CHAPTER 2 EFFICIENCY IN TAIWAN’S INTERNATIONAL TOURIST HOTEL INDUSTRY
2.4 C ONCLUSIONS
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visitors are significantly different at the 1% significant level, but the pure technical efficiency measure is not significantly different (see Table 2.7). These imply that the difference of technical efficiency among three types of visitors mainly results from the difference of scale efficiency.
Furthermore, the Wilcoxon rank sum test is used to investigate the multiple comparisons of technical and scale efficiencies among three types (see Table 2.8). These results show that these technical and scale efficiency measures between TYPE 1 and TYPE 2 as well as TYPE 1 and TYPE 3 are significantly different at the 1% significant level, but these technical and scale efficiency measures between TYPE 2 and TYPE 3 are not significantly different. These indicate that if an international tourist hotel mainly receives group visitors, the efficiency will be lower. A possible reason for this outcome is that group visitors book rooms and ask the relative services through travel agencies. However, travel agencies have the better bargaining power and technique to reduce prices or request more services. International tourist hotels which mainly receive group visitors may use more quantities of inputs and still produce the same quantities of outputs. Thus, international tourist hotels which mainly receive group visitors perform lower than others.
2.4 Conclusions
Since the prohibition of building tourist hotels in Taiwan was deregulated in 1977 to encourage building new international tourist hotels, the number of international tourist hotels sprang up. Furthermore, the average occupancy rate of international tourist hotels in Taiwan was the downward trend in recent years. Individual international tourist hotels’ profitability is significantly different from each other. The phenomena motivate this paper to evaluate the efficiency of international tourist hotels. To accurately examine the efficiency of international tourist hotels in Taiwan, the three-stage DEA approach with the quasi-fixed input is used to eliminate the effects of external factors and random noise on efficiency measures based on the 2003-2009 data conducted by the Annual Operation of the International Tourist Hotels.
In the first stage, the data of original variable inputs, quasi-fixed input and outputs are used to evaluate the technical efficiency of international tourist hotels. The efficiency-evaluation results show that the DEA models without quasi-fixed and adjusted inputs overestimate the technical and pure technical efficiencies, but underestimate the scale efficiency of international tourist hotels so that the necessity of considering the existence of quasi-fixed input is justified. The second stage uses SFA model to purge the effects from exogenous
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variables and statistical noise. The SFA results show that the exogenous variables have significant influences on input slacks and pure technical efficiency. The degree of market concentration has positive impacts on labor, F&B expense and operating expense input slacks and has a negative impact on pure technical efficiency because international tourist hotels with the lower degree of market concentration may reduce wasted resources under the competitive pressure. A hotel size has positive effects on all input slacks and has a negative effect on pure technical efficiency because the losses from the complexity of allocating resources dominates the gains from sharing or joint utilization. An international tourist hotel in the resort area has negative relationships with all input slacks and a positive relationship with pure technical efficiency because popular visiting spots can help international tourist hotels to attract more visitors, or managers of resort hotels may adopt superior managerial strategies to improve their efficiency. An international tourist hotel participating in the international and/or domestic hotel chain has positive relationships with labor and F&B expense input slacks, but has a negative relationship with the other expense input slack.
Because marketing chain and technology transfers can help international tourist hotels to attract visitors and obtain the managerial experience, but requiring standard services and facilities can cause them to increase more labors and F&B expenses. SARS has positive effects on labor and F&B expense input slacks and has a negative effect on pure technical efficiency because avoiding SARS infection can cause a decrease in demands for accommodation and F&B in international tourist hotels. The financial tsunami has positive effects on labor and other expense input slacks and has a negative effect on pure technical efficiency because the uncertainty of economic environment can lead to a decrease in the unnecessary tourism expenditure.
After adjusting the variable input data from the SFA results in the second stage, the efficiency-evaluation results in the third stage show that international tourist hotels in Taiwan could reduce inputs by 45.9%, on average, and still produce the same level of outputs. The mean pure technical efficiency measure is 0.990 and the mean scale efficiency measure is 0.546, implying that the technical inefficiency mainly results from the inappropriate production scale. In addition, international tourist hotels have an ample space to improve their technical and scale efficiencies. The efficiency-evaluation results also show that the conventional DEA models overestimate the technical and scale efficiencies, but underestimate the pure technical efficiency of international tourist hotels so that the usage of the three-stage DEA approach is justified. Finally, international tourist hotels which mainly receive group visitors have the worst performance because the better bargaining power of
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travel agencies can cause international tourist hotels to increase the usage of inputs.
