Research on the relationship between government subsidies, R&D investment and high-quality development of manufacturing industry

Yu Guan

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Applied Mathematics and Nonlinear Sciences

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Format: Magazine
eISSN: 2444-8656
Première parution: 01 Jan 2016
Périodicité: 2 fois par an
Langues: Anglais

With the increasingly fierce market competition, independent innovation has become the only means for enterprises to survive and progress, and enterprises pay more and more attention to product R&D investment [1]. The subsidy provided by the government can not only alleviate the problem of insufficient R&D funds in enterprises, but can also serve as a signal to convey to investors the government's expectation of R&D and innovation activities of enterprises and affirmation of the future development of enterprises, which will help enterprises attract more investment and promote the sustainable development and value enhancement of enterprises [2]. However, government subsidy is one of the most commonly applicable ways for the industrial chain to apply the current policies [3], and the effectiveness of its implementation results varies from scholar to scholar.

Scholars generally believe that government subsidies play a positive role in creating value for enterprises. Dongmin and Tianshang [4] studied the listed companies in Shanghai and Shenzhen, and found that government subsidies play a positive role in improving corporate economic performance and social responsibility. The fund use efficiency of private enterprises in terms of operating performance and social responsibility increases with increase in the scale of government subsidies. Ye et al. [5] found that the operating results of enterprises can be improved through the transmission mechanism of government financial subsidies. Shaoxiu et al. [6] found that government subsidies have a significant impact on the enterprise value, which can help enterprises improve their value to a certain extent. For the information technology industry, government subsidies can help enterprises alleviate the difficulties of capital shortage, improve production efficiency and promote the promotion of enterprise value. Chunmei and Pei [7] took 331 listed high-tech enterprises on the gem as samples for empirical analysis. Their research results show that government subsidies have a significant positive incentive effect on both scientific and technological performance and the economic performance of enterprise innovation. Jiahui et al. [8] show that enterprises need to allocate resources reasonably and increase their R&D investment to improve their scientific and technological strength, so as to increase the value of enterprises. By using R&D expenditure, enterprises can introduce advanced production equipment, enterprise management experience, improve the R&D and innovation ability of the whole team, improve enterprise production efficiency, and realise enterprise value. In Fogarty and Simon [9], the relationship between tax preference and RD capital investment in the pharmaceutical manufacturing industry is first established to provide reference for government departments to formulate and regulate tax policies and the independent innovation ability of the pharmaceutical manufacturing industry. Based on co-integration analysis, Granger causality test, impulse response and variance decomposition, this paper empirically analyses the relationship between tax preference and R&D capital investment in the pharmaceutical manufacturing industry. The results show that the comprehensive tax burden of the industry decreased by 1% and the internal R&D expenditure increased by 8.293%. The conclusion is that the current preferential tax policies in China have a significant incentive effect on the R&D capital investment of the manufacturing industry, and the continuous preferential tax policies are reasonable for the scientific R&D and design capital investment of the pharmaceutical manufacturing industry. According to the actual situation of the company's development, government departments further strengthen the relevant tax incentives, encourage enterprises to participate in R&D activities and propose to maintain the long-term stability of tax policies as far as possible.

This paper studies the relationship between government subsidies, R&D investment and high-quality development of manufacturing industry, and analyses the mechanism of government subsidies on R&D investment of Chinese enterprises, in order to improve the acceptability of government subsidies to promote the R&D policy of the manufacturing industry. The quantile regression model is constructed to reduce the constraints, make it more inclusive to heterogeneity, make the estimation more robust, make the estimated coefficients more significant and make the regression analysis results more reliable.

Theoretical analysis

Government subsidies can not only reduce the burden on enterprise assets, but also carry out enterprise credit evaluation on enterprises of financial institutions, which is conducive to enterprises to obtain loans from financial institutions and maintain their long-term development trend. When government subsidies are used for the production and operation of enterprises, they will be affected by the completion process of market value, causing a lag effect on the use value of enterprises [10].

With the gradual improvement of China's market economic system and fierce market competition, there is no doubt that if the manufacturing industry wants to survive and seek the development trend, it must obtain the core competitiveness through independent innovation. The improvement of manufacturing innovation capability requires rational allocation of R&D resources. Product R&D should increase project investment and create enterprise use value [11]. At the same time, it takes a period of time for enterprise product R&D from project approval to successful R&D, and then to market promotion, and the benefits may not be immediately reflected in the enterprise value.

In recent years, the research on enterprise independent innovation shows that the key for government departments to apply enterprise product R&D is the harm to R&D activities. Some enterprises' product R&D and activities are found to be at a high risk for small-scale taxpayers, which hinders the improvement of the enterprise's R&D capability [12]. At this time, government subsidies support the innovation activities of enterprise product R&D investment, improve the expected rate of return and independent R&D can promote work ability [13].

