Document View

Substantial evidence that real estate brokerage firms choosing to franchise are more cost-efficient than firms that remain independent is provided. Cost data in 1995 obtained from a nationwide survey of real estate brokerages are used to analyze the differences in firm efficiency across firm type - franchised and independent. A single stochastic cost frontier is estimated using Bayesian statistics and measure firm efficiency relative to that frontier conditional on firm type is measured. The results indicate that real estate brokerages are relatively efficient, implying a competitive market, but franchised brokerages are substantially more efficient than their independent counterparts.

Determining the efficiency of real estate brokerage firms is an important question due to its far-reaching implications for optimal firm structure and public policy. Previous attempts to analyze efficiency and the implications of franchising within the residential real estate industry supply no consensus on this issue and employ techniques that introduce bias in the efficiency estimates. Understanding the characteristics of this market is crucial for worthy and reliable recommendations to policymakers. We calculate real estate brokerage efficiency by firm type with the goal of correctly analyzing the influence of franchising on firm efficiency.

We calculate residential real estate brokerage efficiency conditional on whether the brokerage is a franchised firm or independent by examining X-inefficiencies, a concept originally proposed by Leibenstein (1966). Leibenstein argues that firms operate sub-optimally for two fundamental reasons. First, allocative inefficiency occurs when a firm fails to allocate resources in the most efficient manner. And second, technical inefficiency occurs when a firm sub-optimally utilizes its resources given their allocation. Two firms may have the same resource allocation, yet one firm produces less output than the other does. The difference between potential utilization of resources and actual resource employment is termed X-inefficiency. Leibenstein argues that the majority of X-inefficiency losses arise from inadequate motivation by firm management. He argues that the manager's motivation levels are linked to the structure and competitiveness of the market in which a firm operates. More recently, X-inefficiency has been defined as deviations from an efficient frontier response surface that is attributable to a misallocation of resources or the lack of effective utilization of current resources. This misallocation and misuse of resources represents the firm's inefficiencies.

Over the years, such notions as monopoly, cartel and price fixing, as well as excessive commissions, have been associated with this market-implying inefficiency and less than competitive behavior. In contrast, other early studies found that this market is relatively efficient (Schroeter 1987; Knoll 1988; Carroll 1989; Anderson, Lewis and Zumpano 1999).

Of the many studies that found the industry to be relatively inefficient, some had limited access to micro-level cost data for real estate firms and/or used techniques that fail to allow for accurate efficiency estimation. Among those who found the brokerages to be inefficient, Miller and Shedd (1979), Yinger (1981) and Crockett (1982) had limited data sources, and Anderson et al. (1998) used data envelopment analysis (DEA), an estimation technique that contains significant bias in the firm efficiency estimates. Others, including Zumpano, Elder and Crellin (1993) and Zumpano and Elder (1994), estimate a translog cost function with a single error term to model the true production function for the residential real estate industry. This methodology also estimates firm efficiency inaccurately because, as with DEA, measurement error is misinterpreted as inefficiency, biasing inefficiency estimates. Because the overall efficiency results are rather mixed, it is difficult to make a conclusive and quantitative statement about the economics of franchising.

Aside from the discrepancy concerning estimation, structural changes have recently influenced the real estate brokerage market ultimately affecting the product mix, the agency and brokerage arrangements and the legal liability of real estate brokerage firms. Consequently, earlier literature on the market may no longer be relevant, leaving some of the same persistent questions unanswered.

The purpose of this paper is to provide insight into the real estate brokerage franchising issue via current and accurate efficiency estimates for residential real estate brokerage firms. In a Bayesian context, we are capable of calculating group efficiency for franchised firms and independent firms using a single stochastic frontier.

Previous attempts to address the franchising issue estimate a frontier assuming both groups share the same mean inefficiency parameter, then regress the efficiency scores on firm characteristics including a dummy for franchising. If average group inefficiency differs across franchising and non-- franchising firms, this approach biases group type efficiency estimates together. This approach could mask large differences in efficiency between franchised and independent firms. The second-stage regression model is also flawed in that it fails to allow for the covariance in efficiency scores that are estimated in the initial model.

