Using an Ordered Probit Regression Model to Assess the Performance of Real Estate Brokers

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1 Usng an Ordered Probt Regresson Model to Assess the Performance of Real Estate Brokers Chun-Chang Lee, Department of Real Estate Management, Natonal Pngtung Insttute of Commerce, Tawan Shu-Man You, Department of Real Estate and Bult Envronment, Natonal Tape Unversty, Tawan Pe-Chun Shen, Department of Real Estate Management, Natonal Pngtung Insttute of Commerce, Tawan ABSTRACT The ordered probt regresson model s used to nvestgate domestc real estate brokers n Tawan, n order to determne the factors affectng the lstngs of realtors and provde a reference for the domestc real estate brokerage market. Based on emprcal analyss, ths study found that the Wald Ch-Square of sx ndependent varables reached a sgnfcance level of 5%, whle the other two ndependent varables reached 10%. The emprcal results ndcate that the base pay plus commsson system brngs n more lstngs than a commsson system and fxed pay. A regular chan type has more lstngs than a voluntary chan type or a non-chan type. The sx varables whch reach sgnfcant level are senor hgh (vocatonal) school, unversty, poston, years of work, the square of the number of years of work, and hours of work per week. Keywords: Real Estate Brokerage Market, Ordered Probt Regresson Model, Lstngs, Type of Management, Salary Structure INTRODUCTION Tawan s real estate brokerage market stll has great growth space, and plays an mportant role n socety. The preowned house market s very actve. Thus, whether the effcency of lstngs of real estate brokerage s rsng must be explored. Compared wth other countres, domestc real estate brokerage frms feature dversfed salary structures and types of management. In Tawan, forms of management nclude the regular chan, the voluntary chan, and the non-chan, whch busness mode, cost bearng, and HR management vary. Thus, whether salary structure affects the performance of real estate brokers should be clarfed. In the study of performance of real estate brokerage, Anderson, Fok, Zumpano, and Elder (1998) employed Data Envelopment Analyss to measure performance, and found that frm sze could ncrease effcency. Benamn, Jud, and Srmans (2000) argued that the salary of real estate brokers s hgher than that of other ndustres. Anderson and James (2000) found that provdng ob tranng and educaton for real estate brokers can ncrease productve capacty, reduce acton rsk, and ncrease frm benefts. Wllam (1995) ndcated that large real estate brokerage frms often acheved better results, and that f frms provde new related servces, the real estate brokers can ncrease transacton effcency. Johnson, Dotson and Dunlap (1988) suggested that the servce qualty of a real estate brokerage s very mportant for ncreasng effcency. Glower and Hendershott (1988) dscussed determnants of real estate broker ncome, such as gender, educatonal background and locaton. Paarsch and Shearer (1999) examned the effects of commsson splt percentage of real estate brokers on ther performance n the same salary system, and found that the commsson rato has sgnfcant mpact on ndvdual performance. L (1999) studed the effects of the type of management of real estate brokerage frms on performance. Fndngs showed that there s no sgnfcant dfference between the average sales volume of a franchse system and a regular chan system. Moreover, the average sales volume of a natonal-brand franchse system and regonal regular chans also show no sgnfcant dfference. In addton, performance of regonal brand frms was found to be nferor to natonal franchse chans and non-chan systems. L (2001) studed the ncome of real estate brokers, and found that educaton, martal status, specalty, years of work, hours of work and locaton of branch offces have sgnfcant effects on ther ncome. The ncome of brokers wth base pay s lower than those wthout base pay, but the dfference s not sgnfcant. 168 The Journal of Internatonal Management Studes, Volume 5, Number 2, August, 2010

