Chapter 3: Research Design
3.1 Methodology And Research Design
The DEA is a linear programming technique for determining the efficiency of multiple decision-making units (DMUs) when the production process has a complex input-output structure. Charnes,A., Cooper, and Rhodes developed the technique, also known as frontier analysis, by building on Farrell's pioneering work and his' efficiency measures (Farrell, 1957). Evaluating the efficiency of decision-making units (DMUs) involves comparing their performance to that of the best performing unit. The optimal unit should be located on the efficiency frontier. A unit is considered inefficient if it is not on the efficiency frontier. This decision-making unit could take the form of a business, a school, a hospital, or a bank. Due to its well-known advantage, DEA has been hailed as the best tool. It does not require the specification of predetermined weights for the input and output variables. Compared to other techniques such as ratio analysis and regression, DEA can easily handle multiple inputs and outputs simultaneously. The current study employed two DEA models, one of which was input-oriented. The CCR model was the first model developed by Charnes et al.
(1978). The BCC model, developed by Banker, was the second model (1984). The CCR approach is founded on constant returns to scale (CRS), whereas the BCC model is based on variable returns to scale (VRS). The CCR model's relative efficiency score is the overall efficiency score. In contrast, the BCC model's relative efficiency score is the pure technical efficiency score. Typically, these scores are defined on the interval.
Financial performance-efficiency nexus in The Healthcare Sector in The GCC Region: A nonparametric
3.1.2 The CCR and BCC Models
The formulation of the models under consideration is extensively described in Cooper et al. (2006). A brief summary: let there be n homogenous DMUs, characterized by m inputs and s outputs. The data set is decomposed into the matrix of inputs (X = (xij € Rmxn), and the matrix of outputs (Y = (yrj)€ Rsxn). The input -oriented models estimate the relative efficiency of DMU0, 0 € {1, 2, . . ., n}, by solving the following linear program(s) (envelopment form):
min θ (θ, λ)
subject to θx0 - X λ ≥ 0 (1) Y λ ≥ y0 (2) λ ≥ 0 (DEA - CCR) (3) e λ = 1 (DEA - BCC) (4) The CCR model measures technical efficiency and is formed by the objective function and its conditions represented by equations (1)-(3). The BCC model measures pure technical efficiency and contains an additional restriction represented by equation (4). The first three conditions consist of m, s and n constraints, respectively. In the analysed case, m is 3, s is 1 and n is 12. The optimal objective function value θ* represents the efficiency measure assigned to the considered unit DMU0 and, the case of its inefficiency, also the input reduction rate (0 < θ ≤ 1): At the same time, λ is a non-negative column vector corresponding to the proportions contributed by efficient entities to efficient frontier projection of DMU0, and e is a row vector with all elements equal to 1 (both of them n-dimensional). This first phase minimizes θ, clearly indicating by the constraints (1) and (2) that (Xλ, Yλ) outperforms (θ*x0 y0) when θ* < 1: In this context, the input excesses and the output shortfalls are identified as
“slack” values and determined by the formulas:
s - = θx0 – Xλ (s- € Rm), (5) s + = Yλ – y0 (s+ € Rs), (6) which are both non-negative for any feasible solution (θ, λ) of the above linear program(s). Potentially remaining input excesses and output shortfalls will be discovered in the second phase by maximizing their sum while keeping θ = θ*.
If the optimal solution obtained in this two-phase process is denoted as
(θ*, λ*, s -*, s +*) the DMU0 is (strongly) efficient if and only if the efficiency score satisfies θ*=1 and has no slack, The DMU0 is weakly efficient if and only if θ*=1 but si -*, ≠ 0 or sr -*, ≠ 0 some i and r in some alternate optima. Otherwise, the DMU0 is inefficient, and its efficiency can be improved if the input amounts are decreased radially by the factor θ* and the input excesses recorded in s -* are removed, and if the output amounts are increased by the output shortfalls in s +* These input and output improvements form the following projection:
ẋ0 =x λ* = θ* x0 - s -*, (7) Ῡ0 = y λ* = y0 + s +*, (8) The components of vector λ* are positive if and only if they correspond to the efficient DMUs that form the reference set E0 of the DMU0, meaning that the above formulas can be expressed as ẋ0 = 𝑗𝐸€0𝑥𝑗λi ∗, y′0 = 𝑗𝐸€0𝑦𝑗λj ∗,
The constraint (4) differentiates the BCC from the CCR model and, together with the condition (3), imposes a convexity condition on allowable ways in which the observations for the n DMUs may be combined, thus also differentiating the shapes of their production frontiers. As a practical consequence, the distance from any inefficient DMU to its CCR projection is no less than its distance to its BCC projection. This generally results in lower CCR than BCC scores and makes CCR efficiency harder to achieve. These differences between global and local efficiency scores come as a result of the scale size of DMU. Therefore, scale efficiency is defined with
θ*scale = ∗
∗ (9) and its value obviously also lies between zero and unity. Consequently, the efficiency can be decomposed as
θ*CCR = θ*BCC × θ*scaley (10) revealing the sources of inefficiency, i.e., whether the inefficiency is caused by the inefficient operation of the DMU itself (θ*BCC) or by the disadvantageous conditions under which the DMU is operating (θ*scale) or by both.
Financial performance-efficiency nexus in The Healthcare Sector in The GCC Region: A nonparametric
3.2 Research Design
The measurement of the quantitative financial performance in related studies must involves Annual data for the ten-year period 2011–2021, provided by the published financial statements, were used for the efficiency measurement of the Healthcare companies. As it is a prerequisite by the DEA, all selected data, i.e., inputs and outputs are comparable and reliable for the entire HED. Thus, the following indicators were selected and will be integrated into a unique efficiency measure as input variables:
Salaries,
Direct costs, and
investments As the output variable:
Revenue,
Net Income
With twelve DMUs (Companies), three inputs and one output, a forementioned rule- of thumb requirement is fulfilled financial ratio analyses and stock price indicators.
However, in this study, we also analyse the efficiency of a healthcare company by measuring efficiency from the data collected from the Balance Sheet and Income statement for all corporates categorized under healthcare sectors in the GCC region using Bloomberg as data source. Also, among of the effeminacy results we considering the financial performance ratios, such as ratio of firm Efficiency, profitability ROA, ROE, and ROS, leverage debt and ROIC with Growth, and firm’s activities. The detailed methods of calculating the variables are shown in Table 1 as input in DEA Method in the following Table (Table 1).
Table 1
The Variables Ratios for financial performance with the financial characteristics Financial Characteristics Variables Calculation
Firm Efficiency, cost FEFFCS Cost of sales/sales
FEFFCER Selling, general and administrative expenses/sales Profitability ROA (%) Net profit/total assets
ROE (%) Net profit/Equity ROS (%) Net profit/sales
Return on Invested Capital ROIC (%) Operation Income × (1-tax rate)/Invested Capital
Leverage DEBT (%) Debt/Equity
Activity TURNOVER Sales/total capital
Growth GTC (%) Total capital at the end of period−total capital at the end of previous year)/Total capital at the end of the year
GSALE (%) (Sales at the end of the year‑sales at the end of the previous year) /Sales at the end of the year