The paper will proceed as follows. First we examine the efficiency implications of franchising, and then we provide the data sources and variable definitions that are used in the Bayesian analysis. The following sections furnish the statistical model and describe the Bayesian empirical results. Finally, the last section concludes.

The Efficiency Implications of Franchising

Overview

Residential real estate brokerage firms have been involved in franchising since 1948, but franchising did not become commonplace in this sector until the 1970s. Franchised firms grew in market share and by 1981 accounted for 19% of the total real estate brokerage market. Since that time, franchised firms have maintained approximately 18-20% of the market (Zumpano and Elder 1992).

Despite the significance of franchising in real estate brokerages and other sectors, little empirical research has focused on examining why a real estate brokerage firm chooses to franchise. The majority of the franchising work rests in the corporate finance literature, where the research focuses on the franchising benefits from the franchiser's perspective.1 We would like to extend this literature to include the firm's decision to franchise, so that regulatory considerations can be made certain.

This study examines the reasons why a real estate brokerage firm would choose to affiliate. A detailed examination of the literature reveals that there are numerous intuitive reasons for a firm to affiliate; yet there have been few direct tests of this intuition.

Enlarge 200% Enlarge 400%

Considerations

Franchising may reflect efficiency considerations in the residential real estate brokerage sector for several reasons. Zumpano and Elder (1992) assert that for the real estate brokerage firm, franchising may be a way of improving stability or survivability by decreasing operating leverage and substituting variable costs for fixed costs. Lower levels of operating leverage reduce bankruptcy costs, but this is offset in potential profits that could be recognized by a highly leveraged firm during economic upturns. However, franchised firms may trade the low degrees of operating leverage for high degrees of financial leverage, and thus the firm's total risk may be unaffected by the ability of franchised firms to decrease operating leverage. Additionally, from early franchising theory, it was argued that a franchising firm could raise capital at a lower cost than traditional firms could (Oxenfeldt and Kelly 1969; Oxenfeldt and Thompson 1969; Ozanne and Hunt 1971; Caves and Murphey 1976). If this were true, the franchised firms would be more efficient. Furthermore, the rental of an established name could help a firm's reputation and selling power, which would increase efficiency. The structure of a franchised firm leads to a lower probability of quality debasing, since the franchise could be terminated if certain standards were not met. Lastly, if advertising and promotion are more efficiently handled at the national level, but production and distribution are more efficiently arranged at the local level, franchising may prove to be an expedient business form in this market.

However, it is also possible that franchising could reduce efficiency. For instance, if several other franchises 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 franchiser's reputation and shirk on quality and customer service. Finally, the payments to the parent company, by increasing variable costs, may also harm profits to a greater extent than the potential increase in revenues due to franchising (Bates 1995).2

Using DEA, Anderson et al. (1998) indirectly tested the efficiency implications of franchising and found that franchising adversely influences firm efficiency. Anderson (1998) used a classical stochastic frontier model to calculate firm efficiency and found using regression analysis that franchising adversely influences it. Hence, these authors concluded that franchising has not been able to sustain growth in market share because franchising is not conducive to efficient performance. Both studies constructed a single cost frontier-assuming that only one firm type exists-and ran a Tobit regression to test the hypothesis that franchised firms are more efficient. Thus, as noted above, they assumed the firm types are the same and did not take into account the covariance between firm efficiencies, so that they reported biased regression results.

Other studies have simply focused on whether the decision to franchise alters output as measured by sales and or listings. The majority of these studies find that franchising increases output (Frew and Jud 1986; Richins, Black and Sirmans 1987; Jud, Rogers and Crellin 1994). While informative, these studies do not examine the implications of franchising for efficiency.

Enlarge 200% Enlarge 400%

Data and Variable Definition

Data from the Economics and Research Division of the National Association of Realtors' 1994-1995 nationwide survey includes microeconomic data from real estate brokerage firms. Professionals who are Certified Real Estate Brokerage Manager designees provide complete information for the first part of the data sample, and the remainder of the data consists of a random sample from the members of the National Association of Realtors. The information provided by these groups includes the number of real estate sales by each firm, its net income and its cost of listing and selling residential real estate.

Following other studies, we include only firms that obtain at least 75% of their revenues from residential transactions. The final data set includes 162 firms-54 franchised firms and 108 independent firms.

