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Franchising has been present in the residential real estate brokerage market for many years. Today, nearly one of every five firms in this sector is organized as a franchise and one of every three agents works for an affiliated organization. Despite this high incidence of franchising, no current study has addressed how the decision to franchise impacts productive efficiency levels for these firms. A study measures the productive efficiency levels of real estate brokerage firms by employing data envelopment analysis (DEA). DEA was used to estimate overall, allocative, technical, pure technical, and scale efficiency levels for a set of franchised and non-franchised firms gathered by the National Association of Realtors. The results suggest that firms in general are productively inefficient. Franchised firms were found to be more efficient in allocating resources, while non-franchised firms were shown to be more scale and technically efficient.

Randy I. Anderson: Assistant Professor of Finance, Northeast Louisiana University, Monroe, Louisiana, USA

Robert Fok: Associate Professor of Finance, National Chung Cheng University, Taiwan

Introduction

Historically, independently owned and locally operated firms have characterized the residential real estate business. With the first appearance of franchising in the residential real estate industry in 1948, franchising has grown into an industry force of some magnitude. Growing steadily in the 1970s, franchising's market share peaked in 1981 at 19 percent. Since that time the share of the market made up of franchised affiliates has remained relatively constant. In 1990, approximately 18 percent of all real estate firms were affiliated with a franchise organization. More importantly, franchise affiliates account for 30 percent of all the salespersons in the industry.

Despite the significance of franchising as a form of business organization within many diverse industries, little research has focused on the reasons why firms choose to join franchise operations. Most of the work (Jensen and Meckling, 1976; Jensen and Smith, 1985; Rubin, 1978) comes from the corporate finance literature where the principal focus has been on the benefits of franchising from the perspective of the franchisor.

In this paper, we examine why a residential real estate brokerage firm would choose to franchise. A review of the literature reveals that there are many intuitive reasons why franchises exist and why franchising may be an efficient organizational form in this sector. However, to our knowledge, there are no studies that directly measure the productive efficiency levels of franchised relative to non-franchised brokerages. The hypothesis that franchising is a more efficient organizational form is tested in the current paper by employing a linear-programming technique termed the data envelopment analysis (DEA). Essentially, the procedure examines all linear combinations of the sample firms and determines the minimum input utilization that is needed to achieve a given output. This approach yields an efficient production frontier. Any deviation from the efficient frontier is considered inefficiency and the firm is classified as X-inefficient in economics terminology. Moreover, the DEA is able to decompose total inefficiency into allocative, technical, pure technical, and scale measures. Allocative inefficiencies represent deviations from the efficient frontier that result from sub-optimal allocation of inputs. Technical inefficiency represents deviations from efficiency that result from poor input utilization (pure technical inefficiency) and from firms failing to operate at the optimal size (scale inefficiency).

Understanding X-efficiency levels is crucial for understanding the competitive structure of a market and/or segments of a market. Leibenstein (1966) was the first to recognize and formally define the term X-inefficiency. Leibenstein (1966) argues that the majority of X-inefficiency losses arise from inadequate motivation by firm management. If managers and/or workers can be encouraged or persuaded to work more effectively, firms could improve performance without changing their resource allocation. If a firm is operating in a competitive market, managers and workers may feel more pressure to work more efficiently. Hence, the greater the level of competition in a market or market segments, the higher the degree ofX-efficiency.

X-efficiency levels are important for consumers, as consumers undoubtedly benefit from efficient resource usage and allocation. In a real estate brokerage context, this may mean lower commission rates, better advertising and promotions, and prompter more professional service. If the decision to franchise increases efficiency, consumers would benefit from franchising firms growing in market share and vice versa.

The next section discusses franchising and its implications for real estate brokerage efficiency. The third section presents the sample data and methodology. The fourth section reports the empirical findings, while the last section summarizes and concludes the study.

Franchising and real estate brokerage firms

In many respects, the residential real estate brokerage market exhibits a number of features that tend to encourage franchising. Typical home sellers and buyers are infrequent participants in the market, and as home sales transactions have become more complex, consumers have become more dependent upon the assistance of real estate agents to assist in the consummation of the sale. At the same time, consumers may have difficulty evaluating ex-ante, the quality of alternative brokers or services they may provide. Moreover, many homebuyers, especially those new to a community have little knowledge of local market conditions. Because the information needed to make enlightened decisions in this market is costly to acquire, and could easily exceed the expected benefits from an extensive search, the assurance provided by a franchise brand name may be particularly valuable to buyers and sellers, and thereby provide a rent to the franchise.

