CHAPTER 2 EFFICIENCY IN TAIWAN’S INTERNATIONAL TOURIST HOTEL INDUSTRY
2.2 M ETHODOLOGY
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立 政 治 大 學
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N a tio na
l C h engchi U ni ve rs it y
Most of the literature does not use the three-stage DEA model to investigate the efficiency of hotels except Shang et al. (2008) and Shang et al. (2008). However, the choice of input and output variables in Shang et al. (2008) and Shang et al. (2008) violates the principle of exclusivity suggested by Thanassoulis (2001) that every input or output should not be counted more than once. In addition, no studies incorporate quasi-fixed inputs into the three-stage DEA model to analyze the efficiency of hotels according to the author’s best knowledge. This paper may first apply the three-stage DEA with quasi-fixed inputs to evaluate the efficiency of international tourist hotels in Taiwan.
In addition to the introduction, the rest of this chapter is organized as follows. Section 2 establishes the three-stage DEA model with quasi-fixed inputs to evaluate the efficiency of international tourist hotels in Taiwan. A description of the data and empirical results are presented in Section 3. Section 4 is a conclusion.
2.2 Methodology
The DEA approach uses a mathematical programming technique to estimate a piecewise linear envelopment surface from the observed input-output data. This envelopment surface is referred to as the efficient frontier. The frontier is generated from efficient DMUs and the technical efficiency measures of these efficient DMUs are 1; the rest of DMUs are termed as inefficient and their efficiency measures do not equal 1.
There are input-oriented and output-oriented models to evaluate the efficiency in the DEA approach. Lovell (1993) suggested that if DMUs could easily adjust the input usage but were difficult to estimate the amount of outputs, it was more appropriate to use the input-oriented model. Otherwise, the output-oriented model seemed suitable. The input-oriented model is used for this paper due to two reasons: First, international tourist hotels in Taiwan have limited control over their revenues which are highly related to conditions in the external environment. Second, international tourist hotels in Taiwan have the flexibility to adjust their input usages in terms of labor and expenses.
Technical efficiency evaluated by the conventional DEA model may be affected by exogenous factors and random noise. This paper applies the three-stage DEA to purge these external effects. In addition, these managers of international tourist hotels cannot adjust or are unwilling to adjust the entire bundle of inputs, because they may spend many adjustment costs to adjust all inputs to their optimal level in the short run. In other words, there are quasi-fixed inputs in international tourist hotels. This paper incorporates quasi-fixed inputs
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introduced by Banker and Morey (1986) as well as Ouellette and Vierstraete (2004) in the three-stage DEA model.5
In the first stage, the original input-output data is applied to the DEA model. According to Banker and Morey (1986) as well as Ouellette and Vierstraete (2004), suppose that there are N international tourist hotels in this market, each using M variable inputs and R quasi-fixed inputs to produce S outputs. Let xmn, k and rn y denote the mth (m=1, 2,…, M) variable sn input usage, the rth (r=1, 2,…, R) quasi-fixed input usage and the sth (s=1, 2,…, S) output production of the nth (n=1, 2,…, N) international tourist hotel. Under the assumptions of the reference technology exhibiting CRS and strong disposability of inputs, technical efficiency (TEi) can be obtained by solving the following model:6
CRS where θiCRS is the technical efficiency of the ith international tourist hotel;λnis the weight of the nth international tourist hotel’s production action used. Technical efficiency of an international tourist hotel is evaluated in terms of its ability to radically reduce its inputs usage. If the radical reduction is possible for an international tourist hotel, its optimalθiCCR <1; if the radial reduction is not possible for an international tourist hotel, its optimalθiCCR =1. The difference between this model and the conventional DEA model is that the technical efficiency measure, θiCRS, multiplies the variable inputs, but does not multiply
5 Banker and Morey (1986) first introduced quasi-fixed inputs in the DEA model, but they called them as non-discretionary inputs. Bilodeau et al. (2004) as well as Ouellette and Vierstraete (2004) called them as quasi-fixed inputs.
6 Strong disposability, or called free disposability, refers to the ability to dispose of unwanted commodity with no private cost. Strong disposability of inputs models the situation in which inputs can be increased without reducing output. That is, this condition excludes “upward sloping” isoquants (Färe et al., 1994).
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國立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
the quasi-fixed inputs in this model.
The technical efficiency measure obtained from the above model is not only influenced by the pure technical efficiency (i.e., the efficiency in resource usage), but also by the scale efficiency (i.e., the efficiency in production scale). To decompose these two factors, the reference technology assumption of above model is relaxed to VRS by imposing the constraint ∑
= N =
n n 1
λ 1. Then, the pure technical efficiency (PTEi) measure, θiVRS , can be produced. The scale efficiency (SEi) measure is computed as SEi ≡TEi PTEi. 0<SEi≤1, since 0<TEi ≤PTEi ≤1. If SEi =1, the international tourist hotel is scale-efficient and operates at the optimal scale which is the point of constant returns on the production frontier;
ifSEi<1, the international tourist hotel is scale-inefficient and operates at the inappropriate scale.
In the second stage, SFA is used to decompose input slacks into exogenous effects, random noise, and managerial inefficiency. The input slacks are the difference in the input usage between an international tourist hotel and a hypothetical international tourist hotel on the efficient frontier.7 The values indicate how much the input usage of the corresponding international tourist hotel needs to be reduced in order to be technically efficient. However, quasi-fixed inputs will not be affected by exogenous effects and random noise since they cannot be adjusted in the short run. Hence, only M variable input slacks are decomposed. The dependent variables are the M variable input slacks and the independent variables are the L observable exogenous variables. The M separate SFA regressions are specified as:
smn=fm(zn;βm)+νmn+umn, m=1,2,Κ,M;n=1,2,Κ,N (2-6)
where ∑
=
−
= N
n
mn n mn
mn x x
s
1
λ* ; λ*n is the optimal solution of the nth international tourist hotel;
[ n n Ln]
n z z z
z = 1 , 2 ,Κ , is a vector of the L observable exogenous variables of the nth international tourist hotel; fm(zn;β is the deterministic feasible slack frontier with m) estimated the parameter vector βm of the mth variable input slack; νmn ~N(0,σvm2 ) represents statistical noise; umn represents the managerial inefficiency which is assumed to be truncated-normal distribution and be independent with vmn.
These adjusted variable inputs are constructed from the results of SFA regressions as
7 Input slacks include the radial and non-radial input slacks.
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國立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
follows:
[
{ }
] [ n{ }
mn mn] mn m n n mn
mn x z z
x max βˆ βˆ max νˆ νˆ
~ = + − + − , m=1,2,Κ ,M;n=1,2,Κ ,N (2-7) where ~ and xmn xmn denote the adjusted and original variable input usage, respectively.
{ }
ˆ ˆ ][maxn znβm −znβm forces all international tourist hotels to operate in the least favorable set of external conditions observed in the sample. [maxn
{ }
vˆmn −vˆmn] forces all international tourist hotels to operate in the worst situation observed in the sample.Finally, the third stage uses the data of the adjusted variable inputs, original quasi-fixed inputs and original outputs to re-evaluate the efficiency in order to yield more accurate measures.