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College of Economics and Management, Huazhong Agricultural University, Wuhan 430070, China

1 Introduction

In the 1960s, human capital theory developed rapidly in Western economics, and was highly valued in most Western countries. Known as the "father of human capital", Schulz is a representative researcher who points out that the important factors that contribute to the country’s economic growth have shifted from the increase of land, population and capital stock to improvement of human ability and technical level, namely the accumulation of human capital[1]. Since then, the contribution of human capital to economic growth has become the focus of attention for researchers. In the late 1980s, Romer established knowledge accumulation model based on Learning-by-doing Model, to study the effects of endogenous technological progress on economic growth, and concluded that human capital was the main factor to promote economic growth[2]. As the state has attached great importance to issues concerning agriculture, countryside and farmers, rural economic growth issue has become a hot topic of academic research. The scholars have conducted a series of in-depth studies on how to promote farmers’ income from various angles. Although there are many ways to increase farmers’ income, they can be broadly divided into two categories: one way is to use a series of income growth mechanisms inside agriculture to increase farmers’ income; the other way is to expand the idea outside agriculture, and increase farmers’ income by accelerating industrialization, urbanization, and transferring rural surplus labor. At present, academic circles have reached a consensus that the key to solving the problem of farmers’ income lies in investing human capital in farmers, and improving the level of human capital for farmers. This paper studies the contribution of human capital and physical capital to farmers’ income growth. According to the contribution rate of the two factors, combined with the capital distribution in rural areas, the reasonable arrangement for the ratio between the two kinds of capital can help to maximize the economic growth rate. This paper performs an empirical analysis of rural economy in Hubei Province, and draws some conclusions, so as to provide some reference for study on the relationship between human capital and economic growth. In addition, in existing studies, there are many articles reporting the use of Cobb-Douglas production function to analyze economic growth issues, and most of them use the C-D function to analyze the contribution of human capital to economic development. Zhao Xinglan (2009)[3]uses Cobb-Douglas function to study the contribution of China’s human capital investment to economic growth, concludes that the elasticity of human capital stock to GDP is 2.381, and makes related recommendations to promote China’s human capital investment. In addition, Shen Baohui (2009)[4], Cheng Xiaoping (2009)[5]use Cobb-Douglas function and Solow growth equation to do empirical analysis on economic growth factors in Shandong Province and Inner Mongolia. Cobb-Douglas function can be used to calculate the elasticity of capital and labor, and Solow residual can be used to calculate the contribution of technological progress to economic growth, to make up for the lack of simple function variables. This paper uses Cobb-Douglas production function and its variation form, establishes econometric model to do empirical analysis on capital and labor that affect rural economic growth in Hubei Province, and makes constructive recommendations for promoting rural economic development and increasing farmers’ income in Hubei Province.

2 Empirical analysis of rural economic growth in Hubei Province

2.1Establishmentofeconometricmodel

2.1.1Model setting. The Cobb-Douglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the amounts of two or more inputs, particularly physical capital and labor, and the amount of output that can be produced by those inputs. The Cobb-Douglas form was developed and tested against statistical evidence by Charles Cobb and Paul Douglas during 1927-1947. The following hypotheses are made: (i) factor may substitute for each other; (ii) marginal output of factors is greater than zero; (iii) marginal output of factors is greater than zero is diminishing; (iv) non-negativity. Thus, the relationship between output and input is simplified into the following C-D production function form, namely assuming there are two kinds of input: physical capital input and human capital input[6]. AssumingYis output,Lis human capital input,Kis physical capital input,Ais the factor other than labor and capital, such as technology and institution, then:Y=AKαLβ. C-D production function was relatively applicable in the previous economic context, but with the economic development, the traditional C-D production function is difficult to explain the complex economic output. Firstly, the traditional C-D production function abstracts the important input factor-technology into a predetermined constant, which is inconsistent with the current rapid development of knowledge economy, and it is difficult to reflect the contribution of knowledge to output. Secondly, the traditional C-D function fails to examine the positive effect of institutional factors on output. Thirdly, the traditional C-D function believes that the factors can completely substitute each other, but in factor, this substitution is limited, and there is more or less loss of efficiency in the production due to "alternative stickiness". Given that taking the logarithm of sequence does not change the nature of sequence, this paper takes the logarithm of both sides of the above equation, and adds the random error term, to build a new C-D function:

LnY=LnA+αLnK+βLnL+ε

whereαandβrepresent the elasticity of physical capital and human capital output;εrepresents the effect of random disturbance, andε<1.