Besides supplying brand-name recognition, franchise organizations in the residential real estate industry provide may other benefits to affiliates. Those listed as important in the NAR's Profile of Real Estate Firms (NAR, 1996) include sales associates and management training programs, salespersons recruiting assistance, market research, and corporate relocations and inter-city referral networks. Satisfaction was also registered for other franchisor-provided services such as errors and omissions insurance, homeowner warranty programs, and legislative updates on efficiency issues affecting the industry.

There may be another, less obvious reason for franchising in this market. Many of the services provided by real estate franchise organizations would prove very costly if paid for directly by local firms. Instead of incurring a sizable increase in costs, much of which would take the form of overhead and capital expenditures, franchisees pay annual royalties to franchisors. These firms are substituting increased variable costs for higher fixed costs of providing these services internally. The reduction in operating leverage thereby achieved may be very desirable for risk averse owners in an industry where demand is highly volatile. By lowering their break-even levels of sales, franchisees may be better able to withstand periods of slack demand in the housing market, especially if prolonged, than their non-affiliated competitors (Zumpano and Elder, 1992).

However, it is possible that franchising could reduce efficiency. For instance, if several other franchisees provide poorer services or inferior products, a high quality-producing firm could still be associated with lower standards. Moreover, franchised firms may feel as if they can "ride" on their franchisor's reputation and shirk on quality and customer service. Finally, the payments to the parent company, by increasing variable costs, may also hurt profits to a greater extent than the potential increase in incremental revenues that may result from franchising (Bates, 1995).

While much of the above discussion suggests that the environment in which residential real estate brokerages operate is conducive to the existence of franchises, no current study has examined either the survivability or productive efficiency levels of franchises. The next section provides the methodology that this study uses to determine the productive efficiency implications of franchising in this sector.

Methodology and sample data

Data envelopment analysis

As noted above, this paper employs DEA, which is a linear-programming procedure that can estimate the relative efficiency level of any economic unit that can be characterized by producing multiple outputs and utilizing multiple inputs. The seminal paper suggesting the use of the DEA to examine efficiency was written by Farrell (1985). The work by Fare et al. (1985) further promoted the usefulness of this technique. Since then, many efficiency studies in other sectors have employed this technique[1].

While the procedure is computationally rigorous, a simple graphical depiction will demonstrate how the methodology works and how the efficiency measures are obtained. Figure 1 displays the overall (OE), technical (TE), and allocative (AE) efficiency measures. For illustration, assume that there are two inputs (X[sub]1 and X[sub]2), one output (Y), and constant returns to scale. Additionally, assume that technology is fixed and that input prices are represented as PP. Firm A is an efficient firm. In other words, firm A produces along output isoquant Y by utilizing the least inputs. However, suppose there is a firm operating at point C and producing an output equivalent of that produced along Y. C is said to be inefficient with an overall efficiency score of 0D/0C (or equivalently an inefficiency score of DC/0C). This ratio is simply a measure of the best practice firm's total cost divided by a firm's actual cost.

Overall inefficiency can be broken down into its technical and allocative components. Assuming that input allocations are fixed, the best that firm C could have done was to operate at point B. The extra input usage that was incurred by firm C as a percentage of total input usage is the technical inefficiency measure and can be expressed as BC/0C. The technical efficiency of firm C is expressed as 0B/0C. Allocative inefficiency measures results from sub-optimal input allocations. Here, allocative inefficiencies for firm C can be represented by DB/0B, and allocative efficiency is expressed as 0D/0B.

Besides the above efficiency scores, technical efficiency can be decomposed further into a pure technical (PTE) and scale (SE) measure. Pure technical inefficiency simply refers to deviations from the efficient frontier that result from failure to utilize the employed resources efficiently. Hence, this measure assumes that firms are operating at constant return to scale. Scale inefficiencies, on the other hand, are losses due to failure to operate at constant returns to scale. An examination of Figure 2 will clearly illustrate these two efficiency measures.

In Figure 2 the Y-axis represents output and the X-axis represents input combinations that contain an equal amount of both input 1 and input 2. The graph shows three observations denoted A, B, and C, respectively. Two frontiers are illustrated, a frontier assuming constant returns to scale 0E, and a frontier assuming variable returns to scale, GBAH. To measure pure technical efficiency, an examination of the variable returns to scale frontier must take place. For observation C, pure technical efficiency is measured as PTE = FJ/FC. Scale efficiency is thus FK/FJ. This measures the possible proportional reduction in input usage if a firm operates at constant returns to scale instead of decreasing or increasing returns to scale.

