MMOBE
The Economics of Performance and Measurement
Created by Yanying Li and Yi Zhang
1. Motivation
China’s tourism sector, with its rich array of attractions, is a fundamental pillar of the national economy. The strategic development of this industry is considered a critical approach to increasing consumer spending, increasing foreign exchange earnings and creating employment opportunities. At the same time, it promotes growth in related up and downstream economic sectors. The aim is to examine the impact of the input-output relationship within the tourism sector on the wider economic environment, and to demonstrate the deep effect of the epidemic on China’s tourism industry. This approach highlights the economic significance of the sector and the challenges presented by global health crises.

2. Announcement
The determination of input and output
This analysis is based on three different datasets selected to capture important time milestones: the first dataset represents the year 2019, which is the period immediately prior to the epidemic; the second dataset is from 2020, which marks the initial phase of the epidemic’s impact on China; and the third dataset from 2021 gives insights into the sector’s evolution one year after the onset of the epidemic. A comparative review of these datasets highlights significant changes in the tourism industry’s inputs, providing a differentiated understanding of how variations in factor inputs impact overall output.

This analysis presents a comparative study using three different datasets, including data from the pre-epidemic year of 2019, the outbreak year of 2020, and the following year of 2021. The aim is to examine the changes between these periods, focusing on the investment inputs and outputs of the tourism industry in ten Chinese provinces, referred to as Decision Making Units (DMUs). These provinces are Guangdong, Xizang (Tibet), Ningxia, Jiangsu, Beijing, Shanghai, Xinjiang, Liaoning, Gansu and Yunan.

The study examines three primary inputs that are closely related to tourism investment:
1. The number of travel agencies, which indicates the availability and accessibility of tourism services.
2. The number of star hotels, which reflects the quality and capacity of accommodation in each province.
3. The number of A-level sites, as a measure of the supply of tourist attractions in the provinces.
The output variable considered in this analysis is tourism revenue, reported in units of 100 million yuan, which serves as an economic indicator of the contribution of the tourism industry to each province’s economy. Through a detailed comparison of these data points over the three years in question, the study aims to highlight the impact of changing investment inputs on tourism earnings, while also providing information on the impact of the pandemic on China’s tourism sector.

3. Data
The reference of the data:

[1] Website of Ministry of Culture And Tourism of the People’s Republic of China
https://www.mct.gov.cn/

[2] Song Rui (2017) The Total Factor Productivity of Tourism: An Empirical
Analysis Based on the Comparison of Star hotels, Travel Agencies and Tourist
Attractions

http://www.cnki.net/KCMS/detail/detail.aspx?dbcode=CJFD&dbname=CJFDLA
ST2018&filename=ZSKY201706009&uniplatform=OVERSEA&v=7jb3-aDOubp0
MPxJHM4nxVxWpT5AJfP7yD1MtVK576A-V–Oyw7RqGjbW-2NZqIn


4. Questions
1. Calculate the output-oriented technical efficiency of these observations of 3 periods, assuming the technology with constant returns to scale (CRS).

2. Try to find the observations that are output-oriented technically efficient of each period and explain what you notice about the results.

3. Calculate the geometric Malmquist productivity index for each province between periods 2019~2020 and 2020~2021. What do you observe about the results?

4. Decompose this geometric Malmquist productivity index into the product of an index of technical efficiency change and an index of technical change.

5. The solutions
1) To calculate technical efficiency using OnFront, follow these steps:
1. Import all the necessary data into OnFront and define all the variables accurately.
2. For model selection, opt for Fo(x,y) with CRS as the assumption. Then, proceed to select “data”. Pick the observations to be analyzed and initiate the model by pressing “LP”.
3. Export the results from OnFront into Excel and calculate the distance function using the formula: Do(x,y) = 1/Fo(x,y). Below, you’ll find the results obtained from this process.


2) In the dataset highlighted with yellow, the units are marked as efficient. When analysing the data from 2019 to 2020, it can be observed that at the beginning of the outbreak, the provinces seemed unprepared for the changes that followed. Input remained largely unchanged; however, due to national travel restrictions imposed to control the spread of the pandemic, there was a significant increase in the number of tourists in the local regions. This rapid increase in domestic tourism did not translate into an increase in tourism earnings in 2020. Instead, there was a significant decline, indicating extensive output-oriented technical inefficiency in all provinces.

