Evaluation of county-level economic efficiency and its spatiotemporal differentiation in Hohhot-Baotou-Ordos-Yulin urban agglomeration in China

In 2018 the State Council approved the development plan for the Hohhot-Baotou-Ordos-Yulin (HBOY) urban agglomeration, a strategically located, energy-centered region in Western China with about 12 million people and a GDP of over 1.65 trillion RMB in 2021. Western China remains relatively underdeveloped, and county economies are crucial yet lagging contributors to national output. This study addresses why HBOY’s development lags by distinguishing insufficient input from low economic efficiency. The research objectives are: (1) to evaluate county-level economic efficiency for 30 county units within HBOY and identify low-efficiency locations; and (2) to reveal temporal and spatial patterns of efficiency and their spatial correlation. By focusing on counties rather than provinces or entire cities, the study provides higher-resolution insights into underperforming areas. The paper contributes by examining counties in an underdeveloped region and by analyzing the spatial distribution and correlation of county-level efficiency in HBOY.

The review contrasts two main efficiency measurement approaches: DEA (nonparametric, no statistical noise, deviations treated as inefficiency) and SFA (parametric stochastic frontier, decomposes deviations into noise and inefficiency, requires a functional form). Total Factor Productivity (TFP) is highlighted as a key indicator of input-output efficiency. Since Aigner et al. (1977), SFA has become a central tool across sectors (manufacturing, hospitals, banking, agriculture, land and water use). In China, many SFA applications exist at firm and regional levels, but most efficiency studies are at provincial or city scales; few examine counties, and those that do typically focus on developed regions (e.g., Jiangsu, Zhejiang, Chongqing, Henan). Prior work often overlooks spatial correlation in county-level efficiency. This study fills gaps by focusing on underdeveloped counties in HBOY and by explicitly analyzing spatial distribution and spatial autocorrelation of county-level economic efficiency using SFA, Moran’s I, and LISA.

Design: A panel stochastic frontier analysis (SFA) following Battese and Coelli’s time-varying inefficiency framework is employed to estimate county-level economic efficiency (TEit = exp(−uit)). The production function is a log-linear Cobb–Douglas with three inputs and one output. Model: Yit = Xitβ + (vit − uit), with vit ~ N(0, σv²), uit ≥ 0 following a truncated normal distribution with mean μit = Zitδ. Efficiency TEit = exp(−uit). Production variables (log form): - Output: Regional GDP (ten thousand RMB), from Statistical Yearbooks. - Inputs: Land Usage (square km; county land area used as proxy due to lack of built-up area data); Labor Force (number of employed persons); Capital Stock (ten thousand RMB), estimated via Perpetual Inventory Method (PIM) using province-level initial stocks (Zhang et al., 2004), allocating to counties by GDP share, depreciation rate 5%. Inefficiency determinants Zit: - Economic Linkage: Index computed via augmented gravity model Gij = Iij / Tij, where Iij reflects the comprehensive development levels of counties i and j, and Tij is shortest one-way driving time between the two. - Government Involvement: Government expenditure per capita (RMB/capita). - Market Size: Retail sales per capita (RMB/capita). - Core Area: Dummy indicating whether the county is the core area of its city. Data: County-level data for 30 HBOY counties, mainly from Inner Mongolia and Shaanxi Statistical Yearbooks and local departments. Efficiency evaluated for years 2012, 2016, and 2020. Spatial analysis: ArcGIS used to visualize efficiency levels. Global spatial autocorrelation assessed via Moran’s I under two spatial weight matrices (Queen contiguity and Euclidean distance). Local spatial autocorrelation and clusters identified using LISA (Anselin, 1995).

