CHAPTER 3 PRODUCTIVITY CHANGE IN TAIWAN’S INTERNATIONAL TOURIST HOTEL
3.2.2 The Malmquist Productivity Index
However, the above model applies the original input-output data to calculate θiCRS. In order to purge the impacts from exogenous factors and random noise, SFA is used to obtain adjusted variable inputs, ~x, in the second stage of the three-stage DEA. According to the adjustment process built by Equation (2-6) and (2-7) in Section 2.2, the adjusted variable inputs can be obtained. Finally, in order to yield more accurate values, the data of the adjusted variable inputs, original quasi-fixed inputs and original outputs are used to the input distance function to measure the Malmquist productivity index.
3.2.2 The Malmquist Productivity Index
The modified input distance function that eliminates external effects and considers the existence of quasi-fixed inputs is further applied to calculate the Malmquist productivity index. According to Ouellette and Vierstraete (2004, 2010), quasi-fixed inputs are incorporated into the Malmquist productivity index to measure the productivity change. This paper uses the bottoms-up method to decompose the factors of productivity change according to Balk (2001). First, the technological change that the set of feasible inputs-outputs combinations expends or contracts under the assumption of the reference technology exhibiting VRS can be written as:
2
where TC>1 represents the technological progress, whereas TC <1 represents the technological regress.
Second, the pure technical efficiency change that the DMU moves closer to or further away from the efficient frontier based on the assumption of the reference technology exhibiting VRS can be expressed as:
)
where PTEC >1 represents the pure technical efficiency improvement, whereas PTEC<1 represents the pure technical efficiency deterioration.
Third, the scale efficiency change that the DMU moves closer to or further away from the optimal scale can be written as:
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where SEC >1 represents the scale efficiency improvement, whereas SEC<1 represents the scale efficiency deterioration.Finally, the input-mix effect that represents the difference in input-mix between period t and period t+1 can be expressed as:
2 where IME >1 represents that the input combination in period t+1 lies closer to the optimal scale, whereas IME <1 represents that the input combination in period t+1 lies further away from the optimal scale.
Thus, the productivity change can be combined by the independent factors of technological change, pure technical efficiency change, scale efficiency change and input-mix effect. It can be expressed as:
IME
where MPI >1 represents the productivity growth, whereas MPI <1 represents the productivity deterioration.
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3.3 Data Description and Empirical Results
3.3.1 Data Description
The data used in this paper are based on Taiwan’s international tourist hotels operated from 2003 to 2009. They were conducted by the Annual Operation of the International Tourist Hotels, published by the Tourist Bureau, Ministry of Transportation and Communications, ROC. After discarding incomplete observations, 47 international tourist hotels are remained and are listed in Appendix 2A. Following Section 2.3.1, guest room revenue, F&B revenue and other revenue are chosen as output variables, as well as guest room, labor, F&B expense and other expense are chosen as input variables. The guest room is represented as the quasi-fixed input. Guest room revenue, 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. The consumer and wholesale price indices are published by the Directorate-General of Budget, Accounting and Statistics of Executive Yuan, ROC. The definitions of the output and input variables mentioned are summarized in Appendix 2B. The descriptive statistics of output and input variables every year is presented in Table 3.1. The values of variable inputs and outputs first increase and then decrease during the period of 2003-2009, approximately. The average number of guest rooms is within the range of 315 to 317 rooms in the sample period. The number of guest rooms in each international tourist hotel is constant during the period 2004 to 2005.
3.3.2 Empirical Results
The Malmquist productivity index calculated by the three-stage DEA model with the quasi-fixed input is applied to measure the productivity change. Since the result of obtaining adjusted variables is the same with the second stage in Section 2.3.2, only the first and third stages are described in this chapter.