Some important lessons may emerge directly from the empirical results in this chapter.
First of all, for studies of efficiency to be more informative to decision and policy makers, the three-stage DEA approach with quasi-fixed inputs should be adopted to control the impacts of exogenous factors, statistic noise and quasi-fixed inputs. Second, managers may have to appropriately adjust the operating scale since most of international tourist hotels are still scale inefficient. Third, managers may have to carefully assess the advantage and disadvantage of hotel chains before participating in or developing them. Finally, the information about service qualities, the form of ownership, labor relations and the data of ordinary tourist hotels might be needed for the empirical results to be more reliable and the policy implications to be more meaningful.
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Table 2.1 Descriptive Statistics of Relevant Variables
Areas Variables Observations Mean SD Maximum Minimum Guest room revenue 3,723.583 3,221.831 14,786.037 255.342
F&B revenue 4,227.565 3,645.644 12,502.824 51.874 Other revenue 870.799 1,101.529 4,540.527 2.051
Guest room 355.607 197.612 873 50
Labor 416.950 274.061 982 53
F&B expense 1,362.625 1,064.094 3,682.263 29.743 Other expense 2,197.203 2,196.285 10,848.029 103.450
H 0.072 0.004 0.077 0.066
SIZE 1 0.550 0.499 1 0
SIZE 2 0.350 0.479 1 0
RESORT 0.050 0.219 1 0
Taipei City
CHAIN
140
0.650 0.479 1 0
Guest room revenue 2,329.135 1,116.231 4,712.820 678.775 F&B revenue 3,486.773 2,192.882 8,489.424 395.214 Other revenue 687.176 883.693 3,370.388 40.655
Guest room 391.095 117.025 592 238
Labor 380.381 195.988 737 100
F&B expense 1,462.839 887.074 3,136.582 172.856 Other expense 1,660.465 1,156.373 4,464.824 367.554
H 0.198 0.007 0.210 0.190
SIZE 1 0.500 0.506 1 0
SIZE 2 0.500 0.506 1 0
RESORT 0 0 0 0
Kaohsiung City
CHAIN
42
0.500 0.506 1 0
Guest room revenue 1,544.367 641.687 3,109.280 777.683 F&B revenue 2,045.303 622.977 3,479.178 846.283 Taichung
City
Other revenue
35
566.177 744.607 2,482.511 7.789 Note: 1. Guest room revenue, F&B revenue, other revenue, F&B expense and other expense are measured in
terms of hundred thousand NT dollars.
2. Guest room reveneue, F&B revenue and other revenue are deflated by the consumer price index with 2006 as the base year. F&B expense and other expense are deflated by the wholesale price index with 2006 as the base year.
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Table 2.1 (Continued)
Areas Variables Observations Mean SD Maximum Minimum
Guest room 271.714 93.802 404 155
Labor 259.857 89.365 449 162
F&B expense 742.620 203.220 1,189.266 430.357 Other expense 1,108.800 607.066 2,649.340 450.758
H 0.223 0.005 0.232 0.216
SIZE 1 0.600 0.497 1 0
SIZE 2 0.200 0.406 1 0
RESORT 0 0 0 0
Taichung City
CHAIN
35
0.571 0.502 1 0
Guest room revenue 1,265.633 331.368 1,662.908 752.985 F&B revenue 744.145 53.440 804.810 635.629
Other revenue 23.576 1.056 25.443 21.988
Guest room 390.000 0.000 390 390
Labor 174.571 11.816 185 155
F&B expense 423.270 94.993 579.822 326.651 Other expense 577.957 166.364 856.823 373.214
H 1 0 1 1
SIZE 1 1 0 1 1
SIZE 2 0 0 0 0
RESORT 0 0 0 0
Taoyuan City
CHAIN
7
0 0 0 0
Guest room revenue 2,035.166 506.606 2,746.688 1,338.384 F&B revenue 2,423.542 1,096.391 3,925.719 1,305.056 Other revenue 557.142 575.173 1,748.228 83.146
Guest room 229.500 27.026 257 198
Labor 288.571 62.790 374 220
Hsinchu City
F&B expense
14
784.991 361.084 1,238.309 415.419 Note: 1. Guest room revenue, F&B revenue, other revenue, F&B expense and other expense are measured in
terms of hundred thousand NT dollars.
