The total dollar value of centrally-let maintenance contracts during the study period was $1,068,916.00, all of which was awarded to firms owned by white men.
During the same time period, the eight district offices awarded a total of 521 maintenance contracts for a total of $42,772,787.00. These contracts ranged in price from a low of $2,184.50 to a high of $623,844.00. Of the district-let contracts, 479 were awarded to prime contractors and 42 were awarded to subcontractors. The 42 contracts awarded to subcontractors accounted for less than 1% of all contract dollars awarded. According to the manager of the FDOT's Minority Programs Office, Ruth Dillard, the vast majority of road maintenance contracts do not lend themselves to subcontracts. The prime contractors, that is, do most, if not all, of the work.
Nine of the district-let contracts awarded to prime contractors six in FY 1989/90 ($810,704) and three in FY 1990/91 ($358,898)were awarded to black-owned businesses for a total dollar amount of $1,169,602.00. Eleven of the contracts awarded to prime contractors five in FY 1989/90 ($366,132) and six in FY 1990/91 ($970,273) were awarded to Hispanic-owned businesses for a sum of $1,336,405. No district-let contracts were awarded to either black or Hispanic subcontractors during the second year of the study. During the first year of the study, Hispanic-owned firms were awarded $54,257 in subcontract dollars while black-owned firms were awarded no subcontract dollars.
Converting the utilization data to percentages, MGT determined that FDOT district offices awarded black-owned firms 4.02% and 1.59% of total maintenance contract dollars in FY 1989/90 and FY 1990/91 respectively. To Hispanic-owned firms, including prime contractors and subcontractors, FDOT district offices awarded 1.82% and 4.29% of total maintenance contract dollars in FY 1989/90 and FY 1990/91 respectively.
After compiling the utilization and availability data, MGT calculated a disparity indexdefined as the ratio of the percentage utilization to the percentage availability times 100 for each group and year. A disparity index of 100 indicates parity. A disparity index under 100 indicates under-utilization. A disparity index over 100 indicates over-utilization. A disparity index below 80, which indicates a significant level of disparity, is generally accepted as evidence of adverse impact. In this case, the disparity indices for black-owned firms were 94.32 for FY 1989/90 and 38.78 for FY 1990/91. For Hispanic-owned firms, the disparity indices were 19.33 for FY 1989/90 and 47.25 for FY 1990/91.
Because MGT did not review actual bids on FDOT maintenance contracts, its study did not reveal (1) how many black and Hispanic-owned firms in fact submitted bids for FDOT maintenance contracts; (2) how many, if any, black or Hispanic-owned firms unsuccessfully submitted bids for FDOT maintenance contracts; (3) how many, if any, black or Hispanic-owned firms submitted low bids that were rejected in favor of higher bids; and (4) how many, if any, black or Hispanic-owned firms submitted bids either successfully or unsuccessfully in each FDOT district. Furthermore, having done no district-by-district analysis of either availability or utilization of minority firms, MGT did not *1312 include, as part of its study, disparity indices for individual districts.
In response to MGT's disparity study, FDOT implemented its minority business program for state-funded road and bridge maintenance projects. Fla. Admin. Code r. 14-78.004. Under this program, FDOT is authorized to set aside contracts for competition solely among black and Hispanic-owned businesses. The decision as to which maintenance contracts are to be set aside is made by the FDOT district office that lets the contract. No attempt is made by FDOT's central office or by its Minority Programs Office to control, oversee, or even track the set-aside decisions made by the district offices.
After this lawsuit was filed, at the request of FDOT, MGT recompiled the availability data using the 1987 and 1992 census reports. Minority businesses from fifteen, rather than seven, SIC codes were included in the new compilations. MGT did not explain why a change was made in the selected codes. The fifteen SIC codes used for the new compilations were:
078 Landscape & Horticulture 0782 Lawn & Garden Services 0783 Ornamental Shrub and Tree Services 4785 Fixed Facilities Services 4959 Sanitary ServicesSweeping Roads 16 Heavy Construction 17 Special Trade Contractors 1721 Painting & Paper Hanging 173 Electrical Work 1731 Electrical Work 179 Misc. Special Trade Contractors 1791 Structural Steel Erection 1794 Excavation Work 1795 Wrecking & Demolition Work 1799 Special Trade Contractors, NEC
The recompiled availability rates were compared to the utilization rates previously calculated for FYs 1989/90 and 1990/91, and new disparity indices were calculated. For black-owned businesses, the new disparity indices for FYs 1989/90 and 1990/91 were 102.29 and 40.15 respectively (compared to the previously-calculated indices of 94.32 and 38.78). For Hispanic-owned businesses, the new indices were 17.25 and 38.17 (compared to 19.33 and 47.25).