The first stage. First, the effect of quasi-fixed input is investigated. The comparison between the measures of productivity change estimated by the Malmquist productivity index without the quasi-fixed and adjusted inputs (Model 4) as well as those estimated by the Malmquist productivity index with the quasi-fixed input and without adjusted inputs (Model 5) is presented in Table 3.2. Following Atkinson and Wilson (1995) as well as Ferrier and Hirschberg (1997), the bootstrap method proposed by Efron (1979) is applied to test whether
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the measures are significantly different from 1 or not. The process is briefly described in Appendix 3A. Following the process, the bias-corrected and accelerated (BCa) confidence interval is constructed by repeating 3000 times.18 The results show that the trend in the mean measures of productivity change estimated by Model 4 and 5 are consistent. The initial increase in productivity during the period of 2003-2005 has been compensated by a decrease during the period of 2007-2009. However, the productivity measures estimated by Model 5 are larger margins in the growth and deterioration than those estimated by Model 4, implying that the productivity change will enlarge when the quasi-fixed input is incorporated into the model. The Malmquist productivity index without quasi-fixed and adjusted inputs underestimates the productivity changes of international tourist hotels. Hence, the necessity of considering the existence of the quasi-fixed input is justified.
For decomposition effects of the change in the productivity, the productivity growth during the period 2003 to 2004 and deterioration during the period 2008 to 2009 result from the technological progress and regress, as well as the productivity growth during the period 2004 to 2005 originates from the pure technical efficiency improvement, regardless of Model 4 or 5. However, the source of productivity deterioration during the period 2007 to 2008 is uncertain based on Model 4, but the productivity deterioration during the period 2007 to 2008 results from the input-mix effect based on Model 5.
The third stage. The third stage re-evaluates the measures of productivity change by using the adjusted variable input data calculated in the second stage. Similarly, the comparison between the measures of productivity change estimated by Model 5 and those estimated by the Malmquist productivity index with quasi-fixed and adjusted inputs (Model 6) is presented in Table 3.3. The bootstrap method is also utilized to test whether the measures are significantly different from 1 or not. The results indicate that the trend in the mean measures of productivity change estimated by Model 5 and 6 are consistent. The initial increase in productivity during the period of 2003-2005 has been compensated by a decrease during the period of 2007-2009. However, the productivity measures estimated by Model 6 are larger margins in the growth and deterioration than those estimated by Model 5, implying that the productivity change will enlarge when the effects of external factors are eliminated from the model. The Malmquist productivity index with the quasi-fixed input and without adjusted
18 Atkinson and Wilson (1995) argued that the repeated time must more than the square of the sample size, when the BCa confidence interval was estimated. Hence, this paper chooses 3000 times to estimate the confidence interval.
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inputs underestimates the productivity changes of international tourist hotels. Hence, the necessity of adopting the three-stage approach is justified.
However, the key factors of the movement in the productivity estimated by Model 5 and 6 are different. The productivity growth or deterioration estimated by Model 6 mainly results from the technological progress or regress and the scale efficiency improvement or deterioration during the period 2003 to 2009. The reasons of an increase or a decrease in the productivity estimated by Model 5 are irrelative with the scale efficiency except during the period 2004 to 2005. It implies that the sources of productivity change will be misestimated when the impacts of exogenous variables and statistical noise are not sorted out. The necessity of adjusting inputs is justified.
Productivity change comparison among international tourist hotels with different types of visitors. This chapter also divides visitors into three types: an international tourist hotel serves group visitors more than 75% in total visitors (TYPE 1); an international tourist hotel serves individual visitors more than 75% in total visitors (TYPE 2) and others (TYPE 3), in order to investigate whether the productivity changes among different types of visitors are different or not. The bootstrap method is also utilized to test whether the measures among different types of visitors are significantly different from 1 or not. In Table 3.4, the results show that the productivities of TYPE 1, TYPE 2 and TYPE 3 are increased during the period of 2003-2005, but the productivity of TYPE 2 is decreased during the period of 2005-2006 and 2007-2009 as well as that of TYPE 3 is decreased during the period of 2007-2009.
Moreover, the rate of an increase in the productivity of TYPE 1 is the greatest, and that of TYPE 2 is the lowest. The rate of a decrease in the productivity of TYPE 3 is lower than that of TYPE 2 during the period of 2007-2009. A possible reason for this outcome is that the efficiency of TYPE 1 is lower than other types so that international tourist hotels with mainly receiving group visitors have an ample space to improve their productivity or pay more attention to decreasing the productivity deterioration.