2 L (2004) examned the effects of gender, age, years of schoolng, educatonal background, years of work, the square of the number of years of work, lcenses of brokers, and three types of management, on ncome of brokers. After applyng the ordered probt regresson model for evaluaton, L found that the three ndependent varables of age, educatonal background and lcense were not sgnfcant. Based on the foregong dscusson, factors such as operatng patterns, salary structure, work experence, and educatonal background appear to affect the performance of real estate brokerage frms and ndvdual brokers. The degree of the effects and ther causes are dscussed n ths paper. In prevous studes, the performance of real estate brokers has been defned as performance-based salary, and lstngs have seldom been dscussed. In practce, real estate brokerage frms make plans for employees to mantan busness performance, such as defnng the requred number of lstngs and performance-based salary as ncentves for employees. Data related to performance-based salary s dffcult to collect, and those from questonnares may be naccurate. Thus, dfferent from prevous studes, ths paper ams to explore lstngs emprcally. Ths s the man contrbuton of ths study. RESEARCH DESIGN Ordered Probt Regresson Model Ths study employed the ordered probt regresson model for analyss of determnants affectng lstngs of real estate brokers. Ths approach s often appled to analyss of the dependent varable as an ordnal scale. The dependent varable n ths paper s lstngs, expressed as an ordnal scale wth three dmensons. The number of lstngs s expressed as Y * (when Y = 1, t means the number of lstngs s 5 or less; when Y = 2, the number of lstngs s 6, 7, or 8; when Y = 3, the number of lstngs s 9 or more) and equals the ndependent varable x functon (x s a vector, ncludng gender, educatonal background, martal status, poston, years of work, square number of years of work, hours of work per week, age of frm, number of salespersons, locaton of branch offces, salary structure, type of management) as shown below: * Y = B x + u where µ s a error term, assumed to be a normally dstrbuted, whch cannot be explaned by gender, educatonal background, martal status, poston, years of work, the square of the number of years of work, hours of work per week, age of frm, number of salespersons, locaton of branch offces, salary structure and type of management. However the error term may be affected by factors other than these varables or by other external factors. Y * cannot be determned drectly, but ts order type s known. Thus, the model can be further expressed by: Pr ob ( Y = 3) = F( B f u < B x Pr ob ( Y = 2) = F( B x + c) F( B f B x < u < B x + c (2) Pr ob ( Y = 1) = 1 F( B x + c) f u > B x + c c > 0 s a parameter where F denotes cumulatve probablty dstrbuton functon. Ths model uses the maxmum lkelhood method to estmate vector β of ndependent varable x. Ths can further explan the deducton process. The lstngs model s as follows: 1 Y = β x + u, = 1,2,... n (3), where s the observed value, n s the number of observed values. Y cannot be observed drectly, and has m types, where m represents number of steps. Ifα 1 < Y < α, = 1,2,..., m, Y s type, and cannot be observed drectly because Y only has an ordnal nature. Through the normalzaton rule, ) 1 ~ IN(0,1. Next, the ordnal varable s defned as: Z = 1, f Y s type Z = 0, others Pr ob( Z 1) = Φ( α β x ) ( α 1 β x (1) Var ( u =, ) = ) (4) u The Journal of Internatonal Management Studes, Volume 5, Number 2, August,

3 L = Φ s cumulatve standard normal dstrbuton. The lkelhood functon s as follows: n m Z [ ] Φ( β x ) ( α 1 β x ) = 1 = 1 α (5) then the log lkelhood functon s presented by: L Y φ [ Φ( β x ) ( α β x ] n m = log L = Z log 1 ) = 1 = 1,, From compactness, we can obtan: = α β x = φ( α β x ) Φ( = φ( x δ, k = 1 f δ, k = 0 L = β L α k other Thus = n = k m φ( x α (6) φ, and = x (, Kronecker delta s defned as: φ, 1 φ, Z x Φ Φ = 1 = 1,, 1 δ φ δ = 0 φ n m, k, 1, k, 1 Z = 1 = 1 Φ, Φ, 1 = 0 Snce Eqs.(9) and (10) are the nonlnear functons of α and β, the asymptotc soluton cannot be deduced by arthmetc, but may be deduced by computer technology and the Newton Raphson method. The teraton method s used to deduce the numercal soluton. Questonnare Desgn and Data Collecton The questonnare contans three parts: (1) personal nformaton, such as gender, martal status, and educatonal background; (2) varables related to poston, years of work, hours of work and smlar; and (3) varables related to real estate brokerage frms, such as locaton of branch offces, age of frms, type of management, salary structure, and number of employees. Ther performance s expressed by the average number of lstngs n the most recent three months. Ths study nvestgated real estate brokerage under dfferent types of management n northern, central, and southern Tawan. To ncrease the recovery rate, the samples were maled out four tmes, and 306 questonnares were retreved. After elmnatng 15 nvald samples, there were 285 vald questonnares for an effectve response rate of 32%. (8) (7) (9) (10) Statstcal Descrpton of Samples For the demographc background, 72% are male, and 29% are female. The maorty are 31~35 years old (30.6%), followed by 36~40 years old (24.6%). Two-thrds (67.7%) are marred, whle 30.9% are sngle. Most have a college educaton (47.4%), followed by senor hgh (vocatonal) school and unversty educaton (both are 25.3%). For the analyss, samples from non-chan frms and