Cost function and its use for intergovernmental educational transfers in Vietnam
2009; Taylor & Francis; Volume: 20; Issue: 1 Linguagem: Inglês
10.1080/09645290903313087
ISSN1469-5782
Autores Tópico(s)School Choice and Performance
ResumoAbstract The purpose of this paper is twofold. First, although many cost function studies have been done in developed countries, there has been no such study for the developing countries such as Vietnam. This paper will make the first attempt at conducting a cost function analysis for Vietnam. Second, it also demonstrates how the results of the cost function analysis can be used to potentially address two weaknesses of the current norms for intergovernmental educational transfers in Vietnam. These norms neither are relevant for output-based budgeting purposes nor fully account for factors influencing provinces' cost of delivering education. The cost function results can be used for a more output-oriented and more adequate, thus more equitable, distribution of educational transfers. Keywords: cost functioneducationVietnamintergovernmental transfers Acknowledgments I would like to thank William Duncombe, John Yinger, Larry Schroeder, and two anonymous referees for their insightful comments and Kelly Bogart for her help with proofreading. Notes For instance, cost function studies have been done for general education in several US states, namely California (Imazeki Citation2008), Massachusetts (Nguyen-Hoang and Yinger Citation2009), New York (Duncombe, Lukemeyer, and Yinger Citation2003), Kansas and Missouri (Duncombe, Lukemeyer, and Yinger Citation2008), Texas and Wisconsin (Reschovsky and Imazeki Citation2001), and higher education in the USA (Koshal and Koshal Citation2000) or in the UK (Johnes Citation1996; Glass, McKillop, and Hyndman Citation1995). A rare cost function study of Dougherty (Citation1990) performs a cost function estimation of economies of scales only in secondary technical and vocational schools in China. However, unlike existing cost function specifications, the model in this paper does not incorporate any performance measure as an explanatory variable. Transfer norms, which are the focus of this paper, are different from allocative norms between the provincial and subprovincial governments. Under the current 2002 State Budget Law, allocative norms can be different across provinces. This is aimed at helping poorer provinces where more school-age children are not enrolled in schools. The GOV has recently been involved in the medium-term expenditure framework (MTEF) program. However, this program which was piloted in four sectors including education in 2003–2004 is primarily designed to provide a framework for budgeting projections in a period of three to five years. Also, given various institutional problems, it remains to be seen when this program will be institutionalized (Clarke Citation2007). As in other education cost studies, efficiency refers to the degree of resources provinces consume to produce a certain output given the current technology. It will be further discussed in later sections. See Yinger (Citation2004) for a thorough discussion of four equity standards in education aid: adequacy, access equality, fiscal neutrality and equality. A few provinces with sufficient own-source revenue do not receive balancing transfers. According to data provided by Vietnam's Ministry of Finance (see the link in the data section), while all provinces received some balancing transfers in 2002, 15 out of 64 provinces did not get the transfers in 2005. However, the eligibility of these 15 provinces for targeted transfers stays unchanged. Note that the term 'own-source' does not mean that provincial governments have complete authority over revenue sources. They in fact cannot change tax rates or base. They include taxes assigned 100% at the provincial level, shared taxes between the central and provincial governments, minor charges and fees, retained collections of revenue assigned to them that exceed budgeted targets. The charges and fees usually account for a small portion (less than 5%) of provinces' total revenue, and richer provinces benefit more from the retained excess collections (Rao, Bird, and Litvack Citation1998). While traditional cost studies may incorporate the median voter model into their modeling framework, the median voter model is irrelevant in the case of Vietnam. The entire provincial process is not subject to popular votes. Rather, the provincial budgets are internally determined (Nguyen et al. Citation2001). This discussion on efficiency draws partly from Duncombe and Yinger (Citation2008). No study has been able to separate these two components of efficiency. First, one approach is to use a nonparametric data envelopment analysis (DEA) to come up with efficiency indices which are then included in the expenditure function (Duncombe and Yinger Citation2000). However, the final DEA index that has taken into account cost (nondiscretionary) factors results in the underestimation of their coefficients in Equation (Equation2). DEA also cannot distinguish between technical inefficiency and statistical noise (Murillo-Zamorano Citation2004). Second, other studies, for example Downes and Pogue (Citation1994), may employ fixed effects to eliminate efficiency which is assumed to be constant over time. The use of fixed effects, however, does not deal with efficiency factors that do change over time. Plus, because S and cost factors exhibit little variation within provinces over the time period of this study, removing cross-section variation constrains a researcher's ability to estimate the effect of S and cost factors on C. In fact, fixed-effects models based on the data used for this study do not yield any significant coefficients and have an overall adjusted R 2 of only 0.02. Without fixed effects, I cannot rule out the possibility that the estimated coefficients may be subject to bias from unobserved factors; however, the lack of data prevents me from estimating the model with fixed effects. Although the weakness of this approach is that these conceptual links to efficiency, M and L, cannot be directly tested, it works well in practice (Duncombe and Yinger Citation2008). Both educational transfers and parental contributions are part of provinces' total balancing transfers and own-source revenue. Tax price refers to how much a local resident has to pay (usually in property taxes) for an increment in S. The lack of the tax-price mechanism results from the fact that provincial governments have no autonomy over (property) tax bases or rates. Both have the same title as 'Decree on the Promulgation of Regulations on the Exercise of Democracy in