First, we seek to define a stochastic cost frontier that is a function of output and the prices of inputs used in the production. Total cost is defined as total operating expenses, which include commissions paid to selling agents, the value of non-selling services provided by broker-owners, the cost of advertisements, and the cost of buildings and occupation. A firm's output is measured in revenue units. A revenue unit is a residential property listed or sold by the company during the survey year. The double counting of an in-house sale is intentional and reflects the dual service output functions of the residential brokerage firms.

As in previous studies, we specify one output quantity and five input prices. The prices of inputs are the following: wages of sales persons (P^sub s^), wages of non-salespersons (P^sub NS^), the rents on buildings and occupancy (P^sub Capital^), advertising and promotion (P^sub Ad^), and all other inputs (P^sub Other^)' The selling expenses include multiple listing service (MLS) fees that vary directly with sales, sales managers' bonuses based on sales-staff performance, commissions paid to owners and commissions paid directly to the sales staff.

We compute the price of a salesperson, P^sub S^, by dividing total sales-related expenses by the number of full-time equivalent salespersons. The price of non-sales labor, P^sub NS^, is calculated by dividing clerical, secretarial and sales managers' salaries by the number of non-sales employees. We intentionally subtract profits paid to the owner of the firm from labor expenses because this expense is ad hoc and does not necessarily reflect the price of the owner's work. We compute the price of the building and occupancy expenses, P^sub Capital^ by dividing total occupancy expense by the number of real estate offices. The last two prices, advertising and promotion (P^sub Ad^) and other inputs, (P^sub Other^), are expressed as a percentage of revenue transactions. Table 1 shows the mean values and standard deviations for output, total costs and input prices for the complete sample, with no distinction between franchised firms and independent firms. Table 2 reports the mean values and standard deviations for output, total costs and input prices for franchised firms and independent firms, separately. Viewing the data, we note large standard deviations, suggesting that firms in the sample are heterogeneous.

The Statistical Model

The Stochastic Frontier

We combine Bayesian statistics and the stochastic-frontier model to estimate firm efficiency, group-type efficiency and the economies of franchising. Bauer (1990) surveys the large literature on stochastic-frontier models first introduced by Aigner, Lovell and Schmidt (1977) and Meeusen and van den Broeck (1977).

Because we employ a parametric approach, we specify the cost frontier to follow the translog functional form.3 We construct the translog frontier to be homogeneous of degree one. Following this approach, the basic translog cost-frontier model using five input prices is4

Enlarge 200% Enlarge 400%

where TC^sub i^ denotes the total cost of firm i, which depends upon input prices P^sub i^ and outputs Y^sub i^. z is a non-negative stochastic error term reflecting firm inefficiency, and v^sub i^ is a symmetric error term that captures measurement error. To impose symmetry and homogeneity of degree one in price, we

Enlarge 200% Enlarge 400%

Enlarge 200% Enlarge 400%

Enlarge 200% Enlarge 400%

force the restrictions b^sub ij^ = b^sub ji^ for i, j = 1, 2, . . .SIgma^sup 5^^sub i^ , =, b^sub i^ = 1, Sigma^sup 5^^sub j-5^ bij= 0.

We make the usual assumption about the two-sided error term, v^sub i^ - IID N(O, (sigma^sup 2^). For the non-negative, one-sided error term, we assume z^sub i^ follows an exponential distribution with shape parameter A that fixes both the mean and the variance of the exponential distribution. In our analysis, we allow almbda to take on two different values, lambda^sub 1^ for franchised firms and lambda^sub 2^ for independent firms.

The Bayesian Statistical Model

Our model's Bayesian context is an application of van den Broek et al. (1994) and Koop, Osiewalski and Steel's (1994) model. We extend their work by allowing the mean inefficiency parameter lambda to differ across firm type. That is, we provide for inefficiency estimates for two groups in our sample under a single cost frontier.

