*6.4. Limitation and Further Studies*

This study has some limitations. First, although a transition matrix forecast by a Markov chain was specified by this study, the relevant probability of the transition matrix needs further research, for example, through interviews with experts from neighboring areas or by conducting a questionnaire survey. In addition, more diversified input indicators, for example, the number of slot machines and casino acreage, could be added into the bootstrapping-DEA model as variables. Last, future research needs to pay more attention to the methods and policies of increasing the non-gambling industry's added value.

In a small economy like Macao, the gambling industry dominates the whole economy. The gambling industry alone occupies more than 50% of Macao GDP on average. Therefore, the degree of diversity is high only when the income of the gambling industry is reduced. This is because the income of the gambling industry is highly related to the index of diversity. However,

the efficiency of gambling industry is calculated from its input-output. So, the index of diversity cannot be used to determine the relationship between the efficiency of the gambling industry and diversification. The future study is recommended to evaluate any relationship between the input of gambling industry and the diversity of the overall economy.

**Author Contributions:** F.C. initially conceived and designed the research. She performed the data analysis and original draft preparation under the supervision of the corresponding authors. C.T.H. provided suggestions for the data analysis. Y.H.M., a corresponding author, developed the original idea of this study and supervised the research project. I.K.W.L., a corresponding author, wrote the manuscript and provided quality assurance.

**Funding:** This research was funded by the key project grant of National Natural Science Foundation of China PRC, "The Establishment of Linkage Mechanism Serving for The Belt and Road Initiative and Development Research of Guangdong, Hong Kong and Macao". (Grant No. U1601218) and the major project grant of the National Social Science Fund of China PRC, "Research on the Coordination Development Mechanism and System of the Guangdong-Hong Kong-Macao Greater Bay Area in the New Era." (Grant No.:18ZDA041).

**Acknowledgments:** The authors are thankful to Jian Xin Rong and Post-doc. Jin Wei Liang for their valuable comment and helpful suggestions. They are core members of the research team of Yanhua Mao.

**Conflicts of Interest:** The authors declare no conflict of interest.