In the context of independent and mass entrepreneurship, competition among enterprises is becoming more and more fierce, and R&D investment is an important factor related to the sustainable development of enterprises. The Chinese government has formulated a series of support plans for development of the information technology industry, and also provided necessary financial support for the creation industry [14]. Government subsidies alleviate the problem of capital shortage faced by enterprises and provide financial guarantee for their R&D investment. The implementation of R&D activities is related to the future development of enterprises. Government subsidies can reduce the cost and income risks brought by R&D activities, encourage enterprises to actively carry out R&D activities, provide guarantee for the long-term development of enterprises and promote the value of enterprises [15]. Therefore, the R&D investment of enterprises links the government subsidy with the enterprise value, and has an intermediary effect on the two.

Build model

3.1

Quantile regression method

The standard mean function of any variable is analysed by traditional least square regression. In other words, some variables are used to describe the mean value of relevant variables [16]. However, in the discussion of social economics and investment, the quantile of any variable at any probability level has attracted more and more attention. To fully consider the real valued random variables Y, [17] its right continuous distribution function is F(y) = P(Y ≤ y). For Y of τ the quantile regression model, the loss function formula is: (1) $ρ_{τ} (u) = u (τ - I (u))$ {\rho_\tau}(u) = u(\tau - I(u)) where $I (u) = {\begin{matrix} 0, u \geq 0 \\ 1, u < 0 \end{matrix}$ I(u) = \left\{{\matrix{{0,u \ge 0} \cr {1,u < 0} \cr}} \right. . To find the optimisation problem expected by the loss function [18], the expression is as follows: (2) $min E [ρ_{τ} (Y - \hat{ξ})] = (τ - 1) \int_{- \infty} (y - \hat{ξ}) dF (y) + τ \int_{\hat{τ}}^{+ \infty} (y - \hat{ξ}) dF (y)$ \min E\left[ {{\rho_\tau}(Y - \hat \xi)} \right] = (\tau - 1)\int_{- \infty} (y - \hat \xi)dF(y) + \tau \int_{\hat \tau}^{+ \infty} (y - \hat \xi)dF(y)

For $\hat{ξ}$ \hat \xi calculating the first derivative, the formula is: (3) $0 = (1 - τ) \int_{- \infty}^{\hat{ξ}} dF (y) - τ \int_{\hat{ξ}}^{+ \infty} dF (y) = F (\hat{ξ}) - τ$ 0 = (1 - \tau)\int_{- \infty}^{\hat \xi} dF(y) - \tau \int_{\hat \xi}^{+ \infty} dF(y) = F(\hat \xi) - \tau

If there is only one solution, and if there are multiple solutions $\hat{ξ} = F^{- 1} (τ)$ \hat \xi = {F^{- 1}}(\tau) , the left endpoint of the interval is taken. Asymmetric linear loss function needs to be substituted with ρ_t(u), obtaining the point estimates of quantiles [19]. To fully consider the samples ${y_{i}}_{i = 1}^{n}$ \left\{{{y_i}} \right\}_{i = 1}^n , the empirical distribution function is as follows: (4) $F_{n} (y) = n^{- 1} \sum_{i = 1}^{n} I, y_{i} \leq y$ {F_n}(y) = {n^{- 1}}\sum\limits_{i = 1}^n I,\quad \quad {y_i} \le y (5) $\int ρ_{τ} (y - \hat{ξ}) {dI}_{n} y \Rightarrow n^{1} \sum_{i = 1}^{n} \int ρ_{τ} y_{i} (- \hat{ξ})$ \int {\rho_\tau}\left({y - \hat \xi} \right)d{I_n}y \Rightarrow {n^1}\sum\limits_{i = 1}^n \int {\rho_\tau}{y_i}\left({- \hat \xi} \right)

For the calculation sample ${y_{i}}_{i = 1}^{n}$ \left\{{{y_i}} \right\}_{i = 1}^n of τ the quantile problem of probability level is transformed into an optimisation problem, namely: (6) $min_{i + R} \sum_{i = 1}^{n} ρ_{τ} (y_{τ} - \hat{ξ})$ \mathop {\min}\limits_{i + R} \sum\limits_{i = 1}^n {\rho_\tau}\left({{y_\tau} - \hat \xi} \right)

