Prediction and Validation of the Promoting Effect of Technological Entrepreneurship on Sustainable Economic Growth

Considering the lack of clear hierarchical division for entrepreneurship, this paper employs the KMC, an unsupervised learning method, to decompose TE into multiple states, because this method is flexible, and easy to implement and understand.

In traditional KMC, the clustering results might be unstable and poor, if the cluster heads are not properly initialized. Here, the KMC is improved to solve the problem. First, the hierarchical clustering was adopted to make an initial division. Then, the mean of each initial cluster was taken as an initial cluster head. By using the class information of the dataset, the spatial distribution of the initial cluster heads was kept consistent with the actual data distribution, which promotes the clustering quality.

As shown in Figure 1, the improved KMC is implemented in five steps:

Step 1. Adjust and verify the number of clusters k;

Step 2. Perform hierarchical clustering on the dataset;

Step 3. Count the number of initial clusters, and take the mean of each cluster as the initial cluster head;

Step 4. Calculate the distance between each of the remaining objects and each of the initial cluster head, and allocate each object into the cluster of the nearest cluster head;

Step 5. Recalculate the head of each cluster.

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Figure 1. The flow chart of improved KMC

After data clustering, the optimal feature subset was derived from the preprocessed dataset by minimizing the difference between samples in the same class while maximizing the difference between samples in different classes.

Let $D S:\left\{x_{i}, y_{i}\right\}_{i=1}^{M} \in D S$ be the original dataset of m samples, where $y_{i} \in\{1,2, \ldots, l\}$ is the class label of sample x_i, and x_i is the sample with m indices x_i={x_i1, x_i2,…, x_im,}; and ε be the class discrimination matrix, in which each element ε_ij={0,1} indicates whether y_i matches with (i=1,2,…,l, j=1,2,…,l). If samples x_i and x_jhave the same class label, then y_i=y_j and ε_ij=1; otherwise, ε_ij=0.

Drawing on the k-nearest neighbors (kNN) algorithm, a neighborhood class record matrix R was established to store the class of the neighborhood composed of samples x_i and x_j with the same class label. In the matrix R, each element $\omega_{i j}: \omega_{i j} \in\{0,1\}$ represents that whether x_i and x_j belong to the same neighbor. If yes, ω_ij=1; otherwise, ω_ij=0.

Following the large loss principle, the feature evaluation function G was modeled to detect the normal and abnormal samples of each index, and then minimize difference between samples in the same neighborhood while maximizing the difference between samples in different neighborhood:

$G=\frac{\max (\sum\limits_{ijp}^{N}{{{\omega }_{ij}}}(1-{{\varepsilon }_{ip}}){{\lambda }_{ijp}})}{\min (\sum\limits_{ij}^{n}{_{ij}}\sum\limits_{h=1}^{m}{{{({{x}_{ih}}-{{x}_{jh}})}^{t}}({{x}_{ih}}-{{x}_{jh}})}+\sum\limits_{i,p}^{n}{{{\theta }_{ip}}})}$                 (1)

where,

${{\theta }_{ip}}=\min (\sum\limits_{h=1}^{m}{{{w}_{h}}{{({{x}_{ih}}-{{x}_{jh}})}^{2}}-\sum\limits_{h=1}^{n}{{{w}_{h}}{{({{x}_{ih}}-{{x}_{ph}})}^{2}}}})$            (2)

where, λ_ijρ is the loss function; θ is a record function for noisy samples.

Two outputs were defined for our analysis framework: intermediate goods, and consumer goods. Labor, as a social product, was taken as an input. For simplicity, it is assumed that all residents have an infinitely long life, and the same preference in consumption throughout their life. This is a common assumption in microeconomic theories. Then, the marginal utility of individual consumption is a constant that can be expressed as an interest rate.

In each period, it is assumed that each individual supplies a unit of labor. For a society of L individuals, the total labor supply equals L. The utility difference in labor can be reflected by the intermediate goods. Thus, L can be defined as:

$L=x+n$       (3)

where, x is the skilled labor input in the production of intermediate goods.

The production of consumer goods y can be defined as:

$y=A{{x}^{\alpha }}$     (4)

where, y=Ax^α is the product flexibility, representing the dependence of consumer goods on the input of intermediate goods x; A is the productivity of intermediate goods, i.e. the technical level of the production of consumer goods.

Taking the production process as a random innovation sequence, this paper defines the realization rate of innovation at any moment in the economy λf(n), where n is the investment of technical labor by research and development (R&D) department; λ is a constant for R&D productivity; f(n) is a concave production function with constant returns to scale: (f(0)=0) and "$\forall n \geq 0$.

In addition, it is assumed that the memory does not accumulate in the R&D process. That is, the realization probability of innovation only depends on the investment in the current period, and has nothing to do with that in the previous periods.

The innovation is mainly achieved in the R&D of intermediate goods. New intermediate goods can be used to produce more efficient consumer products. Using new intermediate goods, the productivity will be increased by a factor ratio of A_t=γA_t-1. If there is no lag in technological diffusion, the factor ratio, i.e. rate of technological progress rate, satisfies:

${{A}_{t}}={{A}_{0}}{{\gamma }^{t}}\text{ }t\text{=1,2,3}...$       (5)

where, A₀ is the initial productivity. 

The patented innovation can be utilized to monopolize the production of intermediate goods, throughout the long valid period of the patent. However, there is eventually an end to the monopoly of any manufacturer in intermediate goods. Once the next innovation emerges, the monopoly will cease to exist.