In the following year, 2021, there was a significant shift as a result of the change in the national travel policy, together with the recognition by the provinces of the need to change their input strategies. As a result, input levels were recalibrated, leading to an improvement in output-oriented technical efficiency. This adjustment phase saw a reduction in the number of provinces classified as technically inefficient, highlighting a gradual adaptation to the evolving scenario and an improved capacity to efficiently manage and adapt to the dynamics of the tourism sector after the outbreak.


3) The procedure involves merging annual data into OnFront, where all variables are clearly defined and periods are allocated to each annual dataset. The model selected for analysis is Mo(x,y) with the underlying assumption of constant returns to scale (CRS). After selecting the ‘master set’ which contains all the data points, the ‘LP’ option is started to begin the analysis. The results of this process are presented below.

In 2020, the start of the pandemic resulted in each province experiencing a notable increase in technological change compared to 2019. However, due to severe national restrictions on people’s mobility, the ability to utilise key inputs - such as travel agencies, star-rated hotels and scenic spots - was severely constrained. This inefficient use of inputs led to a significant decline in tourism revenues, resulting in Malmquist productivity indices falling below 1 for most of the period.

By 2021, although the continuing impact of the epidemic limited the progress of production technology within each province to a minimal growth rate, a marked improvement in technical efficiency change was observed. This improvement was mainly due to the more strategic and rational use of inputs by the provinces. As a result, there was an increase in output, with the Malmquist productivity indices for most provinces rising above 1 during this period.

4) Decompose this geometric Malmquist productivity index into the product of an index of technical efficiency change and an index of technical change.

M0(y,x)=EC*TC:


In order to interpret the data presented on the geometric Malmquist productivity index (Mo(y,x)), which is decomposed into the product of an index of technical efficiency change (EC) and an index of technical change (TC) for the years 2019 to 2020 and 2020 to 2021, it’s essential to understand what each component represents:
-Technical efficiency change (EC) shows the change in how effectively provinces use their inputs to produce outputs. Values greater than 1 indicate an improvement in efficiency, while values less than 1 indicate a decline.
- Technical Change (TC) measures the change in the technology frontier itself, indicating how best practice in production technology has evolved. Values above 1 indicate technological progress, while values below 1 indicate technological regression.
- The Malmquist geometric productivity index (Mo(y,x)) is the product of EC and TC and shows the overall change in productivity from one period to the next. A value above 1 indicates an overall improvement in productivity, while a value below 1 indicates a decline.

Thus, for the period 2019 - 2020:
- EC values are all less than 1 (except for Ningxia), indicating a decline in technical efficiency in most provinces. This suggests that, given the technologies available, the provinces struggled to use their inputs efficiently to produce outputs effectively.
- The TC values are all significantly higher than 1, indicating significant technological progress in all provinces. This could reflect the adaptation of new technologies or the improvement of existing practices.
- Despite technological development (high TC), the Malmquist productivity indices (Mo(y,x)) are below 1 for most provinces, with Ningxia being an exception. This highlights the impact of the pandemic restrictions, which reduced the efficiency of input use, reducing the gains from technological change and leading to an overall decline in productivity.

While for the period 2020 - 2021:
- There is a significant shift in the EC values, with all provinces indicating values well above 1. This represents a significant increase in technical efficiency, indicating that the provinces have become much better at using their inputs.
- The TC values are around or below 1, suggesting that there was little or no technological progress during this period. This could be due to the continued focus on pandemic recovery and adaptation, which may have limited new technological implementations.
- The Mo(y,x) values for this period are predominantly above 1, indicating overall productivity improvements in most provinces. This is mainly due to significant gains in technical efficiency, compensating for stagnation or small declines in technological progress.
It can be concluded that from 2019 to 2020, provinces faced challenges in the efficient use of their inputs even with significant technological progress, leading to an overall decline in productivity. However, there was a significant shift between 2020 and 2021, with increases in technical efficiency leading to overall productivity growth even though technological progress was low. This highlights the importance of not only technological progress, but also the efficient use of resources to achieve productivity gains.

这是我写的可以按照这段话Suppose you are a policy maker for the future development of medical institutions and
need to analyze the performance of medical institutions throughout the year, by
measuring the technical efficiency of medical institutions in 10 cities and ranking the
overall strength of medical institutions in each region, so as to have a preliminary
understanding of the development of these medical institutions:给我写一个类似的question 那部分的前言吗