FDOT continues to set aside certain maintenance contracts for black and Hispanic-owned businesses despite a complete absence of evidence that the agency itself has engaged in past or continuing discrimination. Indeed, FDOT does not argue that its use of set-asides is justified by a history of active discrimination by the agency itself. FDOT agrees with the plaintiff's contention that the agency's record is clean: the department has not discriminated against blacks and/or Hispanic-owned businesses, and there have been no complaints to the contrary. Instead, FDOT contends that MGT's disparity study reveals that FDOT has been a passive participant in the discrimination practiced by groups in the private sector. According to FDOT, the use of a set-aside program was and still is needed to rectify the effects of this passive discrimination.
II.
The Equal Protection Clause of the Fourteenth Amendment provides that "[n]o state shall...deny to any person within its jurisdiction the equal protection of the laws." U.S. Const. amend. XIV § 1. When, as here, a state agency denies certain citizens the opportunity to compete for state contracts based solely upon their race or ethnicity, those citizens are denied their Fourteenth Amendment right to be treated with equal dignity and respect. As explained by the Supreme Court in City of Richmond v. J.A. Croson Co., 488 U.S. 469, 109 S. Ct. 706, 102 L. Ed. 2d 854 (1989), the standard for reviewing governmental programs that create such race or ethnicity-based preferences is strict scrutiny. See Wygant v. Jackson Bd. of Educ., 476 U.S. 267, 106 S. Ct. 1842, 90 L. Ed. 2d 260 (1986) (stressing that "[r]acial and ethnic distinctions of any sort are inherently suspect and thus call for the most exacting judicial examination").
To survive strict scrutiny, FDOT's practice of setting aside certain contracts for minority-owned businesses must first of all be based upon a compelling governmental interest. A governmental interest in favoring one race or ethnic group over another will be compelling only when there is "a strong basis in evidence" for the conclusion that affirmative action is necessary to remedy the effects of past or present discrimination by the governmental unit involved. City of Richmond v. J.A. Croson Co., 488 U.S. at 500, 109 S. Ct. 706 (quoting Wygant v. Jackson *1313 Bd. of Educ., 476 U.S. at 277, 106 S. Ct. 1842). The governmental unit here, the FDOT has the initial burden to produce evidence of the compelling governmental interest that purportedly supports its affirmative action program.
The Supreme Court has made clear that a "strong basis in evidence" cannot rest on amorphous claims of societal discrimination, on congressional findings of discrimination in a particular industry, on legislative assurances of good intention, or on unsupported assumptions regarding past discrimination in a particular industry. City of Richmond v. J.A. Croson Co., 488 U.S. at 499-504, 109 S. Ct. 706; see also Engineering Contractors Ass'n v. Metropolitan Dade County, 122 F.3d 895, 912 (11th Cir.1997), cert. denied, ___ U.S. ___, 118 S. Ct. 1186, ___ L.Ed.2d ___ (1998) (acknowledging that "a strong basis in evidence" can never arise from sheer speculation). Instead, a "strong basis in evidence" must rest on a particularized showing of the governmental unit's active or passive participation in past or present discrimination.
FDOT does not claim that it has evidence of intentional discrimination in the letting of contracts either by the central office or by any of the district offices. Instead, the essence of FDOT's claim is that: (1) MGT's two-year study provides evidence of a disparity between the proportion of minorities awarded FDOT road maintenance contracts and the proportion of minorities supposedly willing and able to do road maintenance work; (2) FDOT did not itself engage in any racial or ethnic discrimination; so (3) FDOT must have been a passive participant in somebody else's discriminatory practices. FDOT suggests that perhaps bonding companies, or maybe financial institutions, or possibly prime contractors, or maybe suppliers, contributed to a lack of business opportunities for black and Hispanic-owned firms, a lack of opportunity that in turn contributed to a statistical disparity in the award of road maintenance contracts.
In City of Richmond v. J.A. Croson Co., the Court wrote:
[I]f the city could show that it had essentially become a "passive participant" in a system of racial exclusion practiced by elements of the local construction industry, we think it clear that the city could take affirmative steps to dismantle such a system. It is beyond dispute that any public entity, state, or federal, has a compelling interest in assuring that public dollars, drawn from the tax contributions of all citizens, do not serve to finance the evil of private prejudice.
488 U.S. at 492, 109 S. Ct. 706, 102 L. Ed. 2d 854. While acknowledging that states and their subdivisions may act to dismantle "a system of racial exclusion practiced by elements of the local construction industry," the Court was nonetheless insistent that race or ethnicity-based programs be based upon discrimination that is identified with particularity. Generalized assertions of discrimination, the Court said, do not provide an adequate basis for race-conscious relief. See also Regents of the Univ. of California v. Bakke, 438 U.S. 265, 307, 98 S. Ct. 2733, 57 L. Ed. 2d 750 (1978) (distinguishing the "focused" goal of remedying wrongs worked by specific instances of discrimination from the unfocused goal of compensating individuals for the amorphous effects of societal discrimination).