Communes.' They are applied to both rural and urban areas. There are cases in which two provinces with the same graduation rate may have different performances. One province incurs higher educational expenditures and obtains higher 'unaccounted' output. In this context, the unaccounted portion can be considered as the first component of efficiency earlier discussed: spending on other outputs. More specifically, the graduation rate for each level of schooling has its own accountability implication. Completing universal primary and lower secondary education is among the strategic goals explicitly stated in the national EFA Action Plan (GOV 2003, 27). Reports on provinces' lower and upper secondary graduation rates attract substantial attention from politicians and the public. Given the importance of all graduation rates, I do not differentially weight the performance index. Also, an equally weighted performance index is standard practice in existing cost function studies (Duncombe et al. Citation2008). More specifically, fifth, ninth and twelfth graders have to take their respective graduation exam. Another reason to treat S as endogenous is that it may be correlated with other unobserved factors including private tutoring. Andrews and Stock (Citation2005) demonstrate that relative to two-stage-least-squares estimation, the Fuller-k estimator is less subject to the bias associated with weak instruments. The average share excludes the ethnicity of the province itself. By 'adjacent,' I mean that provinces are in the same region and do not necessarily share borders. See Figure 3 for a map of regions in Vietnam. The term 'copycat' comes from the original version of their paper (Case, Hines, and Rosen Citation1989). In fact, the exogeneity of this IV and the IV for W fits Pearl's (Citation2000, 248) third definition of IV. The squared log specification is widely used in econometric studies (Greene Citation2002, 119; Wooldridge Citation2005, 189–9) including many of the cited cost functions. The correlation coefficient between the percent of urban population and of college-graduated people is only 0.5, which is far below the 0.8 rule-of-thumb threshold for a threat of collinearity (Kennedy Citation2008). Data are not complete for 2003 and 2004. Data for 2006 were not publicly available by the time this study was conducted. Data are only available at the province level, which prevents me from attempting a value-added model. Besides its estimation challenges using the cost function (Duncombe and Yinger Citation2008), this model requires performance outputs in the same cohort in different grades. The data can be found at http://www.mof.gov.vn/Default.aspx?tabid=5733. Lai Chau was split into the smaller Lai Chau and Dien Bien, Dak Lak into the smaller Dak Lak and Dac Nong, and Can Tho into the municipal Can Tho and Hau Giang. Excluding missing data does not cause estimation bias when they are missing at random (Wooldridge Citation2005). Data for the six reorganized provinces can be considered to be randomly missing in this context because the reorganization has nothing to do with educational cost. Malesky (Citation2009) argues that provincial divisions that have increased the number of provinces by 60% since 1990 come from the gerrymandering strategy adopted by reformists who wanted to free reform-oriented provinces from provinces dominated by the state-owned enterprise sector. As performance (an output) is determined simultaneously with expenditures (an input) and thus treated as an endogenous variable, this interpretation is legitimate. The coefficient of the percent of concrete house owners is −0.0013 and equivalent to that of the percent of owner-occupied housing units found in other cost function studies, for example Duncombe (Citation2006) and Duncombe et al. (Citation2008). This validity assessment is not dependent on the choice of a performance standard. Different standards lead to different levels of the funding gap, but do not change the correlation coefficient under discussion. See Hanushek (Citation2005) for a critical assessment of these two approaches. However, further research is needed on how to adopt either of them in the context of Vietnam. One this point, Downes (Citation2004) argues that 'this failure means that other methodologies should be used in place of the cost function methodology, even if the cost function methodology is theoretically sound and is most likely to generate valid estimates of the spending levels needed to meet the standard. Taken to its extreme, this argument implies that, in choosing a method to determine adequate spending levels, one is better off choosing a method that is easy to understand but wrong rather than a method that is difficult to explain but that produces the right answers.' The cost function analysis is not perfect, but rather is the best currently available method with the strengths needed to address the weaknesses. I have addressed the two most important validity criteria: internal and statistical conclusion validity. I cannot, however, conduct other validity and reliability tests as Duncombe did. For instance, since this is the first cost function study for Vietnam, I cannot test my estimates' interrater reliability that requires several studies. Nor can I assess the test-retest reliability because two years of data used in this study cannot be divided into subperiods. The derivations of the indices are already adopted in American-based cost studies (Duncombe and Yinger Citation2007b). In relation to Equation (Equation6), XC includes W, N, and F whereas Xe consists of T, R, M, and L. Since the dependent variable of the cost function is in logarithmic form, all of its predicted values are adjusted following the procedures in Wooldridge (Citation2005). The efficiency level has to be constant across all provinces so that the cost index reflects only variation in cost factors. Use of the average level of efficiency is a standard practice in other cost function studies, and it also facilitates the interpretation of the cost index. Note that this is just an estimated, not guaranteed, minimum level of cost per pupil to obtain S*. I assume that all unexplained variation in spending across provinces comes from variation in efficiency, not in costs. This assumption is reasonable because it is in line with the unobserved nature of efficiency in the public sector. Also, the distribution of the efficiency index varies negligibly without the residual. The contributions can be ideally linked to provinces' revenue-raising capacity as a common practice in the foundation formula for education aid in developed countries.
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