Abstract: Based on provincial panel data of water footprint and grey water footprint, and with the help of data envelopment analysis model considering and without considering the undesirable output, this paper estimates the water resources utilization efficiency in China from 1997 to 2011. The spatial weighting matrix based on economy-space distance function is established to discuss spatial autocorrelation of water resources utilization efficiency. With the help of absolute β convergence model, this paper concludes that there exists β convergence in the water resources utilization efficiency. Under the condition of considering and without considering the undesirable output, it takes about 52.6 and 5.6 years respectively to achieve the extent of half of convergence. By mean of the space Durbin econometric model, this paper studies spatial spillover effects of the provincial water resources utilization efficiency in China. The results show that, 1) With considering and without considering the undesirable output, there is significant spatial correlation in provincial water resource efficiency in China. 2) Under the two cases, the spatial autoregressive coefficients (ρ) are 0.278 and 0.507 respectively, at 1% significance level. There exist the spatial spillover effects of provincial water resources utilization efficiency. 3) With considering the undesirable output, these factors of the education funds, the transportation infrastructure, and the proportion of industrial and agricultural water have positive impacts. These factors of foreign direct investment, the industrial added value water consumption in ten thousand yuan, per capita water consumption, and the total precipitation have negative impacts. 4) Without considering the unexpected output, the factor of GDP per labor has a greater positive significant influence on the water resources utilization efficiency. However the facts of industrial added value water consumption in ten thousand yuan and the transportation infrastructure have no significant influence. 5) Regardless of undesirable output of water resources utilization efficiency, the assessment of the present real water resources utilization in China will be distorted and policy-making will be misled. The water efficiency measure considering environmental factors (such as gray water footprint) is more reasonable.

Key words: SBM model, undesirable output, space Durbin econometric model, spillover effects, space effect, water resources utilization efficiency