franchse chans are combned for comparson wth samples of regular chans. The number of questonnares collected from the branch offces of frms n northern, central, and southern Tawan s 173, 56, and 56, respectvely. The cross-over analyss for the type of management and salary structure ndcates 65 (75.58%) regular chan offces have adopted base pay plus commsson, 112 franchse chan offces (66.67%) have adopted commsson systems, and 14 (56%) regular chan offces have adopted commsson systems. Emprcal Results Analyss Ths study explores the effects of gender, educatonal background, martal status, years of work, square of the number of years of work, hours of work per week, age of frms, number of employees, locaton of branch offces, salary 170 The Journal of Internatonal Management Studes, Volume 5, Number 2, August, 2010

4 structure and type of management on real estate brokers. The data were analyzed wth SPSS16.0 for regresson evaluaton. As shown n Table 1, the Ch-square value s , the p value s 0.000, and a sgnfcance level s 5%. The ftness of the regresson model s superor. In addton, whether ordnal or categorcal data meet the assumed percentage must be verfed when usng an ordered probt regresson model for estmaton. The test of parallel lnes, conducted for verfcaton, demonstrates that ths ordered probt regresson model s sutable (Ch-square = , d.f = 14, p-value = 0.572). Wald Ch-square values for the sx ndependent varables reached a sgnfcance level of 5%, whle the two ndependent varables reached a sgnfcance level of 10%. The emprcal results ndcate that the coeffcent of gender (male = 1, female = 0) s Ths was not sgnfcant (p <.05), ndcatng that gender has no sgnfcant effect on the sum of lstngs. L (2003) suggested that the ncome of male brokers s greater than that of female brokers because women have to spend extra tme takng care of ther famles whle workng. However, the results of ths study show that the gender dfference s unrelated to the sum of lstngs. In recent years, women are payng ncreasng attenton to work. Wth rsng awareness of gender equalty, women no longer play the man role n homemakng, and ther work enthusasm s equvalent to men. As for educatonal background, college educaton s consdered the base lne n ths analyss. Two dummy varables are set, wth senor hgh (vocatonal) school the ndependent varable (senor hgh (vocatonal) school = 1, college, unversty = 0), the coeffcent s , and a sgnfcance level s 10%. If unversty s consdered an ndependent varable (unversty = 1, senor hgh (vocatonal) school = 0), the coeffcent s , and a sgnfcance level s 5%. Brokers wth a senor hgh (vocatonal) school educaton do not perform as well as brokers wth a college educaton because the latter have better professonal knowledge. However, the performance of the real estate brokers wth a unversty educaton s lower than that of brokers wth college educaton, whch s not consstent wth the emprcal results of Glower and Hendershott (1988). Ths may be because the educaton offered by unverstes and colleges s very smlar, and brokers wth a college educaton begn workng earler (unversty-educated brokers tend to be younger), thus accumulatng greater experence and connectons, and achevng better performance than brokers wth a unversty educaton. For martal status, marred s regarded as ndependent varable (marred = 1, sngle = 0), the coeffcent (0.209) s not sgnfcant. Ths demonstrates that the performance of marred brokers s the same as that of sngle brokers. It s often thought that due to famly responsbltes, marred brokers work harder and make greater efforts to acheve hgher salary or poston. However, our fndngs are consstent wth those of Follan, Lutes and Meer (1987), who found that performance and martal status have no sgnfcant relatonshp. For poston (manager = 1, broker = 0), the coeffcent s 0.533, and the sgnfcance level s 5%. Ths reveals that poston can affect lstngs. The hgher the poston s, the hgher probablty of ncreased lstngs s. The ablty and experence of the employees n hgher poston are greater than those n lower postons, so that employees n hgher postons can acheve better performance. Our results are consstent wth theoretcal expectatons. The coeffcent of years of work s 0.118, and the sgnfcance level s 5%. The greater the number of years of work, the greater the probablty of ncreased lstngs. Ths result s consstent wth the fndngs of Follan, Lutes and Meer (1987), Glower and Hendershott (1988), and Crelln, Frew and Jud (1988). In theory, more years of work ndcate rcher work experence. Wth mproved busness foundaton and abundant, stable connectons, the performance of brokers wth more years of work s better than brokers wth fewer years of work. Ths result s consstent wth expectatons. The coeffcent of square of the number of