2. Guest room reveneue, F&B revenue and other revenue are deflated by the consumer price index with 2006 as the base year. F&B expense and other expense are deflated by the wholesale price index with 2006 as the base year.
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Table 2.1 (Continued)
Areas Variables Observations Mean SD Maximum Minimum Other expense 1,165.691 530.295 2,132.364 519.069
H 0.565 0.019 0.595 0.543
SIZE 1 0.786 0.426 1 0
SIZE 2 0 0 0 0
RESORT 0 0 0 0
Hsinchu City
CHAIN
14
1 0 1 1
Guest room revenue 1,390.102 723.510 2,759.915 745.540 F&B revenue 1,121.778 259.730 1,509.906 677.846
Other revenue 57.421 72.068 226.865 0.108
Guest room 280.714 51.372 343 221
Labor 190.191 79.880 306 100
F&B expense 533.895 142.603 840.086 334.224 Other expense 784.042 430.689 1,712.497 271.772
H 0.349 0.009 0.365 0.338
SIZE 1 1 0 1 1
SIZE 2 0 0 0 0
RESORT 0 0 0 0
Hualien City
CHAIN
21
0.333 0.483 1 0
Guest room revenue 1,524.206 992.131 2,867.378 390.145 F&B revenue 2,749.402 855.241 4,184.827 1,534.876 Other revenue 252.606 221.334 558.004 41.956
Guest room 231.571 82.640 315 152
Labor 272.429 88.938 374 179
F&B expense 1,143.998 205.843 1,517.147 857.243 Other expense 981.986 363.306 1,644.846 540.997
H 0.397 0.082 0.562 0.269
Tainan City
SIZE 1
14
0.500 0.519 1 0
Note: 1. Guest room revenue, F&B revenue, other revenue, F&B expense and other expense are measured in terms of hundred thousand NT dollars.
2. Guest room reveneue, F&B revenue and other revenue are deflated by the consumer price index with 2006 as the base year. F&B expense and other expense are deflated by the wholesale price index with 2006 as the base year.
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Table 2.1 (Continued)
Areas Variables Observations Mean SD Maximum Minimum
SIZE 2 0 0 0 0
RESORT 0 0 0 0
Tainan City
CHAIN
14
0.500 0.519 1 0
Guest room revenue 1,464.446 97.762 1,602.836 1,357.690 F&B revenue 920.820 201.284 1,103.530 543.097 Other revenue 258.526 74.616 373.670 161.011
Guest room 276.000 0.000 276 276
Labor 213.429 28.118 240 166
F&B expense 338.443 72.697 398.732 184.328 Other expense 768.185 95.067 884.121 613.531
H 1 0 1 1
SIZE 1 1 0 1 1
SIZE 2 0 0 0 0
RESORT 0 0 0 0
Taitung City
CHAIN
7
0 0 0 0
Guest room revenue 361.707 47.732 411.718 266.078 F&B revenue 1,194.060 141.070 1,316.305 930.516 Other revenue 58.607 28.974 122.866 36.314
Guest room 107 0 107 107
Labor 156.714 36.206 235 128
F&B expense 402.833 52.133 457.317 324.029 Other expense 477.602 189.555 856.952 234.137
H 1 0 1 1
SIZE 1 0 0 0 0
SIZE 2 0 0 0 0
RESORT 1 0 1 1
Kaohsiung County
CHAIN
7
1 0 1 1
Note: 1. Guest room revenue, F&B revenue, other revenue, F&B expense and other expense are measured in terms of hundred thousand NT dollars.