After completing this analysis, the SE measure is analyzed to determine if it equals one. If the SE measure equals one, firms are operating at constant returns to scale. If SE does not equal one, it is important to determine if firms are operating at increasing or decreasing returns to scale (see Appendix for a mathematical treatment of DEA).

This paper calculates the inefficiency measures in the manner described above for a set of franchised and non-franchised firms. The next section discusses and defines the inputs and outputs used currently.

Sample data

The data employed to estimate the efficiency scores were obtained from the Economics and Research Division of the National Association of Realtors. They conduct periodic nationwide surveys of the real estate brokerage industry. The current data come from the sixth survey that encompasses 1990-1991[2]. The information was obtained from professionals who are Certified Real Estate Brokerage Manager designees and a random selection of members of the National Association of Realtors.

Only a subset of the data will be used. This subset includes real estate brokerage firms who obtained at least 75 percent of their revenues from residential transactions. With adjustment for incomplete and missing data, a final data set of 276 firms was employed. Of the 276 firms, 92 were affiliated with a franchise and the remaining 184 were unaffiliated.

The estimated models contain five inputs: the number of salespersons, the number of non-sales employees, the number of offices, promotion and advertising expenses, and other inputs which is proxied by other expenses. For estimation purposes, it is necessary to convert the inputs into prices. The price of a salesperson was computed by dividing total sales-related expenses by the number of full-time equivalent salespersons. The price of non-sales labor was calculated by dividing clerical, secretarial, and sales managers' salaries by the number of non-sales employees. The price of an office was calculated by dividing total occupancy expense by the number of real estate offices. The last two prices, advertising and promotion and other inputs are expressed as a percentage of revenue transactions. Output was defined as the number of homes listed and/or sold by the firm in the sample period. The double counting of an in-house sale is intentional and reflects the dual service of real estate brokerage firms. The first estimation contains firms that are organized as franchises, while the second estimation contains the non-franchised firms. Tables I and II provide summary statistics of these variables for both the franchised and non-franchised sample sets, respectively.

Efficiency results

The efficiency results for the franchised firms are reported in Table III and the efficiency scores for non-franchised firms are reported in Table IV. The overall results are similar to those found in Anderson et al. (1998). In particular, franchise firms are very inefficient. The overall efficiency scores under 25 percent which indicates that on average, firms could decrease their costs by 75 percent without decreasing output if the firms were productively efficient[3].

The low overall efficiency levels are a function of both technical and allocative inefficiencies. Allocative efficiency ranges from 36 percent for the non-franchised firms to 65 percent for the franchised firms. Non-franchised firms had a technical efficiency level of 51 percent while franchised firms were only 41 percent technically efficient. However, for both sample sets, the pure technical efficiency scores are high (83-87 percent) and the scale efficiency levels are low (49-64 percent) indicating that technical inefficiency is primarily a function of failure to operate at constant returns to scale, rather than from poor input usage. Specifically, an examination of Table V shows that most firms are operating in the increasing returns to scale region. Hence, firms could realize efficiency gains through expansion. These results are consistent to those found by Zumpano et al. (1993) and Zumpano and Elder (1994), and Anderson et al. (1998).

To test if franchised firms and non-franchised firms exhibited statistically different productive efficiency levels, five statistical tests were employed: the Analysis of Variance Test, the Wilcoxon Test, the Median Test, the van der Waerden Test, and the Savage Test. The last four tests are non-parametric and are utilized to test for mean efficiency differences because the efficiency scores are bounded in the [, 1] interval. The results that are reported in Table VI indicate that franchised firms and non-franchised firms exhibit significantly different efficiency levels. In particular, the groups significantly differ from one another in terms of OE, AE, TE, and SE. However, both groups have statistically similar levels of PTE. Franchised firms are more allocatively efficient than non-franchised firms while non-franchised firms perform better in a technical and scale context[4].

Intuitively, it appears as if the organizational structure promoted by franchised organizations allows for better allocation of inputs in the production process than that of unaffiliated firms. Perhaps, the franchised firm's ability to advertise, promote, and train at a national or regional level and still provide local service is driving these results. The brand-name capital and reputation effects of franchising may also promote allocative efficiency. For example, referral networks and name recognition give franchise firms a competitive advantage in producing revenue transactions more efficiently. These transactions are more efficient in the sense that less time, effort, and money is spent in the process of obtaining properties to list or finding buyers to purchase homes.