Following van den Broek et aL (1994) and Koop, Osiewalski and Steel (1994), we choose a flat (constant) prior for beta and sigma^sup 2^. That is, we assume no prior knowledge about these parameters.5 lambda ^sub k^ is the shape parameter that defines the mean of the exponential density function, where k is the firm type (k = 1 if the firm is a franchise, and k = 2 if the firm is independent). We choose gamma priors for both lambda^sub k^^sup 1^, p(almbda^sup -1^^sub k^ ') = f^sub G^(lambda^sup 1^, -1n r^sup *^^sub k^), where f^sub G^(v^sub 1^, v^sub 2^) denotes a gamma density distribution with mean v^sub 1^/v^sub 2^ and variance v^sub 2^/v^sup 2^^sub 2^. Choosing an informative prior for lambda^sup -1^^sub k^ ensures that the posterior is proper, and defines the complete prior as6

Enlarge 200% Enlarge 400%

Note that r^sub ki^ = exp(-z^sub i^) measures the efficiency of the ith firm, type k, relative to a 100% efficient firm facing the same input prices, and r^sup *^^sub k^ is the prior mean for the firm type's efficiency. We set r^sup* ^^sub 1^ = r^sup *^^sub 2^ = 0.875. 7 We are implying that we have no prior about whether franchised firms are more or less efficient than independent firms.

Koop, Steel and Osiewalski (1993) derive the joint conditional density of beta and sigma^sup 2^ for the model above.8 We derive the conditional density functions for lambda^sup -1^^sub 1^, lambda^sup -1^^sub 2^ and z^sub ik^ below:

Enlarge 200% Enlarge 400%

Enlarge 200% Enlarge 400%

where beta = (X' X)^sup -1^ X' Y - z, and f^sub n^,(x |mu, Sigma) is a normal density with mean mu and covariance matrix Sigma, i represents an n x 1 vector of ones, f^sub G^ is a gamma density, I^sub n^ denotes the n x n identity matrix, and I(x) is the indicator function. n is the number of firms in the sample, k^sub 1^ the number of franchised firms, and n - k^sub 1^ the number of independent firms.

Using these conditional densities, the Gibbs sampler follows. Tierney (1991) shows that the Gibbs sampler converges to the actual joint posterior density function as the iterations approach infinity. In this paper, we generate 11,000 parameter vectors and drop the first 1,000 to avoid sensitivity to starting values. The posterior density functions formed using 10,000 randomly sampled points in the Gibbs sampling process are adequate to ensure a small numerical error.9

It is important to note the differences between our approach and the alternatives previously used to evaluate franchising efficiency. From Equation (5), the mean of the firm inefficiency error term is y - XB sigma^sub 2^/lambda^sub k^. Previous studies assume a single firm type, when in fact it may be the case that firm type causes differences in firm efficiency. For example, suppose lambda^sub 1^ < lambda^sub 2^. Previous studies report a lambda that is likely to be a weighted average of lambda^sub 1^ and lambda^sub 2^, biasing the efficiency results together-that is, making type 1 firms appear more inefficient than they truly are, and type 2 firms less inefficient. Thus, Tobit results and simple t-test results that attempt to distinguish whether franchising is a more efficient market structure are biased. If we allowed lambda^sub 1^ and lmabda^sub 2^ to differ across firm types, then on average, type 1 firms would have smaller mean firm inefficiencies, type 2 firms would have larger mean firm inefficiencies, yielding more accurate calculated efficiency effects of franchising.10 This could explain why the literature has not formed a consensus on the economics of franchising.

Bayesian Stochastic Frontier Results

Previous studies that analyze the efficiency effects of franchising implicitly assume the parameter lmbda is the same across both firm types-franchising and independent. In fact, of the studies that actually found a statistically significant relationship between franchising and firm efficiency, most found a negative association. Anderson et al. (1998) used DEA efficiency estimates and found in a regression analysis that franchising decreased efficiency by 5-10%, depending upon which measure of efficiency they used.11 Anderson's (1998) traditional stochastic frontier efficiency results report franchised firms to be 89.35% efficient and independent firms 91.56% efficient, a relatively small but statistically significant result. In contrast, Lewis and Anderson's (1998) regression results find that franchising increases firm efficiency by approximately 3%. All of these former results concerning franchising efficiency are biased because of the lack of attention to the covariance between efficiency scores and the fact that separating based on firm type before efficiency calculation occurs is ignored.

Under a stochastic frontier methodology employing traditional maximum likelihood, allowing lambda to vary is difficult, if not impossible. Using Bayesian statistics, we are able to allow lambda to vary with firm type, explicitly constructing a single frontier, but calculating firm efficiency more accurately by allowing mean efficiency to differ for franchising and non-franchising firms.

