## 1 Introduction  
High-speed rail (HSR) has been introduced and planned in many countries over the last fifty years since the first HSR line (Shinkansen line in Japan) operated in 1964. Following Japan, more and more countries started to provide a HSR service, such as France, Germany, Spain, Italy, Korea, and China [1]. Korea operated the Korea Train Express (KTX) services of the Gyeongbu HSR Line in 2004. The operation of the KTX resulted in significant changes in the transportation network of Korea, which changed the entire country from a \"one-day life zone\" into a \"half-day life zone\", that reduced the travel time within Korea to less than 3 h [2]. This change has exerted profound influences on the local society, economy, and culture of each district in Korea. On the one hand, the development of HSR contributes to maintaining close economic relations between different areas. This would strengthen the cooperation between upstream and downstream enterprises a then lead to the decrease in the cost of them, while at the same time more jobs will be created with the expansion of production and market [2; 3; 4]. On the other hand, the outstanding performance of high-speed transport modes in increasing the volume and speed of interregional migration contributes to improving the efficiency of domestic trades and creating new economic growth points, such as new commercial areas based on new high-speed railway stations [5; 6; 7]. In addition, the HSR was also conducive to improving the efficiency of land use, technological innovation, and trade liberalization in Korea [2]. However, some researchers raise concerns about the local economic growth of socioeconomically disadvantaged areas, as they may face the adverse shocks resulting from the operation of HSR, that is the so-called \"straw effect\", which refers to the relative concentration of economic resources in a developed city at the expense of weakening the economic vitality of neighboring smaller cities [8; 9], just like juice in a glass is sucked up by a straw [8]. The theory behind this effect can be traced to the growth pole theory, which was developed by [PERSON] (1950), who emphasized that the existence of growth poles would lead to the imbalance of regional development [10]. In this connection, some researchers developed this theory from different perspectives, such as [PERSON] (1958), who proposed the trickling down effect, which referred to the positive impact of a growth pole or growth center on adjacent regions [11]. [PERSON] (1957) used the terms \"spillover effect\" and \"backwash effect\" to describe the relationship between core areas and the periphery [12]. [PERSON] (1950) systematically summarizes the center-periphery theory that was introduced into the regional economic analysis by [PERSON] (1966) [13]. He found that the ongoing economic and political success of one region or state may be achieved at the expense of neighboring areas [14]. With the development of the New Economic Geography (NEG) theory, [PERSON] (1991) constructed a core-periphery model from the perspective of spatial economics, who emphasized the role of transportation cost in forming a core-periphery structure [15]. In terms of empirical research on the straw effect, most of them have inferred that investment in public transport infrastructure would have a strong and positive effect on regional economic development through reducing travel costs and increased interregional economic activity [16; 17; 18]. Some early works on the U.S. and Europe found the positive effects of new transport infrastructures on local economic productivity and narrowing the gaps between core cities and other cities [19; 1; 20]. At the same time, the positive effects may not be consistent, and the straw effects tend to result in an uneven distribution of benefit from a new high-speed railway construction for different cities [21; 22; 23].