International Journal of Forestry Research

Volume 2016, Article ID 4970801, 6 pages

http://dx.doi.org/10.1155/2016/4970801

## Modelling Analysis of Forestry Input-Output Elasticity in China

^{1}School of Economics and Management, Beijing Forestry University, Beijing 100083, China^{2}Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China^{3}Center for Chinese Agricultural Policy, Chinese Academy of Sciences, Beijing 100101, China

Received 22 April 2016; Revised 20 August 2016; Accepted 28 August 2016

Academic Editor: Piermaria Corona

Copyright © 2016 Guofeng Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Based on an extended economic model and space econometrics, this essay analyzed the spatial distributions and interdependent relationships of the production of forestry in China; also the input-output elasticity of forestry production were calculated. Results figure out there exists significant spatial correlation in forestry production in China. Spatial distribution is mainly manifested as spatial agglomeration. The output elasticity of labor force is equal to 0.6649, and that of capital is equal to 0.8412. The contribution of land is significantly negative. Labor and capital are the main determinants for the province-level forestry production in China. Thus, research on the province-level forestry production should not ignore the spatial effect. The policy-making process should take into consideration the effects between provinces on the production of forestry. This study provides some scientific technical support for forestry production.

#### 1. Introduction

The reform of collective forest rights is another major revolution of the rural management system after land reform in China [1, 2]. This reform has endowed farmers with partial forestry rights, so that these farmers are able to use their own forest resources and thereby gain revenue [3–5]. Thereby, in order to calculate the elasticity of labor, capital, and land inputs during the forestry growth, this study used a spatial econometric model to compute the contributions of all elements. The production flexibility and efficiency of capital are always a research hotspot [6–8]. Solow proposed an economy growth accounting model and applied new classical growth theory to economic accounting [9]. The existing research mainly focused on the input-output elasticity of agricultural production [10–12]. However, there is little research about forestry, a special agriculture department, and even the existing findings are controversial [13, 14]. The researchers argued the output elasticity coefficients from the first, second, and third industries of forestry are 1.44, 0.72, and 0.89, respectively, during 1998–2005; 1.66, 0.88, and 0.81, respectively, during 2006–2021; 1.82, 0.96, and 0.91, respectively, during 2022–2030 [15]. These findings should be further validated from new perspectives and with new methods immediately.

This paper consists of four parts, the first part gives a brief description of relative research, the second part specifies the materials and methods used in this paper, the third part gives out results and discussion, and the last part is the conclusion part. Through this paper, we try to prove that the forestry production in one province influences that in another province.

#### 2. Materials and Methods

##### 2.1. Spatial Autocorrelation Test of Forestry Production

The forestry production in China is found with severe spatial differences and is largely correlated with the differences and fluidity of regional forestry resource [16, 17]. Forestry production is modestly different among regions, but there may be spatial correlations among provinces [18–20]. In order to figure out the correlations and heterogeneity of province-level forestry production, we used global Moran’s index: where and describe the observations of forestry output in regions and , respectively, represents the number of regions, is the average observation of forestry outputs, and is the spatial weight.

Under the circumstance of zero correlation, Moran’*I* was used to construct a standard normal index as follows: where and are decided by the spatial distribution of data and the arrangement of spatial lag matrix. When the -value is significant and positive, there is positive space correlation, indicating the presence of regional agglomeration among similar production regions. When the -value is significant but negative, there is negative significant correlation, indicating the presence of regional dispersity among similar production regions. When the -value is equal to zero, there exists random spatial distribution.

The global Moran’s index can partially represent the space autocorrelation. However, owing to the repeated computation or mutual cancellation during computations, we used a local Moran’ index reflecting spatial autocorrelation, the local spatial correlation index, and Moran scatter diagram to further reveal whether or not there exists local spatial agglomeration. Local Moran’s index is computed as follows:where is the standardized space weight matrix (the sum of each row is one). The expected value of local Moran’s index is as follows:

When is larger than the expected value of , there exists spatial agglomeration of similar forestry outputs around region or local space positive correlation. When is smaller than , there exists large differences among similar forestry outputs around region or local space negative correlation.