years of work s , and a sgnfcance level s 5%. More years of work ndcate a smaller rate of ncrease n expected lstngs. Ths s consstent wth the vew related to dmnshng margnal return. These results are consstent wth expectatons. The coeffcent of hours of work per week s 0.01, and the sgnfcance level s 10%. Ths demonstrates that the greater the number of hours of work per week, the hgher the probablty of ncreasng lstngs. These fndngs are consstent wth those of Follan, Lutes and Meer (1987), Glower and Hendershott (1988), and Crelln, Frew and Jud (1988). Real estate brokers wth longer work weeks have more tme to expand ther customer base, and the probablty of ncreasng ther commtments ncreases. As expected, the number of ther lstngs ncreases. These results are consstent the expectatons. The Journal of Internatonal Management Studes, Volume 5, Number 2, August,

5 The coeffcent of age of frms s , and a sgnfcance level of 5% s not reached. Ths means that the age of frms has no sgnfcant mpact on lstngs. Ths result s not consstent wth that of Epley (2001). Generally, branch offces wth greater age have better connectons wth surroundng busnesses and local resdents, thus possessng hgher customer trust. Our results are not consstent wth expectatons, possbly because nformaton access s now easly accessble, and many branch offces engage n onlne transacton. In addton, the real estate market n Tawan has recovered. Wth all real estate frms dong well, age may not necessarly confer an advantage n performance. The coeffcent of number of salespersons s 0.007, and a sgnfcance level of 5% s not attaned. Ths shows that the number of salespersons has no sgnfcant effect on the sum of lstngs. Ths s dfferent from Crelln, Frew and Jud (1988), possbly because the real estate market n Tawan has recovered and the number of branch offces s ncreasng rapdly. Relatvely, estate brokers face more and more rvals, and regonal lstngs are dvded up easly. Accordngly, the number of salespersons has no sgnfcant effect on the number of lstngs. Based on the analyss of the locaton of branch offces, southern Tawan s consdered the base lne, two dummy varables are set, and northern Tawan s the ndependent varable (northern Tawan = 1, central and southern Tawan = 0), and the coeffcent s When the north s the ndependent varable (central Tawan = 1, northern and southern Tawan = 0), the coeffcent s The two varables do not reach the sgnfcance level of 5%, ndcatng that the performance of brokers n branch offces n north s not sgnfcantly better than that of brokers n southern Tawan. Smlarly, the performance of brokers n central Tawan s not sgnfcantly better than that of brokers n the south. These fndngs are dfferent from those of Glower and Hendershott (1988) and L (2000). In the analyss of the salary structure, base pay plus commsson system s treated as the ndependent varable (base pay plus commsson system = 1, commsson system and fxed salary = 0), the coeffcent s 0.470, and a sgnfcance level of 5% s reached. Ths shows that base pay plus commsson system has a greater probablty of ncreasng lstngs than ether a commsson system or a fxed salary system. The base pay plus commsson system ensures basc salary whle provdng a commsson, enhancng the ncentves for brokers. A commsson system has no base pay, meanng that the employees have a reduced sense of belongng to a frm. A fxed salary system s appled to new employees from regular chans because new staff cannot acheve better performance due to ther nsuffcent experence and mmature busness crcle foundaton. Consequently, the base pay plus commsson system appears to result n better performance than the commsson system and fxed salary system. These fndngs dffer from those of L (2001) who found no sgnfcant dfference n ncome between brokers wth base pay and those wthout. Ths may be because performance-based bonuses and group bonuses were taken nto account. In terms of management types, regular chan (regular chans = 1, franchse chan and non-chan frm = 0) s consdered the ndependent varable, the coeffcent s 0.442, and a sgnfcance level of 10% s reached. Emprcal studes show that the probablty of ncreasng lstngs for regular chans s greater than that of franchse chans and non-chan frms. For regular chans, employees of branch offces are apponted by headquarters, and all operatng profts go to the headquarters; any losses are ts responsblty as well. Regular chans focus on personnel tranng, as well as pre-ob and post-ob tranng, and offer a seres of courses for brokers to deepen ther professonal knowledge. In addton, regular chans feature well-known brands and a rgorous organzatonal management system, and are trusted by customers. It s easy for such frms to expand lstngs. In franchse systems, organzatonal management