Non-franchised firms were shown to be more scale efficient than franchised firms. An examination of Tables I and II shows that this result is a function of non-franchised firms being the larger of the two groups. Large firms may already have name recognition and an established reputation in the local market and would gain little from joining a franchise. Thus, the smaller franchised firms are operating further from the constant returns to scale region than their larger non-franchised counterparts.

Before turning to the paper's conclusions, it is important to discuss the methodological limitations of the DEA. The DEA assumes that any deviation from the efficient frontier represents inefficiency. This assumption has been criticized in that inefficiency scores may be overstated due to measurement error. To investigate this problem, the efficiency scores were computed multiple times by deleting outlying firms. No matter which firms were deleted, the results were virtually identical. Thus, the results appear to be robust.

Conclusions

The franchised firm has become commonplace in the residential real estate brokerage market. While there are many intuitive reasons why franchising seems to be a rational choice for some brokerage firms, little empirical research exits that suggests anything about the productive efficiency levels of these firms. Hence, this paper measured the overall, technical, allocative, pure technical, and scale efficiency levels for a set of franchised firms and a set of non-franchised firms. The main results indicate that both franchised and non-franchised firms are operating relatively inefficiently. However, non-franchised firms perform better in a scale and technical sense, while franchised firms were shown to be more efficient at resource allocation. If strong results were found in favor of one organizational form over the other, there should have been a movement towards that type of firm. However, the percentage of franchised firms relative to non-franchised firms has remained relatively constant in recent years, which is consistent with the mixed efficiency results found in the current study. Future research should focus on the determinants of brokerage efficiency; such that firms may be able to take proactive measures to improve performance.

Notes

1. This technique has been applied in examining the efficiency of schools (Bessent et al., 1982; Charnes et al., 1981), the performance of pharmacies (Banker and Morey, 1986), the performance of small business development centers (Lang and Golden, 1989), the performance of nursing home centers (Fizel and Nunnikhoven, 1993), and many other similar papers.

2. Most of the respondents reported income and expenses for the year ending December 31, 1990. However, some of the firms operate on a fiscal year that carried into 1991. Hence, the data comes from both 1990 and 1991.

3. While this inefficiency level seems high, it is not uncommon. For example, Fecher et al. (1993) finds productive inefficiency in the French insurance industry of this magnitude.

4. These results are not necessarily in conflict with the results of Anderson et al. (1998), who measured X-efficiency for a set of all real estate firms and then indirectly measured the efficiency of franchising using regression analysis. Their study showed franchising to hurt efficiency, in the presence of other variables such as firm age, market density, ownership structure, multiple listing service affiliation, and others. This study directly tests for the efficiency of franchising using two separate samples, which allows for the construction of two separate frontiers, which is more appropriate when the implications of franchising are the primary objective of the study.

References

1. Anderson, R.A., Fok, R. Zumpano, L.V. and Elder, H. (1998, "Measuring the efficiency of residential real estate brokerage firms: an application of the data envelopment analysis", Journal of Real Estate Research (forthcoming).

2. Banker, R.D. and Morey, R.D (1986, "The use of categorical variables in the data envelopment analysis", Management Science, Vol. 32, pp. 1613-27.

3. Bates, T. (1995, "Analysis of survival rates among franchise and independent small business startups", Journal of Small Business Management, pp. 26-35.

4. Bessent, A., Bessent, J., Kennington, and Regan, B. (1982, "An application of mathematical programming to assess productivity in the Houston independent school districts", Management Science, Vol. 28, pp. 1355-67.

5. Charnes, A.C., Cooper, W.W. and Rhodes, E. (1981, "Evaluating program and managerial efficiency: an application of the data envelopment analysis to program follow through", Management Science, Vol. 27, pp. 68-697.

6. Fare, R., Grosskopf, S. and Lovell, C.A.K. (1985, The Measurement of Efficiency of Production, Kluwer-Nijhoff, Boston, MA.

7. Farrell, M. (1985, "The measurement of productive efficiency", Journal of the Royal Statistical Society, Series A, General, Vol. 125 No. 2, pp. 252-67.

8. Fecher, F., Kessler, D., Perelman, S. and Pestieau, P. (1993, "Productive Performance in the French Insurance Industry", European Journal of Operational Research, pp. 77-93.

9. Fizel, J.L. and Nunnikhoven, T.S. (1993, "The efficiency of nursing home chains", Applied Economics, Vol. 25, pp. 49-55.

10. Jensen, M. and Meckling, W. (1976, "Theory of the firm: managerial behavior, agency costs and ownership structure", Journal of Financial Economics, Vol. 3, pp. 305-60.