Furthermore, the components of the change in the productivity of three types are decomposed. The productivity growth of TYPE 1 mainly originates in the scale efficiency improvement. The productivity growth or deterioration of TYPE 2 mainly results from the scale efficiency improvement or deterioration, beside the main source of productivity growth during period 2003 to 2004 is the technological progress. The productivity growth or deterioration of TYPE 3 mainly originates in the technological progress or regress and the scale efficiency improvement or deterioration. The results imply that the sources of
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productivity changes among three types of visitors are different, but the scale efficiency change plays an important role in all types.
3.4 Conclusions
Under the rising number of international tourist hotels and the movement of internationalization, the international tourist hotel industry must face the higher and higher competitive pressure. In order to survive, how to improve managerial performances of international tourist hotels is a more and more important issue. Hence, this paper further evaluates the productivity changes of international tourist hotels. To accurately examine the productivity change of international tourist hotels in Taiwan, the Malmquist productivity index with quasi-fixed inputs computed by the three-stage DEA approach is used to discuss the productivity change based on the 2003-2009 data conducted by the Annual Operation of the International Tourist Hotels.
The first stage uses the data of original variable inputs, quasi-fixed input and outputs to measure the productivity changes of international tourist hotels. The results show that the Malmquist productivity index without quasi-fixed and adjusted inputs underestimates the productivity change so as to justify the necessity of considering the existence of the quasi-fixed input. After adjusting the variable input data from the SFA results in the second stage, the productivity index in the third stage shows that the initial increase in productivity has been compensated by a decrease. The productivity growth or deterioration mainly results from the technological progress or regress and the scale efficiency improvement or deterioration during the period of 2003-2009. The results also show that the Malmquist productivity index with the quasi-fixed input and without adjusted inputs underestimates the productivity change. The key factors of productivity changes estimated by the Malmquist productivity index with the quasi-fixed input and without adjusted inputs as well as those estimated by the Malmquist productivity index with quasi-fixed and adjusted inputs are different so as to justify the usage of the three-stage approach. Finally, international tourist hotels with mainly receiving group visitors have the better improvement of productivity than those with receiving simultaneously group and individual visitors as well as mainly receiving individual visitors, because international tourist hotels have an ample space to improve their productivity or pay more attention to decreasing the productivity deterioration. The sources of productivity changes among three types of visitors are different, but the scale efficiency change plays an important role in all types.
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Some important lessons may emerge directly from the empirical results in this chapter.
First of all, for studies of the productivity change to be more informative to decision and policy makers, the Malmquist productivity index estimated by 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 the productivity changes of international tourist hotels mainly originate in the scale efficiency changes. 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 3.1 Descriptive Statistics of Output and Input Variables
Year Variables Mean SD Maximum Minimum
Guest room revenue 2,232.985 1,874.876 10,374.229 255.342 F&B revenue 2,763.579 2,506.037 10,322.856 51.874 Other revenue 516.797 767.392 3,572.228 2.051
Guest room 315.532 160.457 873 50
Labor 326.021 219.177 945 59
F&B expense 1,064.289 861.347 3,527.770 32.942 2003
Other expense 1,496.708 1,394.773 8,114.614 103.500 Guest room revenue 2,626.100 2,346.445 13,417.715 324.600 F&B revenue 2,889.335 2,655.362 11,176.602 78.233 Other revenue 636.729 871.168 3,842.579 2.627
Guest room 316.766 159.863 873 50