2. Guest room reveneue, F&B revenue and other revenue are deflated by the consumer price index with 2006 as the base year. F&B expense and other expense are deflated by the wholesale price index with 2006 as the base year.
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Table 2.1 (Continued)
Areas Variables Observations Mean SD Maximum Minimum Guest room revenue 3,922.906 724.305 4,936.942 3,215.874
F&B revenue 1,851.529 328.194 2,322.083 1,515.907 Other revenue 418.171 124.050 690.110 322.250
Guest room 381.000 0.000 381 381
Labor 381.571 56.909 425 263
F&B expense 554.282 151.552 864.370 453.689 Other expense 1,549.637 446.933 2,316.897 1,185.174
H 0.681 0.142 1 0.598
SIZE 1 1 0 1 1
SIZE 2 0 0 0 0
RESORT 0 0 0 0
Hualien County
CHAIN
7
0 0 0 0
Guest room revenue 1,509.476 975.519 2,676.391 438.893 F&B revenue 708.843 334.764 1,160.421 319.747 Other revenue 714.252 790.222 2,173.444 32.255
Guest room 148.500 54.481 201 96
Labor 171.571 52.392 234 102
F&B expense 383.007 154.496 704.904 129.822 Other expense 960.192 525.444 1,721.423 249.017
H 0.624 0.138 0.712 0.413
SIZE 1 0.500 0.519 1 0
SIZE 2 0 0 0 0
RESORT 1 0 1 1
Tainan County
CHAIN
14
0.500 0.519 1 0
Guest room revenue 1,688.476 262.646 2,047.610 1,332.377 F&B revenue 855.503 113.463 984.588 681.738 Taitung
County
Other revenue
7
367.479 72.743 459.348 261.177 Note: 1. Guest room revenue, F&B revenue, other revenue, F&B expense and other expense are measured in
terms of hundred thousand NT dollars.
2. Guest room reveneue, F&B revenue and other revenue are deflated by the consumer price index with 2006 as the base year. F&B expense and other expense are deflated by the wholesale price index with 2006 as the base year.
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Table 2.1 (Continued)
Areas Variables Observations Mean SD Maximum Minimum
Guest room 183.000 0 183 183
Labor 222.857 12.199 238 204
F&B expense 287.663 46.893 346.964 227.365 Other expense 925.564 127.316 1,076.829 764.333
H 1 0 1 1
SIZE 1 0 0 0 0
SIZE 2 0 0 0 0
RESORT 1 0 1 1
Taitung County
CHAIN
7
1 0 1 1
Guest room revenue 2,871.178 493.095 3,512.117 2,166.017 F&B revenue 1,294.808 194.512 1,575.503 964.045 Other revenue 295.381 201.377 680.409 95.045
Guest room 327.500 80.426 405 250
Labor 249.929 39.943 305 165
F&B expense 479.520 70.071 580.222 364.415 Other expense 1,329.978 210.360 1,752.341 975.006
H 0.517 0.015 0.536 0.500
SIZE 1 0.500 0.519 1 0
SIZE 2 0.500 0.519 1 0
RESORT 1 0 1 1
Pingtung County
CHAIN
14
1 0 1 1
Guest room revenue 2,657.911 2,416.783 14,786.037 255.342 F&B revenue 2,957.086 2,849.618 12,502.824 51.874 Other revenue 623.560 888.616 4,540.527 0.108
Guest room 316.395 158.321 873 50
Labor 332.027 217.314 982 53
Total
F&B expense
329
1,041.146 874.707 3,682.263 29.743 Note: 1. Guest room revenue, F&B revenue, other revenue, F&B expense and other expense are measured in
terms of hundred thousand NT dollars.
2. Guest room reveneue, F&B revenue and other revenue are deflated by the consumer price index with 2006 as the base year. F&B expense and other expense are deflated by the wholesale price index with 2006 as the base year.
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Table 2.1 (Continued)
Areas Variables Observations Mean SD Maximum Minimum Other expense 1,595.268 1,623.232 10,848.029 103.450
H 0.291 0.284 1 0.066
SIZE 1 0.587 0.493 1 0
SIZE 2 0.255 0.437 1 0
RESORT 0.149 0.357 1 0
Total
CHAIN
329
0.593 0.492 1 0
Note: 1. Guest room revenue, F&B revenue, other revenue, F&B expense and other expense are measured in terms of hundred thousand NT dollars.