11. Jensen, M. and Smith, W.C. (1985, "Stockholder, manager, and creditor interests", in Altman, E. and Subrahmanyam, M. (Eds), Applications of Agency Theory: Recent Advances in Corporate Finance, Irwin Press, Homewood, IL, pp. 615-41.

12. Lang, J.R. and Golden, P. (1989, "Evaluating the efficiency of SBDCS with data envelopment analysis: a longitudinal approach", Journal of Small Business Management, Vol. 27, pp. 42-9.

13. Leibenstein, H. (1966, "Allocative efficiency vs. 'X-Efficiency'", American Economic Review, Vol. 56, pp. 392-414.

14. National Association of Realtors (NAR) (1996, Profile of Real Estate Firms, NAR, Washington, DC.

15. Rubin, P.H. (1978, "The theory of the firm and the structure of the franchise contract", Journal of Law and Economics, Vol. 21, pp. 223-33.

16. Zumpano, L.V. and Elder, H.W. (1992, "Organizational form in the residential real estate brokerage industry", working paper, The University of Alabama, Tuscalousa, AL.

17. Zumpano, L.V. and Elder, H.W. (1994, "Economies of scope and density in the market for real estate brokerage services", AREUEA Journal, Vol. 22, pp. 497-513.

18. Zumpano, L.V., Elder, H.W. and Crellin, G.E. (1993, "The market for residential real estate brokerage services: costs of production and economies of scale", Journal of Real Estate Finance and Economics, Vol. 6, pp. 237-50.

Appendix. Overall, technical and allocative efficiencies

Overall efficiency (OE) is defined as the ratio of the best practice firm's production cost to the actual cost of a particular firm. OE can be decomposed as the product of technical efficiency and allocative efficiency, i.e. OE = TE * AE, where TE and AE represent technical and allocative efficiency, respectively. The following linear program can estimate OE for firm j:

Min Px (A1)

s.t.

y[sub]j <= ZY (A2)

x[sub]j >= ZX (A3)

Z [set membership] R (A4)

Here, y[sub]j is a m x 1 vector of outputs produced by firm j; x[sub]j is a n x 1 vector of inputs utilized by the firm; and P is a 1*n vector of input prices. Y is a K x m matrix of firm outputs where K is the number of firms in the sample. X is a K x n matrix of inputs and Z is a vector of weights attached to each firm when constructing hypothetical efficient firms. To identify efficient firms, the program examines all linear combinations of sample firms that produce an output equal to or greater than that produced by firm j (equation 2) and use no more than the input used by firm j (equation 3). The linear combination that has the lowest production cost is the best practice firm. The solution represents the minimum cost level that an individual firm should achieve given its output. Dividing the minimum cost by the cost of firm j yields the overall efficiency measure for firm j.

The following linear program is used to calculate technical efficiency:

Min TE (A5)

s.t. y[sub]j <= ZY (A6)

TEx[sub]j >= ZX (A7)

Z [set membership] R (A8)

TE is the ratio of inputs utilized by the best practice firm to the inputs actually utilized by firm j. Therefore, if firm j is efficient, TE = 1. When TE < 1, firm j can reduce its input usage without reducing its outputs. Efficient firms are constructed by a process similar to that stated in the program for calculating overall efficiency. Efficient firms are linear combinations of sample firms that produce output equal to or greater than that produced by firm j (equation 6) and uses no more than TE percent of input used by firm j (equation 7). Within a set of efficient firms, the program chooses the combination that minimizes TE. The solution to this minimization problem is the efficient index for firm j.

The measures of pure technical and scale efficiency can also be shown mathematically. The following linear program derives pure technical efficiency:

Min PTE (A9)

s.t. y[sub]j <= ZY (A10)

PTEx[sub]j >= ZX (A11)

Az[sub]i = 1 (A12)

Z [set membership] R (A13)

The only difference between the program for calculating TE and that for PTE lies on the constraints on the vector Z. Equation (12) allows for variable returns to scale. As previously mentioned, scale efficiency is obtained by dividing TE by PTE. In order to determine the nature of the returns to scale when SE [logical not] 1, another linear program must be solved. This program constructs a frontier that allows for non-increasing returns to scale. The following linear program can calculate this frontier:

Min [sigma] (A14)

s.t. y[sub]j <= ZY (A15)

[sigma]x[sub]j >= ZX (A16)

Az[sub]i <= 1 (A17)

Z [set membership] R A18)

Equation (17) allows for non-increasing returns to scale. It can be shown that when SE [logical not] 1, decreasing return to scale exist if [sigma] = PTE, and increasing returns to scale exist if [logical not] PTE (see Fare et al., 1985).