Labor 326.277 214.757 952 59
F&B expense 1,017.784 787.015 3,232.532 29.743 2004
Other expense 1,561.376 1,630.939 10,293.711 112.196 Guest room revenue 2,870.068 2,486.669 14,042.570 368.824 F&B revenue 3,207.661 2,948.041 12,200.963 85.418 Other revenue 670.097 904.529 3,799.908 3.404
Guest room 316.766 159.863 873 50
Labor 334.468 221.219 934 60
F&B expense 1,185.191 956.586 3,682.263 49.074 2005
Other expense 1,676.452 1,797.138 10,848.029 240.993 Guest room revenue 2,918.335 2,672.267 14,684.076 349.236 F&B revenue 3,083.987 2,954.774 11,514.368 83.767 Other revenue 650.529 903.480 3,708.486 0.108
Guest room 316.766 159.797 873 50
Labor 335.660 223.025 982 64
F&B expense 1,086.191 928.158 3,346.855 45.822 2006
Other expense 1,654.621 1,774.209 10,571.352 221.786 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 3.1 (Continued)
Year Variables Mean SD Maximum Minimum
Guest room revenue 2,868.628 2,761.359 14,786.037 342.959 F&B revenue 3,049.399 3,125.591 12,019.735 87.150 Other revenue 660.698 920.901 3,918.250 3.403
Guest room 316.681 159.701 873 50
Labor 336.255 218.892 912 53
F&B expense 1,015.647 896.809 3,325.283 33.502 2007
Other expense 1,638.219 1,751.715 9,890.515 129.830 Guest room revenue 2,663.324 2,517.997 12,998.162 266.078 F&B revenue 2,988.088 3,003.055 11,672.933 80.305 Other revenue 614.072 939.934 4,171.961 3.255
Guest room 316.638 159.403 865 50
Labor 338.255 222.480 868 53
F&B expense 980.051 856.293 3,160.315 41.885 2008
Other expense 1,539.628 1,499.741 8,393.132 124.546 Guest room revenue 2,425.938 2,221.627 11,149.871 279.082 F&B revenue 2,717.550 2,858.161 12,502.824 75.026 Other revenue 570.996 951.474 4,540.527 2.380
Guest room 315.617 159.430 865 50
Labor 327.255 215.214 856 55
F&B expense 938.867 860.636 3,671.750 43.568 2009
Other expense 1,599.875 1,568.680 7,778.290 217.396 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 3.2 Comparison of Productivity Indices with and without Quasi-Fixed Input
Model 4 Notes: 1. The values in the table are the geometric mean.
2. The numbers in parentheses are confidence intervals.
3. ** represents that the coefficients are significantly different from 1 at the 0.05 level.
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Table 3.3 Comparison of Productivity Indices with and without Adjusted Inputs
Model 5 Notes: 1. The values in the table are the geometric mean.
2. The numbers in parentheses are confidence intervals.
3. ** represents that the coefficients are significantly different from 1 at the 0.05 level.
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Table 3.4 Comparison of the Adjusted Productivity Indices among Different Types of Visitors Notes: 1. The values in the table are the geometric mean.
2. The numbers in parentheses are confidence intervals.
3. ** represents that the coefficients are significantly different from 1 at the 0.05 level.
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Table 3.4 (Continued)
TYPE 3 Notes: 1. The values in the table are the geometric mean.
2. The numbers in parentheses are confidence intervals.
3. ** represents that the coefficients are significantly different from 1 at the 0.05 level.
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Appendix 3A
The bootstrap method is proposed by Efron (1979). According to Atkinson and Wilson (1995) that apply this method to estimate the confidence interval of productivity, the procedure is briefly illustrated in this appendix. A more complete description refers to Atkinson and Wilson (1995). Suppose a random sample
{ }
zn nN=1, the following steps derive the bootstrap estimate of the confidence interval of productivity:1. Calculate the sample mean z z N
N
n
∑ n
=
=
1
.
2. Calculate~zn = zn⋅ N (N−1)+z(1− N (N−1)).
3. Independently and fairly draw and replace N times from the set
{ }
z~n nN1= and obtain new set
{ }
zn* Nn=1.4. Calculate the new sample mean z z N
N
n
∑ n
=
=
1
*
* .
5. Repeat steps 3 to 4 Q times to obtain
{ }
zq Qq 1*
= , where Q is suitably large in the size.
6. Values in
{ }
zq Qq 1*
= can be arranged by the algebraic value to infer the confidence interval.
The confidence interval for the mean score can be constructed by using the normal based method, the bootstrap percentile method (Efron, 1982) or the BCa method (Efron and Tibshirani, 1993). Following the suggestion of Atkinson and Wilson (1995), the BCa method is used in this paper.
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