s not as rgorous as n regular chans, and the ndvdual franchse offces must assume sole responsblty for profts or losses. Brokers should thus acheve better performance cope wth the expenses of branch offces. Employee tranng lacks comprehensve plannng. Thus, the performance of a regular system s superor to that of a franchse system. The non-chan frms represent local orgnal brands, and bear greater rsk than regular chans and franchse chans. Personnel tranng s not as thorough and mature as regular chans and franchse chans. The non-chan frms are smaller and lack popularty. They must rely on stronger local busness relatonshps to strengthen sales. The sum of lstngs of regular chans s sgnfcantly better than that of non-chan frms. However, L (1999) found no sgnfcant dfference n average sales volume between franchse chans and regular chans. The reason for ths dfference s that L used dfferent dependent varables and a smaller number of samples. 172 The Journal of Internatonal Management Studes, Volume 5, Number 2, August, 2010

6 Table 1: Ordered regresson analyss (Ordered Probt Model) Coeffcent Wald Ch-square value Intal value ( = 1) ** Intal value ( = 2) ** Gender (male = 1, female = 0) Senor hgh (vocatonal)school (senor hgh (vocatonal ) school = 1, * college, unversty = 0) Unversty (unversty = 1, senor hgh(vocatonal) school, college = 0) ** Martal status (marred = 1, sngle = 0) Poston (manager = 1, broker = 0) ** Years of work ** Square number of years of work ** Weekly hours of work * Age of frm Number of salespersons Northern Tawan (northern Tawan = 1, central and southern Tawan = 0) Central Tawan (central Tawan = 1, northern and southern Tawan = 0) Salary structure (base pay plus commsson system = 1, commsson ** system, fxed salary = 0) Type of management (regular chan = 1, franchse chan and non-chan = 0) ** Ch-squared Degree of freedom 14 Number of observed samples 285 Note: 1.ndepedant varable s average lstngs of estate brokers n the past three months 2. ** represents sgnfcance level of 5%, * represents sgnfcance level of 10%. 3.Ch-squared represents Ch-squared value of ftness nformaton of model reaches sgnfcance level of 5%. Table 2 shows the margnal effect of lstngs. When the lstngs are fewer than 5, senor hgh (vocatonal) school, unversty and type of management have the greatest effects. The probablty of ncreasng lstngs s 15.54% when the number of brokers wth senor hgh (vocatonal) school educaton exceeds the number wth a college or unversty educaton. The probablty of ncreasng lstngs s 12.95% when the number of brokers wth a unversty educaton exceeds the number wth a senor hgh (vocatonal) school educaton. The probablty of ncreasng lstngs s 15.34% when brokers of regular chans are fewer than those of non-chan frms. When the number of lstngs s 6 to 8, senor hgh (vocatonal) school, unversty and type of management have the greatest mpact. The probablty of ncreased lstngs s 3.03% when the number of brokers wth a senor hgh (vocatonal) school educaton s less than the number wth a unversty educaton. The probablty of ncreasng lstngs s 2.53% when the number of brokers wth a unversty educaton s less than the number wth a senor hgh (vocatonal) school educaton. The probablty of ncreasng lstngs s 2.99% when the number of brokers of regular chans s greater than the number of franchse chans. When the number of lstngs exceeds 9, senor hgh (vocatonal) school, unversty and type of management have the greatest mpact. The probablty of ncreasng lstngs s 12.51% when the number of brokers wth a unversty educaton s less than the number wth a senor hgh (vocatonal) school educaton. The probablty of ncreasng lstngs s 10.43% when the number of brokers wth a unversty educaton s less than the number wth a senor hgh (vocatonal) school educaton. The probablty of ncreasng lstngs s 12.35% when the number of brokers of regular chans s greater than the number brokers for franchse chans. Accordng to the analyss of margnal effects, senor hgh (vocatonal) school educaton, unversty educaton, and type of management have greater effects on lstngs. To ncrease lstngs, educatonal level, and type of management need to be further understood and selected. The Journal of Internatonal Management Studes, Volume 5, Number 2, August,

