**1. Introduction**

As a leading gambling destination, in 2017, Macao attracted more than 30 million tourists and created the highest gambling revenue (33 billion US dollars) in the world [1]. The development of Macao's gambling industry is the result of its history, economic development, resource limitations and preferential policy [2]. Although these factors helped Macao to obtain a competitive advantage in gambling tourism, this typical small economy raises a problem—economic dependence on gambling restricts economic diversification. The gambling industry increases labor wages and provides good treatment, which results in its strong absorption of economic resources. However, faster growth of gambling industry leads to higher income inequality [3] which limits other industries' survival and development. Scholars contend that a low level of diversification or concentrated economy can dramatically react to external influences, such as changes in demand for one product [4,5] and a diversified regional economy is less responsive to fluctuations to extra-regional economic growth [6]. Since diversification can reduce a nation's economic volatility and increase its real activity performance, so having a diverse economy has long been thought to play a key role in a sustainable economy [5]. Therefore, both the Macao government [7–10] and scholars [11–14] have recognized the importance of economic diversification, which is the source of long-term economic growth [5,15,16]. Moderate diversification of the economic structure is a way to drive economic sustainability in Macao. Thus, it is critical to establish moderate economic diversification in Macao.

To establish a moderate economic structure, the Macao government is facilitating the development of other industries, such as Meetings, Incentives, Conferences and Exhibitions (MICE), Traditional Chinese Medicines (TCM), Cultural and Creative Industries (CCI) and featured financial services. The Macao government also announced its policy spindle for gambling industry development, "adjustment of the appropriate scale of gambling industry" [7,9]. Recently, some researchers have studied the sources of threats and challenges to Macao's economic development [11,17], the ways Macao's economy is developing and diversifying [11,13,14,17,18] and sustainable tourism development in Macao [12]. They supported the development of moderate economic diversification and agreed that by controlling the scale of the gambling industry, more resources could be unlocked and reallocated to non-gambling industries [19]. However, some academics advocate the advantages of cluster economies or agglomeration economies [20–22], which have the advantages of sharing common resources (i.e., technology and labor), lower unit costs and better innovations for increasing returns to scale and enhancing the growth opportunities of other industries and clusters [20–22]. In a recent study, Aratuo and Etienne [23] studied the relationship between economic growth and tourism-related industries in the US in 1998–2017. They found that tourism-related industries providing local offerings drive the performance of other industries. Although most of the research on agglomeration economies and cluster economies consider the agglomeration of manufacturing industries [24,25], the agglomeration of service industries may occur if they can benefit from the concentration of customers [25]. Therefore, Macao's gambling industry tends to concentrate in certain areas in Macao instead of being scattered across Macao. Considering the needs for supporting service industries such as banks and other financial intermediaries, restaurants, tourism and other business services, the agglomeration of casinos can derive similar benefits to the agglomeration of manufacturing industries, especially regarding the enhancement of the growth opportunities of other industries and clusters [22]. In other words, the agglomeration of casinos may lead to the growth of other industries and clusters. This implies that over-adjustment of the gambling industry may harm the development of moderate economic diversification in Macao. Thus, how to strike a balance between moderate economic diversification and further development of the gambling industry must be determined.

The concept of appropriate scale comes from the economies of scale. Appropriate extension or reduction of the production scale will make the distribution of production factors, like land, capital and labor, more reasonable and will achieve optimal management efficiency under existing conditions [26,27]. To adjust the scale of the gambling industry appropriately, we should know how to calculate this 'appropriate scale.' In general, if the scale of the gambling industry is higher than this 'appropriate scale,' it will limit the development of moderate economic diversification. Then, it causes the sustainable issue of non-gambling industries. On the other hand, if the scale of the gambling industry is lower than this 'appropriate scale,' it will also reduce its support of non-gambling industries to achieve a moderate and diversified economy. It causes the sustainable issue for both gambling and non-gambling industries. Therefore, our study relates the appropriate scale of the gambling industry not only in terms of the economic efficiency of this industry but also the overall economic diversification in Macao. This study helps to address the paradox between economic growth of the gambling industry and sustainable growth of non-gambling industries.

To contribute to a solution for sustainable economic development in Macao, this study aims to determine the appropriate scale of the gambling industry for optimal development of moderate economic diversification in Macao. Firstly, this study applies an entropy index of economic diversification [28] to measure the levels of diversification of Macao's economy from 2008–2016. Then, a Data Envelopment Analysis (DEA) [29–31] is used to measure the efficiency of the gambling industry. A transition probability matrix for three scenarios (rapid, stable and slow transitions) is developed based on expert interviews. To evaluate the appropriate scale, a Markov chain [32] is applied to forecast the future scale of the non-gambling industry and the gambling industry until 2021. The results of this study can be applied to other gambling destinations (such as Cambodia) that may soon face a similar sustainable economic problem of a concentration in the gambling industry and may want to promote industrial diversification. For sustainable economic growth caused by technological innovation and human capital accumulation, it is essential to transform and upgrade the industrial structure. This study also contributes to sustainability through the understanding of the transformation of the industrial structure and its relationship with sustainable economic growth.