2.1.2Variable definition. In this paper, we choose the total income of rural residents as outputY, and fixed capital stock as physical capital inputK. In the specific calculation, the commonly used "perpetual inventory method" is employed to measure the capital stock in a given year, namely:

wheretrepresents yeart;Iis fixed capital investment;Ptis the fixed asset investment price index (with 1993 as base period);δis the depreciation rate, and based on the method of Liu Wenetal.[7],δtakes 5%.

As for the definition of capital stock in the base period (1993), this paper learns from the practice of Zhang Junetal.[8], to use the fixed capital investment in the primary industry (mainly agriculture) to be divided by 10% as the initial capital stock of rural areas. As for the measurement of human capital stockL, we use the average years of schooling to measure human capital. For the application of method of years of education, we mainly determine the weight corresponding to different years of education. According to the China’s educational system at all levels, we get the weight to measure of human capital accumulation: illiteracy or semi-illiteracy, 2 years; primary school education, 6 years; junior high school education, 9 years; senior high school education, 12 years; technical secondary school education, 12 years; junior college and above, 16 years. Thus, we get the following calculation formula:

whereLidenotes the number of rural labor force with illiteracy or semi-illiteracy, primary school education, junior high school education, senior high school education, technical secondary school education, junior college and above, respectively;Eidenotes the human capital accumulation weight of rural labor force with illiteracy or semi-illiteracy, primary school education, junior high school education, senior high school education, technical secondary school education, junior college and above, respectively.

The data used in this paper are mainly fromChinaRuralStatisticalYearbookandHubeiStatisticalYearbook, and in order to keep in line with the statistical standard, the total number of labor force at all levels of education is as follows:

whereLiis number of persons with education leveliamong every hundred rural labor forces.

By the above formula, we calculate the average years of education for the rural labor force in Hubei Province, so the rural human capital stock in Hubei ProvinceL=per capita capital stock of rural labor force (average years of schooling)×rural working population.

2.2Modelparameterestimation,testandanalysisThe data related to rural economy in Hubei Province can be shown in Table 1. Using SPSS17.0 statistical software, based on the statistics in Table 1, we perform regression analysis on C-D production function (Table 2). The regression equation is: LnY=-27.577+0.273 LnK+3.331 LnL.tvalue of constant term and all parameters in this model is greater thantcritical value, and the parameter value is greater than 0, so the model passes economic significance testing; the goodness of fit is 0.895, indicating that the above model well fits the observation value of sample. Tolerance is greater than 0.1 andVIF<10, so two independent variables are within the non-collinearity test standards. The results of the econometric analysis show that the elasticity of rural physical capital input in Hubei Province to net income is 0.273, and the elasticity of human capital input to rural per capita income is 3.331, indicating that for each additional percentage point of physical capital input and human capital input, rural per capita net income will increase by 0.293 and 3.331 percentage points, respectively, and human capital makes greater contribution than physical capital. Constant term value is -27.577, mainly containing the influence of technical, institutional and policy factors and errors. Technological progress is not an independent factor. Farmers can purchase the means of production with high technological content to organize production and business activities, and education and training for farmers and other human capital investment forms can be used to achieve the diffusion effect of social technology. The technological progress factors are also integrated into physical capital and human capital.

