1. DEA Analysis and Malmquist Approach
DEA is a non-parametric method to measure relative efficiency (21), which has been frequently used for measuring health system performance (22). As a data-oriented approach, DEA can examine the performance of a set of Decision-Making Units (DMUs) that transform multiple inputs into multiple outputs (23). DEA employs linear programming (LP) methods to calculate the efficiency measures that relative to non-parametric frontiers (20).
There are two versions for DEA: input-oriented and output-oriented. If the aim is to minimize available inputs to provide given levels of outputs, the model would be called input-oriented. On the other hand, if it is assumed that outputs are manageable and the target is to maximize outputs from given levels of inputs, then the model is called output-oriented (20). Pictorial health warnings and taxes on cigarettes have been mentioned in the past as the most effective policies to control tobacco use (24, 25). Hence, in order to promote the efficiency, lowering inputs were found out irrational decisions. On the other hand, countries can concentrate on the outputs and improve them by engaging the other tobacco preventive policies (which were quoted in the introduction) from given levels of inputs. Now this can be concluded with regard to definitions of the DEA orientations, an output-oriented version seems to be appropriate for this study (20) as formulated below (21):
Where is the amount of output from DMU j, amount of input to DMU j, weight given to output r, weight given to input i, number of DMUs, number of outputs, and numbers of inputs. The sign of shows the reveals returns to scale. In fact, DEA is based on two different models; variable returns to scale (VRS or BCC) or constant returns to scale (CRS or CCR). Under BCC models, returns to scales can change. If the proportions of increases in both inputs and outputs are the same, the return to scale is constant (). And if outputs increase by a larger proportion than each of inputs, the returns to scale would be increasing (). Finally, decreasing returns to scale happens when outputs are bigger than inputs by a smaller proportion (). Under CCR model, returns to scale is always constant and doesn’t change.
Because efficiency can change over time, the DEA model is appropriate for a specific time period, not over time. This study covers 2008 until 2014, the period when creativity and technology in applying tobacco preventive policies might have changed. Therefore, we used a DEA analysis of panel data across selected countries during the mentioned time period. Consequently, we measured productivity by using DEA-based Malmquist indexes framework (26) and considered a two-input, one-output model. The Malmquist productivity index (MPI) structure is as follow:
This Malmquist index has been made up by the geometric mean of two different parts. The first expresses that the distance between the two production points, G and B (showing a country in the two periods) is measured relative to the production frontier of period 1. The second factor states, this time the distance of these production points (G and B) is measured relative to the production frontier of period 2. The score of the MPI is interpreted as:
If the score was greater than unity (MPI>1), it would indicate the DMU has raised the productivity.
If the score was equal to unity (MPI = 1), then it would suggest the productivity is constant.
If the score was less than unity (MPI < 1), therefore it would imply that the DMU in period 2 is less efficient than itself in period 1.
The MPI can be decomposed into two factors: technical change and change in technical efficiency (“catching up”). So according to this decomposition, the MPI will turn into:
The first factor which is outside the brackets shows technical efficiency in both periods and measures efficiency change when transferring from period 1 to period 2 (See Fig. 1). It shows that the DMU will be more efficient (with a score greater than unity) provided it nears to its production frontier; and conversely, if the DMU recedes from its production frontier, it will be less efficient and have less efficiency score (with a score less than unity). Neutrally, if the DMU stays in the same position relative to its frontier and doesn’t move, the efficiency will be constant (with a score equal to the unit). The second factor in this MPI (inside the brackets), calculates transfers of the actual frontier between both periods. Shifting in the frontier means a change in technology and creativity of each DMU, which depends in turn on how this DMU functions. The result of each function can be an increase in technology (frontier) with a score greater than the unit, a decrease with a score less than unit, or staying in the same position with a score equal to the unit.
2. Variables and assumptions
Out of six MPOWER policies, only two: taxation of tobacco products and pictorial warning labels on tobacco products had numerical datasets, and were included as the inputs in the model (12). The others had mostly been expressed as “Yes” or “No”, meaning whether they have executed or not, and their statistical analysis was not conducted. Taxes on most sold brand of cigarettes (taxes as a percent of price) were considered as measures of tobacco taxation. Pictorial warnings are percentages of principal display area mandated to be covered by health warnings (front and back of cigarette packaging). Smokers’ prevalence with the measure of smokers’ population as a percentage of the population aged greater than 15 years old who are daily smokers, and also the number of cigarettes used per smoker per day were variables of the outputs. To preserve the positive concept of outputs in the DEA models, and because the efficiency measurement techniques basically suppose that “more outputs are better” (27), the smokers’ prevalence and the number of cigarettes used per smoker were conversely entered into the model ().
The Malmquist indexes were calculated under both CRS and VRS, hence no difference which one to be selected (28). Nonetheless, when the study design is cross-national and variables are expressed as ratios, the BCC model is preferable (29). Therefore, we selected the BCC model in this study. We selected the countries and the time period of panel data based on the maximum data availability. Eventually, we chose 16 OECD countries and four point times (2008, 2010, 2012, and 2014). Previous studies recommend that efficiency depends on a number of degrees of freedom, meaning that if the number of DMUs (n) is less than the sum of inputs and outputs, then most of the DMUs will be likely to be determined as efficient. They introduce a rough rule of thumb in the envelopment model which suggests the number of DMUs (n) should be equal to or greater than max (20). To observe this assumption in our study, the rule thumb is equal to 12 which is less than 16 (the number of countries). We used the DEA-SOLVER-LV8 (2014-12-05) application for panel data analysis.
We gathered the WHO data of the four selected variables for both inputs and outputs, and panel data of pictorial warnings and taxes on cigarette for all 16 countries and for four selected time periods (30). We found no data for pictorial warnings for the year 2008, and used the 2007 data instead. Data for smokers’ prevalence and cigarettes used per smoker were taken from OECD Health Database (2017). There were a few missing data points that were properly fixed using a single imputation method.