2. Guest room reveneue, F&B revenue and other revenue are deflated by the consumer price index with 2006 as the base year. F&B expense and other expense are deflated by the wholesale price index with 2006 as the base year.
Table 2.2 Pearson Correlation Coefficients of Input and Output Variables
Output input
Guest room revenue F&B revenue Other revenue
Guest room 0.813***
(0.000)
0.779***
(0.000)
0.466***
(0.000)
Labor 0.856***
(0.000)
0.930***
(0.000)
0.656***
(0.000) F&B expense 0.786***
(0.000)
0.955***
(0.000)
0.625***
(0.000) Other expense 0.894***
(0.000)
0.786***
(0.000)
0.680***
(0.000) Note: 1. The numbers in parentheses are p-values.
2. *** represents that the coefficients are significantly different from 0 at the 0.01 level.
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Table 2.3 Pearson Correlation Coefficients of Input-Output Mixes
Technical efficiency
Mix 1 Mix 2 Mix 3 Mix 4
Mix 1 1
Mix 2 0.940***
(0.000)
1
Mix 3 0.967***
(0.000)
0.923***
(0.000)
1
Mix 4 0.922***
(0.000)
0.854***
(0.000)
0.854***
(0.000)
1
Pure technical efficiency
Mix 1 Mix 2 Mix 3 Mix 4
Mix 1 1
Mix 2 0.936***
(0.000)
1
Mix 3 0.962***
(0.000)
0.919***
(0.000)
1
Mix 4 0.929***
(0.000)
0.860***
(0.000)
0.856***
(0.000)
1
Note: 1. The numbers in parentheses are p-values.
2. *** represents that the coefficients are significantly different from 0 at the 0.01 level.
Table 2.4 Comparison of DEA Models, with and without the Quasi-Fixed Input, as well as with and without Adjusted Inputs
Model 1 Model 2 Model 3
TE PTE SE TE PTE SE TE PTE SE Mean 0.797 0.842 0.946 0.791 0.835 0.946 0.541 0.990 0.546 SD 0.135 0.117 0.080 0.135 0.118 0.079 0.257 0.026 0.258 Minimum 0.380 0.525 0.547 0.380 0.525 0.549 0.080 0.839 0.080 Number of
observations
37 52 37 37 51 37 20 173 20
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Table 2.5 Results of Wilcoxon Signed Rank Test
Model 2 versus Model 1 Model 3 versus Model 2
TE -9.133*** Notes: 1. The numbers in parentheses are p-values.
2. ** and *** represent that the coefficients are significantly different from 0 at the 0.05 and 0.01 levels.
Table 2.6 SFA Parameter Estimates of Input Slack Equations
Dependent variable Labor input slack F&B expense input slack Other expense input slack Constant -35.608***
(1.048) Log-likelihood function -1,730.529 -2,127.501 -2,205.786 LR test Notes: 1. The numbers in parentheses are standard errors.
2. *** represents that the coefficients are significantly different from 0 at the 0.01 level.
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Table 2.7 Summary of the Adjusted Efficiency Measures among Different Types of Visitors
Type TE PTE SE Number of observations
TYPE 1 0.331 0.983 0.337 28
TYPE 2 0.564 0.990 0.570 100
TYPE 3 0.558 0.992 0.564 201
K-W test 23.357***
(0.000)
1.178 (0.555)
22.509***
(0.000) Notes: 1. The numbers in parentheses are p-values.
2. *** represents that the coefficients are significantly different from 0 at the 0.01 level.
Table 2.8 Results of Wilcoxon Rank Sum Test
Type TE SE TYPE 1 versus TYPE 2 -5.297***
(0.000)
-5.257***
(0.000) TYPE 1 versus TYPE 3 -4.224***
(0.000)
-4.111***
(0.000) TYPE 2 versus TYPE 3 0.484
(0.629)
0.489 (0.625) Notes: 1. The numbers in parentheses are p-values.