Moran scatter diagram shows the 2D scatter plot that visualizes (a vector composed of the deviation between the observed value and the mean) and (space weighted average, or space lag vector). The vector-form global Moran’*I* index is computed as follows: where ; when is the standardized space weight matrix, then ; at this moment, the global Moran’s index is the linear regression slope of relative to . The first and third quadrants on Moran’*I* scatter plot represent the positive space correlations, while the second and fourth quadrants indicate the negative space correlations. Specifically, the first quadrant indicates the regions with large observed values are surrounded by large-value regions; the second quadrant indicates the regions with small observed values are surrounded by large-value regions; the third quadrant indicates the regions with small observed values are surrounded by small-value regions; the fourth quadrant indicates the regions with large observed values are surrounded by small-value regions. The first and third quadrants represent typical positive space correlations, while the second and fourth quadrants indicate the local negative space correlations.

LISA (Local Indictors of Spatial Association) analysis is used to figure out the spatial differences in production. When LISA passes the significance test, there is local positive spatial autocorrelation, or this region is surrounded by regions with similar performance, called spatial agglomeration. When this region and its nearby regions are all found with large observed data, it is called a high-high region, and otherwise, it is called a low-low region.

##### 2.2. Selection of Weights for Forestry Space Autocorrelations

The selection of spatial weight is associated with the results of spatial autocorrelation and spatial regression. is defined as the contiguity or distance of any element from other elements. Currently, there are many types of weight matrices, including contiguity, -nearest neighbors, and distance threshold. Specifically, contiguity matrices are divided into Rook (contiguity estimated from four directions of east, south, north, and west) and Queen (besides these four directions, it also involves other corners). As for -nearest neighbors, several points closest to a test point are called its neighbors and each is assigned a weight 1, and other points are given a weight 0. Many researches figured out that different matrix may lead to different results, including spatial coefficient and the signs of the coefficient [21].

##### 2.3. Space Econometric Model in Forestry Economy Growth

According to traditional economics, the economic growth mainly depends on two endogenous factors: labor and capital, but it is affected by technological progress, an exogenous factor. In this model, the land element is considered as an internal factor of economic growth. In other words, the output level from each forestry region is decided by the labor input , land input , and capital input . Then, this model is expressed aswhere is the forestry economic development level in region ; is the technical level, is the labor input into forestry; is the land area; is the capital input; , and are the corresponding output elasticity, respectively. If , , and , then the return to scale is unchanged, increases, and gradually drops, respectively. Logarithm of both sides of (6) yields

##### 2.4. Space Lag Model (SLM) for Forestry Production Function

The basic model of forestry production does not involve space correlations. Taking spatial effects into account means the regional forestry production is affected not only by the local investment level, but also by the spillover effect from other nearby forestry regions. In this way, SLM is determined:where is the space weight matrix and is the weighted variable from a nearby forestry region. This model reflects the effects of regional forestry production from the input-output levels in nearby regions through the space effect.

##### 2.5. Space Error Model (SEM) for Forestry Production

SEM takes into account the variables that may be ignored in the decision model, such as human capital, research level, and climate change. The space error model is used to measure the roles that may be played by the spatially interacting errors. SEM is expressed aswhere is the space weight matrix, and measures the space error effect on regional forestry production due to observational errors.

##### 2.6. Space Units and Data Sources

This study was targeted at 31 provinces or autonomous regions or municipality cities of Mainland China in 2013. The data were cited from* China Forestry Statistical Yearbook 2013*. The output variable was the total regional forestry production value. Regarding the release time of forestry statistical yearbooks, we used the forest areas in the statistics as the forestry area input. The number of labor forces by the end of 2013 was used as the regional labor force input. The fixed assets investment was used as capital input.

#### 3. Results and Discussion

##### 3.1. Global Moran’s Index for Space Correlation of Forestry Production

To study the interferences of weight indices on the space effect, we used three space weight matrices, and through stepwise distance increment, we tested the attenuation effect of distance (Table 1). Clearly, global Moran’*I* index gradually decreases and shows the attenuation effect of distance. Moreover, Moran’s index estimated from Queen1 weight matrix is 0.3685, indicating the most significant space autocorrelation () and the strong spatial dependence and evident space effect of forestry production.