Table1ThedatarelatedtoruraleconomyinHubeiProvince

YearPercapitanetincome∥yuanTotalruralpopulation∥104OutputY∥108Fixedassetsinvestment∥108yuanPriceindexPhysicalcapitalstockKRuralworkingpopulation∥104PercapitahumancapitallevelTotalhumancapitalstockL1993670.803887.78260.79012.16/121.602149.66.8214660.2721994626.924079.27255.74012.48135.8115.612173.37.0715365.2311995677.823942.17267.21012.42148.6121.682195.57.1815763.6901996783.183921.82307.15011.89161.4127.392216.77.2616093.24219971172.744114.68482.54014.97174.2132.332216.87.2816138.30419981511.223971.18600.13027.22182.9140.012217.57.4516520.37519991863.623859.73719.31029.76190.2158.882224.77.7317196.93120002102.234038.00848.88041.02194.2179.272240.77.8817656.71620012172.244022.82873.85059.48195.2209.382234.67.9217698.03220022217.083947.86875.27071.22194.2255.492247.68.0518093.18020032268.503547.80804.82070.60192.5310.392261.17.9918066.18920042352.163349.50787.86077.48197.5361.992265.88.1018352.98020052444.063323.80812.36080.08197.3417.532266.08.1218399.92020062566.763297.30846.34088.80203.8472.782265.08.1318414.45020072890.012466.70712.88077.55216.0533.452262.08.2018548.40020083099.203243.301005.16092.88220.8580.532266.08.2318649.18020093419.353199.501094.020107.64224.8639.822267.08.3118838.77020103997.413174.301268.900149.40234.0710.272262.08.3818955.56020114656.383129.601457.260231.25256.0816.982270.08.4219113.40020125035.263088.801555.290321.59252.9996.232265.08.5019252.500

Data source:ChinaRuralStatisticalYearbookandHubeiStatisticalYearbook(1994-2013).

Table2RegressionanalysisofC-Dproductionfunction

CoefficientModelNon-normalizedcoefficientBStandarddeviationStandardcoefficientTrialversiontSig.CorrelationZeroorderPartialPartCollinearitystatisticsToleranceVIFConstant-27.57711.791-2.3390.032Physicalcapitalstock∥108yuan0.2730.1650.3601.6520.0170.8510.3720.1780.2454.083Humancapitalstock∥104persons3.3311.2880.5642.5870.0190.8780.5310.2790.2454.083

3 Conclusions and recommendations

3.1ConclusionsThe paper selects the correlation data about rural economic growth in Hubei Province as samples to analyze the contribution of physical capital and human capital to rural economic growth by the new C-D function and SPSS22.0. (i) Human capital input makes greater contribution to farmers’ income than physical capital input. This can also explain the reason for the current transfer of considerable rural labor to the non-agricultural sector. The productive inputs to agriculture contribute little to farmers’ income growth. From farmers’ income structure, we can also see that the proportion of agricultural income to total income shows a downward trend with the transfer of rural labor in recent years. (ii) The government and farmers’ emphasis on human capital investment needs to be further improved. We can see from Table 1 that the average years of schooling for Hubei’s farmers are still less than 9 years (compulsory education). Human capital investment is different from material investment, and it is very difficult to make the investor get the profit quickly in the short period, so many farmers have weak consciousness in human capital investment. (iii) Farmers’ income-generating capacity can be improved by optimizing allocation of factors of production. For example, the government can increase the investment in human capital for farmers, formulate relevant training policies for farmers according to local conditions, effectively organize and guide the production and flow of rural labor force, and construct incentive mechanism to im-prove the enthusiasm of farmers for investing in human capital.

3.2Policyrecommendations(i) Increasing investment in human capital in rural areas. The government should change the thought of over-emphasizing physical capital but neglecting human capital. On the basis of optimizing physical capital input structure and improving physical capital use efficiency, there is a need to increase the proportion of investment in rural education and farmers’ training, so as to gradually raise the education level of rural labor force. In the process of technical and skill training for farmers, it is necessary to conduct job training concerning primary, secondary and tertiary industries, provide services for the transfer of rural labor and agricultural development, and enhance the skill training and advanced farming and breeding technical training. At the same time, it is necessary to actively guide farmers to invest in education, medical skill training to improve rural human capital stock, and further increase the support for rural areas and agriculture to make high-quality labor force find ways to get rich in rural areas and achieve a virtuous circle of agricultural and rural development. (ii) Establishing two-way flow mechanism of rural human capital. The government can provide employment information, rights protection and other services, to ensure the effective transfer of rural surplus labor and reduce the transfer cost of rural human capital. In addition, it is necessary to allot special funds for the development of all types of adult education in rural areas, and organize cultural quality education and labor skill training for the rural labor, so that farmers’ basic quality and professional level are improved, and the new generation of farmers become both educated technicians and hard-working laborers, thereby increasing the rural per capita human capital stock and promoting the rapid development of rural economy. At the same time, it is necessary to improve the rural employment environment, improve the benefit of talent in rural areas, and attract high-quality talent to flow to rural areas.

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