2. *** represents that the coefficients are significantly different from 0 at the 0.01 level.
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Appendix 2A
Table 2A The List of 47 Taiwan’s International Tourist Hotels in Sample
Ambassador Hotel Hsinchu Howard Prince Hotel Taichung Ambassador Hotel-Kaohsiung Hualien Chateau de Chine Hotel Ambassador Hotel Taipei Hualien Farglory Hotel
Brother Hotel Imperial Hotel Taipei Caesar Park Hotel Taipei Kaohsiung Grand Hotel Caesar Park Hotel Kenting Lalu Hotel
Emperor Hotel Landis Resort Yangmingshan Hotel Evergreen Laurel Hotel Taichung Landis Taipei Hotel
Formosan Naruwan Hotel and Resort Taitung Marshal Hotel Gloria Prince Hotel Taipei Parkview Hotel
Golden China Hotel Plaza International Hotel Grand Hi-Lai Hotel Regent Taipei Hotel Grand Hyatt Taipei Hotel Santos Hotel
Han-Hsien International Hotel Shangri-La’s Far Eastern Plaza Hotel Taipei Hibiscus Resort Hotel Sheraton Taipei Hotel
Hotel Holiday Garden Sherwood Taipei Hotel Hotel National Splendor Kaohsiung Hotel Hotel Riverview Taipei Splendor Hotel-Taichung Hotel Royal Chihpen Taipei Grand Hotel Hotel Royal Hsinchu Taoyuan Hotel Hotel Tainan Tayih Landis Hotel Howard Beach Resort Kenting United Hotel Howard Plaza Hotel Kaohsiung Westin Taipei Hotel Howard Plaza Hotel Taipei
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Appendix 2B
Table 2B Data Descriptions of Relevant Variables
Variables Definition Outputs
Guest room revenue The revenues from guest room plus service fees multiply the ratio of guest room revenue to guest room revenue and F&B revenue
F&B revenue The revenues from F&B plus service fees multiply the ratio of F&B revenue to guest room revenue and F&B revenue
Other revenue Total revenues minus guest room revenue and F&B revenue Inputs
Guest room The number of guest rooms Labor The number of employees F&B expense F&B expenses
Other expense Total operating expenses minus guest room expense, labor-related expense and F&B expense
Exogenous variables
H The sum of the squared ratios of revenues from each international tourist hotel to total revenues of all international tourist hotels in the same city or county
SIZE The dummy variable SIZE 1=1 indicates that the number of guest rooms is between 201 to 400 rooms; otherwise, SIZE 1=0. The dummy variable SIZE 2=1 indicates that the number of guest rooms is more than 401 rooms;
otherwise, SIZE 2=0
RESORT The dummy variable RESORT=1 indicates that an international tourist hotel is the resort hotel; RESORT=0 indicates that an international tourist hotel is the city hotel
CHAIN The dummy variable CHAIN=1 indicates that an international tourist hotel is the international and/or domestic chain hotel; CHAIN=0 indicates that an international tourist hotel is the independent hotel
SARS The dummy variable SARS=1 indicates the year 2003; otherwise, SARS=0 FT The dummy variable FT=1 indicates the year 2008 and 2009; otherwise,
FT=0
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Appendix 2C
Table 2C Quantities of Guest Rooms of Individual International Tourist Hotel in Taiwan during the Period of 2003-2009
Areas Hotel 2003 2004 2005 2006 2007 2008 2009
A 405 405 405 405 402 402 402
B 432 432 432 432 432 432 432
C 336 336 336 336 336 336 288
D 220 220 220 220 220 220 220
E 97 97 97 97 97 97 97
F 201 201 201 201 201 201 201
G 388 388 388 388 388 388 388
H 215 215 215 215 215 215 215
I 250 250 250 250 250 250 250
J 287 287 287 287 287 287 287
K 209 209 209 209 209 209 209
L 243 243 243 243 243 243 243
M 686 686 686 686 686 692 692
N 606 606 606 606 606 606 606