The Supreme Court's particularity requirement is not relaxed just because a claim of discrimination is supported by evidence of statistical disparities. To be sure, the Court acknowledged in City of Richmond that "gross statistical disparities...may constitute prima facie proof of a pattern or practice of discrimination." 488 U.S. at 501, 109 S. Ct. 706 (quoting Hazelwood School Dist. v. United States, 433 U.S. 299, 307-308, 97 S. Ct. 2736, 53 L. Ed. 2d 768 (1977)). The Court did not even suggest, however, that evidence of statistical disparities would be sufficient to support an affirmative action program where, as here, the identity of the wrongdoers is unknown. The Court, in fact, explained that, where evidence of a significant statistical disparity creates an inference of discriminatory exclusion, a governmental unit may act to dismantle the closed business system "by taking appropriate measures against those who discriminate." 488 U.S. at 509, 109 S. Ct. 706. It goes without saying that the identity of "those who discriminate" must be known before a governmental unit may take appropriate measures against "those who discriminate." *1314 An affirmative action program that is not focused on "those who discriminate" may well serve the illegitimate purpose of providing certain racial or ethnic groups with compensation for some ill-defined social disadvantages, but it probably will not serve the legitimate purpose of dismantling a closed business system.
In this case, it is agreed that FDOT did not discriminate against minority contractors bidding on road maintenance contracts. The record is virtually silent, however, about who, if anyone, did discriminate. FDOT officials have speculated that the agency may have acted in passive complicity with bonding companies, or financial institutions, or prime contractors (even though maintenance contracts rarely involve the use of subcontractors), or suppliers. FDOT's experts have guessed about the possible causes for the disparities. Individuals responding to FDOT's telephone survey have described their perceptions about barriers to FDOT's bidding procedures. But FDOT has presented no evidence to establish who, if anyone, in fact engaged in discriminatory acts against black and Hispanic-owned businesses. The record at best establishes nothing more than some ill-defined wrong caused by some unidentified wrongdoers; and, under City of Richmond, that is not enough!
III.
The court is mindful that the record in this case contains divergent expert opinions about the validity of MGT's disparity study. FDOT argues that these divergent opinions, among other things, create a genuine issue of material fact sufficient to require the case to go to trial. The court disagrees and has determined that the plaintiff is entitled to summary judgment.
Assuming, for the sake of argument, that MGT's methodology was sound and its findings of disparity valid, the fact remains that none of the experts has been able to do anything but speculate about the cause of the disparities. Despite having the initial burden of producing evidence of identified discrimination, FDOT has relied on generalized assertions that black and Hispanic-owned businesses may have been harmed by the discriminatory practices of bonding companies, or financial institutions, or prime contractors, or suppliers. FDOT's generalized assertions, however, do little to help define the precise scope of the alleged harm or to help identify, with specificity, the purported wrongdoers. Quite simply, the court finds no basis for determining that FDOT has demonstrated "a strong basis in evidence for its conclusion that remedial action was necessary." Wygant, 476 U.S. at 277, 106 S. Ct. 1842. Because FDOT has failed to produce evidence consistent with the standards set forth in City of Richmond, and because given the evidence that it did produce FDOT's set-aside program cannot survive scrutiny under the Equal Protection Clause, the court finds that P & J is entitled to summary judgment.
IV.
Having assumed the validity of MGT's disparity findings for purposes of P & J's motion for summary judgment, the court nonetheless wishes to note its concern about the choice and use of MGT's statistical pool.
Although the vast majority of FDOT maintenance contracts are let at the district level, and although the demographics vary considerably from district to district within the State of Florida, MGT did not analyze the disparity data on a district-by-district basis. Instead, the data from individual districts and counties were aggregated; availability and utilization rates were determined on a state-wide basis; disparity indices were calculated for the state as a whole; and program goals were ultimately set on a statewide basis. FDOT's experts, Kenneth Tatum and Gerald L. Jackson, have suggested that district-by-district analysis was eschewed simply because it would have increased the administrative burdens and costs to FDOT.
In a similar case, involving as this one does a challenge to an affirmative action program supported, in part, by the results of a disparity study, a judge in the Southern District of Florida declined to assign dispositive weight to the study's aggregated data. Engineering Contractors Ass'n v. Metro. Dade County, 943 F. Supp. 1546 (S.D.Fla. 1996), (a challenge to Dade County's use of an affirmative action program in awarding county construction projects), aff'd, 122 F.3d *1315 895 (11th Cir.1997). The district judge noted that aggregated data may result in illusory disparities because of a statistical phenomenon known as "Simpson's Paradox." Simpson's Paradox, he wrote, may arise when heterogeneous or dissimilar data populations are grouped together for statistical purposes. Data so aggregated may yield disparities that disappear when the data are disaggregated. Eng'g Contractors Ass'n, 943 F.Supp. at 1560 n. 16.