7 Table 2: Margnal effect of lstngs number (lstngs number s consdered as dependent varable) Independent varable Below 5 6~8 Above 9 Gender (male = 1, female = 0) Senor hgh (vocatonal) school (Senor hgh (vocatonal) school = 1, college, unversty = 0) Unversty (unversty = 1, senor hgh (vocatonal) school, college = 0) Martal status (marred = 1, sngle = 0) Poston (manager = 1, broker = 0) Years of work Square number of years of work Weekly hours of work Age of frm Number of salespersons Northern Tawan (northern Tawan = 1, central and southern Tawan = 0) Central Tawan (central Tawan = 1, northern and southern Tawan = 0) Salary structure (base pay plus commsson system = 1, commsson system and fxed salary system = 0) Type of management (regular chan = 1, franchse chan and non-chan = 0) Note: bold face represents the varable s sgnfcant n the model. CONCLUSIONS Conclusons In ths study, gender, educatonal background, martal status, poston, years of work, square of the number of years of work, hours of work weekly, age of frms, number of salespersons, locaton of branch offces, salary structure and type of management are consdered ndependent varables, and an ordered probt regresson model s used to evaluate mpact of these varables on lstngs of real estate brokers. Results ndcate that Wald Ch-square value of eght ndependent varables reached the sgnfcance level. Based on emprcal results, brokers wth a college educaton exhbt performance superor to brokers wth a senor hgh (vocatonal) school educaton. Hgher poston leads to greater probablty of ncreasng lstngs; more years of work leads to a greater probablty of ncreasng lstngs. However, more years of work also leads to smaller rate of ncrease n lstngs. Real estate brokers wth base pay plus commsson have a greater probablty of ncreasng lstngs than the brokers wth a commsson and fxed salary. In addton, brokers of regular chans have a greater probablty of ncreasng lstngs than brokers of franchse chans and non-chan frms. Based on the analyss of margnal effect, the effects of senor hgh (vocatonal) school educaton, unversty educaton, and type of management on lstngs are greatest. If managers of real estate frms ntend to ncrease overall lstngs, the educatonal level of ther brokers, along wth the type of management, should be addressed. Future Studes Ths study dscusses the effects of dfferent varables on lstngs. Ths s dfferent from past studes, and s the man contrbuton of ths paper. Further study may explore ncreasng the sample of non-chan frms, and compare the dfferences between regular chans, franchse chans, and non-chan frms. The effects of ndvdual commsson percentage and group bonus of dfferent types of management on busness performance should also be analyzed. In addton, how performance may be related to gender, martal status and whether brokers have chldren would also be good topcs for nvestgaton. 174 The Journal of Internatonal Management Studes, Volume 5, Number 2, August, 2010

8 REFERENCES Anderson, R. I., and R. W James, (2000), The Educaton of Real Estate Salespeople and the Value of the Frm, Journal of Real Estate Research, 20(1): Anderson, R. I., R. Fok, L. V. Zumpano and H. W. Elder (1998), Measurng the Effcency of Resdental Real Estate Brokerage Frms, Journal of Real Estate Research, 16(2): Benamn, J. D., G. D Jud and G. S Srmans, (2000), What Do We Know About Real Estate Brokerage?, The Journal of Real Estate Research, 20(1):5-30. Crelln, G. E., J. R. Frew, and G. D. Jud, (1988), The Earnngs of REALTORS: Some Emprcal Evdence, Journal of Real Estate Research, 3(2): Epley, D. R.,(2001), US Real Estate Agent Income and Commercal/Investment Actvtes, Journal of Real Estate Research, 21(3): Follan, J. R., T. Lutes, and D. A. Meer, (1987), Why Do Some Real Estate Salespeople Earn More Than Others?, Journal of Real Estate Research, 2(1): Glower, M. and P. H. Hendershott, (1988), The Determnants of REALTOR Income, Journal of Real Estate Research, 3(2): Johnson, L. L., M. J. Dotson, and B.J. Dunlap, (1988), Servce Qualty Determnants and Effectveness n the Real Estate Brokerage Industry, Journal of Real Estate Research, 3(2): L, C.C., (2000), Dscusson on Real Estate Broker Income, 1 st Sesson of Academc Symposum of Land Admnstraton n 2000, Department of Land Economcs, Natonal Chengch Unversty. L, C.C., (1999), Effects of Type of Management of Real Estate Brokerage on Busness Performance, Proceedngs of the Natonal Scence Councl: Humantes and Socology, 9-3, L, C.C., (2001), Salary structure, Incentves, and Real Estate Broker Income, Symposum on Tawan Land Research, Natonal Tape Unversty. L, C.C., (2003), Determnng Pattern of Real Estate Brokerage SERVQUAL, Cty and Plannng, 30(1), L, C.C., (2004), Determnng of Real Estate Broker Income Ordered Regresson Model, Journal of Housng Studes, 12(2), Paarsch, J. H and B.S. Shearer, (1999), The Responses of Worker Effort to Pece Rates, Journal of Human Resources, 4: Wllam, T. H., Jr., (1995), Brokerage Frms' Characterstcs and the Sale of Resdental Property, Journal of Real Estate Research, 10(1): NOTES 1 For the deducton of the lkelhood functon refer to Maddala (1999) and L (2004). The Journal of Internatonal Management Studes, Volume 5, Number 2, August,

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