O 873 873 873 873 873 865 865
P 569 569 569 569 569 569 569
Q 349 345 345 345 343 343 343
R 422 422 422 422 420 420 420
S 288 288 288 288 288 288 288
Taipei City
T 50 50 50 50 50 50 50
U 274 274 274 274 274 274 274
V 457 457 457 457 457 457 457
W 436 436 436 436 436 436 436
X 238 283 283 283 283 283 283
Y 592 592 592 592 592 592 592
Kaohsiung City
Z 311 311 311 311 311 311 311
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Table 2C (Continued)
Hotel 2003 2004 2005 2006 2007 2008 2009
AA 404 404 404 404 404 404 404
AB 226 226 226 226 226 226 226
AC 354 354 354 354 354 354 354
AD 155 155 155 155 155 155 155
Taichung City
AE 205 222 222 222 222 222 222
Tayuan City
AF 390 390 390 390 390 390 390
AG 198 198 198 208 208 208 208
Hsinchu
City AH 254 254 254 254 257 257 257
AI 289 289 289 270 270 270 270
AJ 221 221 221 221 221 221 221
Hualien City
AK 343 343 343 343 343 343 343
AL 152 152 152 152 152 152 152
Tainan
City AM 306 306 306 315 315 315 315
Taitung City
AN 276 276 276 276 276 276 276
Kaohsiung County
AO 107 107 107 107 107 107 107
Hualien County
AP 381 381 381 381 381 381 381
AQ 96 96 96 96 96 96 96
Tainan
County AR 201 201 201 201 201 201 201
Taitung County
AS 183 183 183 183 183 183 183
AT 250 250 250 250 250 250 250
Pingtung
County AU 405 405 405 405 405 405 405
Total 14,830 14,888 14,888 14,888 14,884 14,882 14,834
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The method that examines the problem of data error proposed by Wilson (1995) is briefly illustrated in this appendix. A more complete description refers to Wilson (1995). First, a modified DEA approach proposed by Lovell et al. (1994) is used to evaluate the super- efficiency that allows the efficiency measure greater than 1. This approach removes the ith DMU from the constraint set when the ith DMU is evaluated. It is written as follows:
* the following model is solved.
*
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infeasible. The value of total effect, d*j ×δj, is calculated, where δj ≡d−j1
∑
(θij* −θi*) isthe average effect by removing the jth DMU.
The higher δj indicates that the observation has a great influence on other observations, and the higher d*j indicates that the observation impacts more observations in the sample.
Hence, the higher d*j×δj represents that the observation will be the potential influential observation and need to be deleted.
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Appendix 2E
Table 2E Results of the Identification of Influential Observations
Observations d*j δ j d*j×δj
6 6 0.019 0.111
35 30 0.012 0.374
36 33 0.002 0.067
53 117 0.006 0.647
57 0 0 0.000
65 3 0.017 0.051
66 0 0 0.000
82 26 0.007 0.177
83 104 0.013 1.364
84 1 0.158 0.158
96 4 0.000 0.000
104 35 0.016 0.538
111 42 0.008 0.351
113 1 0.106 0.106
114 4 0.006 0.022
125 3 0.004 0.011
129 15 0.007 0.099
130 4 0.265 1.059
131 4 0.030 0.121
144 41 0.007 0.290
146 3 0.003 0.009
151 8 0.003 0.024
157 4 0.000 0.000
158 49 0.004 0.179
159 2 0.011 0.022
160 2 0.005 0.009
161 5 0.014 0.069
178 20 0.006 0.115
‧
國立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
Table 2E (Continued)
Observation d*j δ j d*j×δj
193 8 0.008 0.060
196 60 0.010 0.611
198 25 0.004 0.093
201 34 0.008 0.266
204 31 0.007 0.202
205 169 0.006 1.059
207 2 0.004 0.008
223 34 0.007 0.225
224 10 0.005 0.054
225 28 0.013 0.364
240 4 0.038 0.153
248 68 0.004 0.298
251 60 0.002 0.104
252 3 0.009 0.026
254 53 0.003 0.145
271 55 0.007 0.394
272 1 0.002 0.002
274 35 0.006 0.217
275 2 0.001 0.002
287 32 0.002 0.064
299 4 0.063 0.252
302 28 0.001 0.041
318 23 0.007 0.162
‧
國立 政 治 大 學