- Production function (Table 2): - Labor elasticity β1 = 0.3393 (t = 5.0525, p < 0.01): a 1% increase in labor raises output by 0.3393% ceteris paribus. - Land elasticity β2 = 0.0538 (t = 0.8795, ns): land effect not significant. - Capital elasticity β3 = 0.5163 (t = 7.0931, p < 0.01): a 1% increase in capital raises output by 0.5163%. - Inefficiency model (δ): - Economic Linkage δ1 = −0.3374 (p < 0.01): stronger inter-county linkages reduce inefficiency (increase efficiency). - Government Involvement δ2 = 0.1426 (ns): higher government spending tends to increase inefficiency (not statistically significant). - Market Size δ3 = −0.1663 (p < 0.10): larger local markets reduce inefficiency (weak significance). - Core Area δ4 = 0.6522 (p < 0.01): core-area status increases inefficiency. - Model stats: Sigma-squared = 0.1224 (p < 0.01); Gamma = 0.0226 (ns); Log likelihood = −33.0822; LR one-sided error test = 30.9575. - Efficiency trends (Table 3): Mean efficiency increased from 0.505 (2012) to 0.641 (2016) to 0.753 (2020). Min efficiency: 0.285 (2012), 0.343 (2016), 0.360 (2020). Max efficiency: 0.863 (2012), 0.983 (2016), 0.993 (2020). - City-level (2020): Baotou 0.829; Ordos 0.815; Hohhot 0.804; Yulin 0.662. - Notable county-level changes: Largest efficiency gains 2012–2020 in Hengshan District (+102.39%), Wushen Banner (+95.14%), Helin County (+90.24%). Slowest gains: Jia County (+12.63%), Hohhot District (+15.06%), Baotou District (+18.01%). High 2020 efficiency near frontier: Baotou District 0.993, Dalat Banner 0.992; several counties exceeded 0.98. - Spatial pattern: High-efficiency clusters formed and strengthened over time in the middle-east junction of Hohhot, Baotou, and Ordos; low-efficiency cluster concentrated in the southeast (Yulin City counties). By 2020, only three counties had efficiency <0.5, all in Yulin. - Global spatial autocorrelation (Moran’s I): - Queen matrix: 2012 I = 0.232 (p = 0.012); 2016 I = 0.288 (p = 0.002); 2020 I = 0.363 (p = 0.001). - Euclidean matrix: 2012 I = 0.306 (p = 0.009); 2016 I = 0.346 (p = 0.002); 2020 I = 0.391 (p = 0.001). Positive and strengthening spatial autocorrelation over time. - Local spatial autocorrelation (LISA): - 2012: H-H cluster around Tumed Right Banner, Dalat Banner, Ordos District, Yijinholo Banner; L-L cluster in Yulin (Hengshan, Zizhou, Mizhi, Wubao, Qingjian). L-H outliers: Guyang, Qingshuihe; H-L: Suide. - 2016: Stronger clustering; six H-H and six L-L (all in Yulin); L-H: Guyang, Qingshuihe; H-L: Suide; several clusters significant at 0.001. - 2020: 15 significant counties; H-H count similar to 2016; L-L persists in Yulin (Jia, Mizhi, Zizhou, Suide, Wubao, Qingjian). New L-H: Wuchuan, Qingshuihe; Hengshan shifts to H-L. - Determinants: Economic linkage is the primary positive driver of efficiency; market size also positive; core area status and (to a lesser extent) government spending can undermine efficiency.

The findings directly address the research questions by locating low-efficiency counties, documenting steady improvements in efficiency, and revealing clear spatial patterns and correlations. High-efficiency counties form clusters in the middle-eastern HBOY, indicating spillovers whereby efficient cores (e.g., Baotou–Ordos corridor) may lift neighboring areas. Significant and strengthening Moran’s I confirms that county efficiencies are spatially interdependent. The SFA results identify mechanisms: stronger inter-county economic linkages and larger market size improve efficiency, suggesting benefits from integration, connectivity, and scale. Conversely, being a city’s core area and higher government spending can raise inefficiency, consistent with potential resource misallocation or crowding-out from excessive public outlays in favored cores. These insights are relevant for regional policy in underdeveloped western China, emphasizing networked development and cautious public expenditure in core areas.

This study evaluates county-level economic efficiency in the HBOY urban agglomeration using a stochastic frontier approach and spatial analysis. Main contributions include: (1) providing county-scale evidence from an underdeveloped region; (2) documenting rising efficiency from 2012 to 2020; (3) identifying robust spatial clustering and positive spatial autocorrelation; and (4) quantifying determinants, with economic linkage and market size improving efficiency while core-area status and government spending tend to reduce it. Policy implications include improving inter-county transport to reduce time distance, enhancing counties’ comprehensive development levels, expanding local markets to stimulate consumption, and moderating government expenditure—especially in core areas—to avoid inefficiency. Future research should incorporate economic linkage metrics in county efficiency models, further probe mechanisms behind core-area inefficiency, and expand temporal and geographic coverage.

- Technology as a production factor was excluded; authors argue inter-county technological differences are limited at this small regional scale, but omission may bias estimates. - Land input used county land area as a proxy due to lack of built-up area data, potentially overstating productive land. - Capital stock was not directly observed; estimated via PIM with a uniform 5% depreciation and allocated from provincial stocks by GDP shares, which may introduce measurement error. - Analysis uses three time points (2012, 2016, 2020), limiting temporal dynamics. - Efficiency and spatial analyses rely on available statistical yearbook data; data quality and consistency constraints may affect results.