Table 3 contains the posterior moments for the model's parameters that summarize the translog frontier results, and Figure 1 shows the posterior density of sigma^sub 2^. Because we use Bayesian statistics and the Gibbs Sampler, we are able to construct 90% confidence intervals for all parameters. Table 4 shows the posterior mean industry efficiency parameter for the franchised firms, almbda^sub 1^ to be approximately 9.8% inefficient (90.7% efficient), while the group inefficiency parameter for independent firms, almbda^sub 2^, indicates that independent firms are approximately 19.7% inefficient (82.1% efficient).12 That is, independent firms are nearly twice as inefficient as franchised firms are. On average, franchised firms could decrease their costs by approximately 10% with no change in inputs, while independent firms could decrease their costs by nearly 20% without changing inputs. Figure 2 and Figure 3 show the posterior marginal density plots of lambda^sub 1^ and lambda^sub 2^. Table 4 also reports the posterior mean relative ratio almbda^sub 1^/lambda^sub 2^ with the 90% confidence interval. Figure 4 shows the posterior marginal density plot for the relative ratio of inefficiencies. We can conclusively say that franchising firms are less inefficient than are their counterparts, independent firms. From the 10,000 sample points gathered using the Gibbs sampler, we find that prob (lambda^sub 1^/lambda^sub 2^ <= 1) is 98.4%. That is, there is strong evidence that franchised firms are more efficient (less inefficient) than independent brokerages. The posterior odds that those franchising firms are more efficient than independent firms are 61.5 to 1.

Table 5 shows the estimates for the first ten franchised and independent firms' efficiencies with the 90% confidence levels alongside. For a representative graphical illustration, Figures 5 and 6 depict the density plots for the first franchised firm and the first independent firm in the sample. By allowing mean firm inefficiency to vary across firm type, we find franchising to increase firm efficiency by 10%. Our results are in direct opposition to Anderson et al. (1998) and Anderson (1998), which show that franchising lowers firm efficiency. While both types of firms were shown to be operating somewhat efficiently, the higher efficiency of the franchised firms may help explain their strong presence in this sector.

Conclusions

This study takes advantage of recent advances in technology and data within the real estate industry to show that real estate brokerage firms that franchise are more efficient than those that do not franchise. We use reliable microeconomic data from the Economics and Research Division of the National Association of Realtors' nationwide survey and from Certified Real Estate Brokerage Manager designees. The Bayesian version of the stochastic frontier model allows us to vary the mean firm inefficiency by firm type and summarize the precision of the efficiency measures by calculating posterior standard deviations and 90% confidence intervals.

The basic industry efficiency results that we find support Anderson, Lewis and Zumpano (1999) in that the market is relatively efficient. However, these results conflict with some earlier studies that used less complete data and/ or cruder forms of estimation (Anderson et al. 1998; Zumpano and Elder 1994; Zumpano, Elder and Crellin 1993; Yinger 1981; Crockett (1982); Miller and Shedd 1979; Wachter 1985).

We assume that real estate firms have access to the same technology, but allow the mean inefficiency A to vary based on firm type-franchised and independent. By constructing a single cost frontier and allowing firm type to vary between franchised and independent firms, we are able to make a definitive statement about the efficiency effects of franchising. We find that independent firms are twice as inefficient as are franchised firms. Using the Bayesian methodology, we calculate the probability that franchised firms are more efficient than independent firms. Using this probability, the posterior odds that franchising is more efficient are 61.5 to 1. The results that we report may explain why franchised firms have sustained market share within the residential real estate brokerage industry.

Enlarge 200% Enlarge 400%

Enlarge 200% Enlarge 400%

Enlarge 200% Enlarge 400%

Enlarge 200% Enlarge 400%

Enlarge 200% Enlarge 400%

Enlarge 200% Enlarge 400%

Enlarge 200% Enlarge 400%

Enlarge 200% Enlarge 400%

Enlarge 200% Enlarge 400%

Enlarge 200% Enlarge 400%

Enlarge 200% Enlarge 400%

Enlarge 200% Enlarge 400%

Enlarge 200% Enlarge 400%