For a monopolist of intermediate goods, the goal is to maximize the present value of the expected profit during the monopoly period:

${{\pi }_{t}}=\underset{x}{\mathop{\max }}\,\left[ {{p}_{t}}(x)x-{{w}_{t}}x \right]$         (6)

where, w_t is the salary of the manufacturing industry; p_t(x) is the price of intermediate goods sold by the second innovator at time t to the manufacturer, or set by the manufacturer through internal innovation.

In a competitive market, the optimal conditions for the production of consumer goods can be modeled as p=MC. Since the sector of intermediate goods is monopolized, the manufacturer will definitely set the price of intermediate goods p_t(x) equal to that of consumer goods x to maximize his/her profit:

${{p}_{t}}(x)={{A}_{t}}\alpha {{x}^{\alpha -1}}$       (7)

Judging by whether the enterprise could produce new products, technologies, or services, entrepreneurship can be easily divided TE and general entrepreneurship (GE). An enterprise with TE can provide novel products/services, and boast strong pricing power and competitiveness. By contrast, an enterprise with GE only provides homogenous products, and passively accepts the price set by TE enterprises.

Without the loss of generality, it is assumed that the society has N1 TE enterprises and N2 GE enterprises, that is, a total of N=N1+N2 enterprises. The TE enterprises generally possess a group of R&D personnel, which are skilled labor force in technological R&D (hereinafter referred to as technical labor force), and have the ability to cultivate new technical labor force. On the contrary, GE enterprises are unable to cultivate technical labor force. Therefore, the technical labor force of the whole society comes from TE enterprises. Thus, the proportion of technical labor force in manufacturing industry can be described as:

${{n}^{\text{*}}}=\eta {{N}_{1}}$     (8)

where, η is the proportionality parameter.

When it comes to data availability, there is a severe lack of TE data or reports on TE quantification. But there is abundant literature on the quantification of entrepreneurship and the influence of entrepreneurship over SEG. In most studies, the entrepreneurship is measured by the number or proportion of private enterprises.

The previous studies have demonstrated the following advantages of measuring entrepreneurship with the number of enterprises: First, the number of enterprises is easy to obtain, and the number of the enterprises with property rights is a good indicator of entrepreneurship level in terms of SEG. Second, the entrepreneurship can be decomposed easily based on the ownership and other attributes of enterprises. Third, the number and proportion of enterprises can be monitored for a long time, reflecting the continuity of entrepreneurial activities.

Therefore, a similar method was developed to select TE indices. The most active areas of TE in China are high-tech zones in major cities. Under the guidance of national policies, many high-tech zones, especially early starters, have become major gathering places of TE enterprises. Suffice it to say that the high-tech zones are the synonym of TE in contemporary China. The high presence of TE in these high-tech zones is attributed to multiple factors: an institutional environment that encourages innovation, the complete infrastructure that supports the high-tech development, and the abundance of specialized talents that facilitates technical R&D.

As mentioned before, this paper aims to predict and validate the promoting effect of TE on SEG. Like any other country, China has been vigorously pursuing SEG, a key indicator of social welfare. Since the TE index is a scalar and a total factor index, the regional gross domestic product (RGDP), also a scalar and a total factor index, was selected to measure the SEG of each region. For convenience, the natural logarithm of RGDP was taken to highlight its sustainability in the face of TE. Instead of nominal GDP, the RGDP was calculated based on the actual GDP with 1994 as the base period, using the consumer price index (CPI).

As for the prediction model, regression analysis was adopted rather than black box-based methods like deep learning (DL). The regression analysis aims to verify the dependency between different variables by finding the optimal linear mapping from the feature space to the output space, such that the model can describe the TE-SEG relationship intelligently and intuitively. Hence, the regression model can be defined as:

$\begin{align}  & \text{lnGD}{{\text{P}}_{\text{i,t}}}={{\beta }_{0}}+{{\beta }_{1}}\text{lnSen}{{\text{t}}_{i',t'}} \\ & +\gamma {{Z}_{i',t'}}+{{\lambda }_{i'}}+{{\eta }_{t}}+{{\varepsilon }_{i',t'}} \\ \end{align}$             (9)

where, i and t are the serial numbers of city and period, respectively; lnGDP is the natural logarithm of GDP; InSent is the logarithm of TE Sent; $Z_{i^{\prime}, t^{\prime}}$ is the set of control variables, including fixed asset investment, inflation rate, economic openness, financial development, etc.; $\lambda_{i^{\prime}}$ is the individual-fixed effect; $\eta_{t^{\prime}}$ is the time-fixed effect; β₁ is the impact of TE on SEG. If β₁<0, TE has a negative impact on SEG; if β₁>0, TE has a positive impact on SEG.

For the above econometric model, ordinary least squares (OLS) estimation will bring biased and inconsistent results, due to the problem of endogeneity. In our model, the endogeneity might arise from the influencing factors of SEG that are not covered by the control variables. The estimation might also be biased, owing to the reverse causal relationship between TE and control variables.

In addition, an instrumental variable related to TE but independent of SEG was designed for regression: the TE with 1-period lag was chosen as the instrumental variable of the current TE. This variable was designed based on the following considerations: Internally, TE is a gradual process to output technologies and products that satisfy the growing demand of residents. The current TE is strongly correlated with the TE in the previous periods. Externally, the current TE is not directly affected by the previous TE. The effect is mediated by many exogenous factors. Thus, it is to use the TE with 1-period lag as an instrumental variable of the current TE.