Spatial Decomposition of Funding Inequality in China's Basic Education: A Four-Level Theil Index Analysis

Various education finance and taxation reforms in the past several decades have substantially changed China’s system for funding basic education, but the present system is still characterized by insufficient funding and large inequalities across localities. Using data of more than 2000 county-level units all over the country during 1998-2005, this study uses Theil index to spatially decompose the pattern of funding inequality in China’s basic education across four geographic and administrative levels. The analysis shows that the level of inequality remained high after the rural taxation and education finance reforms since 2000, despite the efforts to increase education-purpose fiscal transfers to local governments, and that the gaps are especially severe across provinces in the same region and across prefectures in the same province

Rural Taxation Reforms and Compulsory Education Finance in China

In recent decades, the responsibility for the financing of compulsory education in rural China has rested with townships and villages which, with limited tax authority and uneven revenue capacity, increasingly relied on a plethora of arbitrarily imposed fees for funding. To reduce farmers‘ fiscal burdens, since 2000 the central government has installed a series of rural taxation reforms. Correspondingly, the central government shifted the administrative responsibilities of rural compulsory education to the county level in 2001, and implemented a series of policies to make up for the loss of revenues to education. Using a provincial-level dataset from 1998 to 2006, this study examines whether and how the rural taxation reforms have affected the adequacy and equality of compulsory education finance in China, and addresses related theoretical and policy implications from the perspective of intergovernmental fiscal relations

Fiscal Effects of Local Option Sales Tax on School Facilities Funding: Evidence from North Carolina

Since the 1970s, the North Carolina Legislature has authorized its counties to levy four local option sales taxes (LOST). Proceeds from two of them are partially restricted for school capital needs; two other LOST are used to augment counties’ general revenues that may also affect school capital funding. Experiences from other states have raised concerns that the adoption of LOST may increase inequality in school finance, but the empirical results have been mixed. Using a data set of one hundred North Carolina county school districts from 2004 to 2006, this study examines how public school facilities are funded, and investigates whether the adoption of LOST aggravates or alleviates inequality in public school capital revenues in the state

Generalize Hilbert operator acting on Dirichlet spaces

Let $\mu$ be a positive Borel measure on the interval $[0,1)$. For $\gamma>0$, the Hankel matrix $\mathcal{H}_{\mu,\gamma}=(\mu_{n,k})_{n,k\geq0}$ with entries $\mu_{n,k}=\mu_{n+k}$, where $\mu_{n+k}=\int_{0}^{\infty}t^{n+k}d\mu(t)$. formally induces the operator $$\mathcal{H}_{\mu,\gamma}=\sum_{n=0}^{\infty}\left(\sum_{k=0}^{\infty}\mu_{n,k}a_k\right)\frac{\Gamma(n+\gamma)}{n!\Gamma(\gamma)}z^n,$$ on the space of all analytic functions $f(z)=\sum_{k=0}^{\infty}{a_k}{z^k}$ in the unit disc $\mathbb{D}$. Following ideas from \cite{author3} and \cite{author4}, in this paper, for $0\leq\alpha<2$, $2\leq\beta<4$, $\gamma\geq1$. we characterize the measure $\mu$ for which $\mathcal{H}_{\mu,\gamma}$ is bounded(resp.,compact)from $\mathcal{D}_{\alpha}$ into $\mathcal{D}_{\beta}$.Comment: 7 page