In Eng'g Contractors Association, the judge was concerned about the effects of aggregating SIC codes 15 (general building construction), 16 (heavy construction other than building), and 17 (specialty trade construction, which includes electrical, plumbing, heating, ventilating, and air conditioning, among others) for purposes of calculating disparities involving a single county's capital construction contracts. The judge noted that "[f]irms that build hospitals (SIC 15) do not compete for County contracts with firms that lay asphalt (SIC 16) or firms that install plumbing (SIC 17); therefore comparisons between these disparate entities would not produce a reliable portrait of County contracting trends." Eng'g Contractors Ass'n, 943 F.Supp. at 1560.
In contrast, disparities in this case were calculated after the data from all districts within the state and all purportedly relevant SIC codes were aggregated. The disparity indices for each of two study years were then averaged. FDOT used the resulting average disparity indices, which were below 80 for black and Hispanic-owned firms, to justify its set-aside program. Although the record here contains no mention of Simpson's Paradox, the court is nonetheless dubious that an average disparity index for a two-year period of time, calculated after data from disparate districts and SIC codes were aggregated, provides a strong basis in evidence for a program that erects race or ethnicity as the sole criterion in an aspect of public decision-making.
The court is also unconvinced that it was appropriate to assume as MGT did that every firm included in the selected SIC codes was qualified and/or willing and able to bid on an FDOT road maintenance contract. See Richmond v. Croson, 488 U.S. at 501-502, 109 S. Ct. 706 (explaining that the "relevant statistical pool for purposes of demonstrating discriminatory exclusion must be the number of minorities qualified to undertake the particular task"). Common sense alone suggests reasons to question such assumption. Do all firms in the selected two-digit codes, representing such large categories as transportation services (SIC 47), electric, gas, and sanitary services (SIC 49), heavy construction (SIC 16), and special trade construction (SIC 17) perform road maintenance work? The probable answer is: "No." Would a plumbing firm, or a heating and air conditioning firm, both included in code 17, necessarily be ready, willing and able to bid on a road maintenance contract? Again, the probable answer is "No." Yet it appears that plumbing firms and heating and air conditioning firms just to name two unlikely participants in the road maintenance business were included in MGT's disparity study as available firms, ready, willing and able to bid on FDOT road maintenance contracts. Is it not likely that MGT's statistical pool of "qualified" businesses was too large? The likely answer is: "Yes."
It also appears that MGT may have improperly enlarged its statistical pool by aggregating firms in related two, three and four-digit SIC codes. Did MGT double-count firms, for example, when it added firms in SIC 078 to firms in SIC subgroups 0782 and 0783? Did MGT triple-count firms when it added firms in SIC 17 (special trade contractors) to firms in SIC 179 (miscellaneous special trade contractors), the sum of which was then added to firms in SIC 1791, 1794, 1795, and 1799 (structural steel erection, excavation work, wrecking and demolition work, and special trade contractors, NEC, respectively)? The probable answer is: "Yes."
FDOT's counsel suggested at oral argument that, because the numbers for minority and non-minority firms would be similarly affected and because availability and utilization are expressed as rates, the net result would be the same whether or not MGT's statistical pool of available firms was too large. The court, however, is skeptical of counsel's suggestion and remains concerned that the statistical pool used by MGT may *1316 not be the "relevant statistical pool" required under City of Richmond.
V.
Through its set-aside program, FDOT has denied certain citizens the opportunity to compete for selected road maintenance contracts based solely on their race or ethnicity. Having thus employed a highly suspect tool in its bid-letting process, FDOT was required to come forward in this lawsuit with evidence demonstrating that its set-aside program was and is necessary to remedy the effects of specific identified discrimination. Because FDOT instead produced nothing more than evidence of an ill-defined wrong allegedly caused by some unknown wrongdoers, FDOT's set-aside program cannot survive P & J's motion for summary judgment under the Fourteenth Amendment.
Accordingly, it is ORDERED:
1. P & J's motion for summary judgment (doc. 46) is GRANTED.
2. The court hereby DECLARES that FDOT's set-aside program, as it applies to state funded highway maintenance contracts, violates the Equal Protection Clause of the Fourteenth Amendment.
3. FDOT, through its central office and all its district offices, is hereby ENJOINED from setting aside state funded highway maintenance contracts for competition solely among minority businesses.
4. The clerk is directed to enter judgment accordingly. Costs shall be awarded to the plaintiff.
NOTES
[1] Because the SMOBE reported data only for 1982 and 1987, MGT calculated the overall rate of growth or decline in firms from 1982 to 1987, then divided the rate of change for each minority group by five to obtain an annual rate of growth or decline. The resulting rates were then used to approximate the number of firms available in the two study years.
