The Hohhot-Baotou-Ordos-Yulin (HBOY) urban agglomeration in China, approved in 2018, presents a significant development opportunity. Located in the less-developed western region of China, HBOY comprises four cities covering 175,000 square kilometers with a population of nearly 12 million. In 2021, its GDP exceeded 1.65 trillion Yuan, accounting for over 33% of the total economic output of the two provinces. Given the underdevelopment of China's western region and the significant role of counties in the national economy (despite contributing only 38.3% of the national GDP), understanding and improving county-level economic efficiency is crucial. This study aims to evaluate the economic efficiency of each county within HBOY, identify spatially and temporally varying efficiency levels, and pinpoint areas for economic improvement to balance China's national economy. The research gap addressed by this study lies in the limited focus on county-level efficiency, especially in underdeveloped areas, and the neglect of spatial correlation in such analyses. The paper uses a county-level analysis to achieve higher resolution compared to city or province-level studies.

Existing growth accounting methods in development economics often overlook factors affecting economic growth. Standard regression analyses typically filter out core factors using control variables, treating deviations as statistical errors. This approach assumes full efficiency for all Decision-Making Units (DMUs). However, real-world inefficiencies exist due to factors like information asymmetry or market incompleteness. Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) are commonly used to estimate economic efficiency by measuring the distance from actual to optimal performance. DEA, a nonparametric method, doesn't assume a specific frontier form but treats all deviations as inefficiency. SFA allows decomposition of deviations into random error and inefficiency terms but requires specifying a functional form for the frontier. Total Factor Productivity (TFP) is a key indicator reflecting input and output efficiency. The Stochastic Frontier (SF) model, proposed in 1977, is a valuable tool in efficiency analysis, considering both random errors and inefficiency. Previous SFA studies have focused on specific sectors or industries, while domestic Chinese research primarily involves microeconomic DMUs or provincial/city-level analyses. Few studies focus on county-level economic efficiency, particularly in underdeveloped areas, and spatial correlation is often ignored. This study addresses these gaps by focusing on county-level data in a less-developed region and incorporating spatial econometrics.

The study uses a stochastic frontier production function, adapted from Battese and Coelli (Zhang et al., 2004), allowing for time-varying effects. The model is: Yit = Xitβ + (vit − uit), where Yit represents the log of county output, Xit is a vector of log inputs (labor force, land usage, capital stock), β are parameters, vit is a random error term, and uit is a non-negative inefficiency term following a truncated normal distribution N(μ, σu2) with μit = Zitδ, where Zit is a vector of variables affecting efficiency (economic linkage, government involvement, market size, core area status), and δ are parameters. Economic efficiency is calculated as TEit = exp(−uit). Data from the Inner Mongolia and Shaanxi Statistical Yearbooks and local statistical departments were used. Land usage was proxied by land coverage area. Capital stock was estimated using the Perpetual Inventory Method (PIM). Economic linkage was calculated using an augmented gravity model (Miao, Zeng, 2020). Government involvement was proxied by government expenditure per capita, and market size by retail sales per capita. A three-factor Cobb-Douglas production function was employed with the log transformation. Maximum Likelihood Estimation (MLE) was used in Frontier 4.1 software for estimation, using OLS and a grid search. ArcGIS was used for spatial visualization, and Moran's I for spatial autocorrelation analysis. Local spatial autocorrelation was examined using LISA diagrams.

The MLE results (Table 2) show that labor and capital significantly affect output. Economic linkage significantly and negatively impacts inefficiency (i.e., positively impacts efficiency). Government involvement and market size have less significant, though negative, effects on inefficiency. Being a core city area significantly increases inefficiency. Table 3 shows that overall economic efficiency increased steadily from 0.505 in 2012 to 0.753 in 2020. Baotou consistently had the highest efficiency, followed by Ordos and Hohhot, while Yulin had significantly lower efficiency. Hengshan District showed the most significant efficiency improvement (102.39%), while Jia County's efficiency improvement was slow. Figure 7 shows the spatial distribution of economic efficiency. In 2012, high-efficiency counties were concentrated in the middle of the agglomeration. By 2020, high-efficiency areas (efficiency > 0.9) were concentrated in the east, forming a contiguous area. Table 4 and Figures 8 and 9 demonstrate significant positive spatial autocorrelation in county economic efficiency, strengthening over time, for both Queen adjacency and Euclidean distance weight matrices. Figure 10 (LISA diagrams) reveals local spatial autocorrelation, with high-high clusters in the east and low-low clusters in Yulin City in 2012, with increasing spatial autocorrelation over time.

The findings confirm the steady improvement in county-level economic efficiency in HBOY. The spatial clustering of high-efficiency counties highlights the importance of spatial spillover effects and agglomeration economies. The negative impact of being a core city area on efficiency suggests potential issues with resource allocation or excessive government expenditure in these areas. The positive impact of economic linkage underscores the importance of transportation infrastructure and inter-county cooperation. The results support the need for policy interventions focused on improving transportation networks, boosting comprehensive county development, expanding local markets, and managing government expenditure, particularly in core city areas.

This study provides valuable insights into the economic efficiency of counties within the HBOY urban agglomeration. The findings highlight the importance of spatial factors and inter-county linkages in economic efficiency. The identified policy implications can guide strategies to promote balanced regional development. Future research could focus on exploring the reasons behind the negative impact of being a core area on efficiency and expanding the analysis to incorporate technological progress as a production factor. Further research might also explore the dynamic interplay between different spatial scales (county, city, province) and economic efficiency.

The study's reliance on secondary data limits the depth of investigation into the drivers of inefficiency at a more granular level. The choice of proxy variables for land usage, capital stock, and economic linkage may influence the results. The study's focus on a specific urban agglomeration in China limits the generalizability of the findings to other regions. Future research could refine methodology and address these limitations.