Given information set x and y the conditional quantile function is q_y(τ/x) = x′β, and parameter β estimates are as follows: (7) $min_{β \in R^{m}} \sum_{i = 1}^{n} ρ_{τ} (y_{i} - x_{i}^{'} β)$ \mathop {\min}\limits_{\beta \in {R^m}} \sum\limits_{i = 1}^n {\rho_\tau}\left({{y_i} - x_i^{'}\beta} \right)

3.2

Finite sample distribution and asymptotic distribution

Setting Y₁, ⋯, Y_n is i.i.d. Sequence for the cumulative distribution function is F. For the probability level τ, set the distribution F in the neighbourhood of ξ_τ = F⁻¹(τ), where f (ξ_τ) > 0. With continuous density f [20], sample τ of the horizontal quantile is: (8) ${\hat{ξ}}_{τ} \equiv inf_{\hat{ξ}} {\hat{ξ} = \underset{ξ \in R}{arg min} n^{- 1} \sum_{i = 1}^{n} ρ_{τ} (Y_{i} - ξ)}$ {\hat \xi_\tau} \equiv \mathop {\inf}\limits_{\hat \xi} \left\{{\hat \xi = \mathop {\arg \min}\limits_{\xi \in R} {n^{- 1}}\sum\limits_{i = 1}^n {\rho_\tau}\left({{Y_i} - \xi} \right)} \right\}

Objective function $\sum_{i = 1}^{n} ρ_{r} (Y_{i} - ξ)$ \sum\limits_{i = 1}^n {\rho_r}\left({{Y_i} - \xi} \right) is the sum of convex functions; it is also a convex function and the right ξ of the first derivative is as follows: (9) $g_{n} (ξ) = n^{- 1} \sum_{i = 1}^{n} (I (Y_{1} < ξ) - τ)$ {g_n}(\xi) = {n^{- 1}}\sum\limits_{i = 1}^n \left({I\left({{Y_1} < \xi} \right) - \tau} \right)

Basis of g_n(ξ) monotonicity of [21], events ${\hat{ξ}}_{τ} > ξ$ {\hat \xi_\tau} > \xi and g_n(ξ) < 0 the formula is: (10) $P {\sqrt{n} ({\hat{ξ}}_{t} - ξ_{τ}) > δ} = P {g_{n} (ξ_{r} + \frac{δ}{\sqrt{n}}) < 0} = P {n^{- 1} \sum_{i = 1}^{n} (I (, Y < ξ_{τ} + \frac{δ}{\sqrt{n}}) - τ)$ P\left\{{\sqrt n \left({{{\hat \xi}_t} - {\xi_\tau}} \right) > \delta} \right\} = P\left\{{{g_n}\left({{\xi_r} + {\delta \over {\sqrt n}}} \right) < 0} \right\} = P\left\{{{n^{- 1}}\sum\limits_{i = 1}^n \left({I\left({,Y < {\xi_\tau} + {\delta \over {\sqrt n}}} \right) - \tau} \right)} \right.

The expected value of $g_{n} (ξ_{τ} + δ / \sqrt{n})$ {g_n}\left({{\xi_\tau} + \delta /\sqrt n} \right) is: (11) $\begin{array}{l} E (g_{n} (ξ_{τ} + δ / \sqrt{n})) & = n^{- 1} \sum_{i = 1}^{n} E (I (Y_{1} < ξ_{τ} + δ / \sqrt{n}) - τ) \\ = n^{- 1} \sum_{i = 1}^{n} (1 - τ) F (ξ_{τ} + δ / \sqrt{n}) - τ (1 - F (ξ_{τ} + δ / \sqrt{n})) \\ = (1 - τ) F (ξ_{τ} + δ / \sqrt{n}) - τ (1 - F (ξ_{τ} + δ / \sqrt{n})) \\ = F (ξ_{τ} + δ / \sqrt{n}) - τ = \frac{F (ξ_{τ} + δ / \sqrt{n}) - F (ξ_{τ})}{δ i \sqrt{n}} \cdot δ / \sqrt{n} \to f (ξ_{τ}) δ / \sqrt{n} \end{array}$ \matrix{{E\left({{g_n}\left({{\xi_\tau} + \delta /\sqrt n} \right)} \right)} \hfill & {= {n^{- 1}}\sum\limits_{i = 1}^n E\left({I\left({{Y_1} < {\xi_\tau} + \delta /\sqrt n} \right) - \tau} \right)} \hfill \cr {} \hfill & {= {n^{- 1}}\sum\limits_{i = 1}^n (1 - \tau)F\left({{\xi_\tau} + \delta /\sqrt n} \right) - \tau \left({1 - F\left({{\xi_\tau} + \delta /\sqrt n} \right)} \right)} \hfill \cr {} \hfill & {= (1 - \tau)F\left({{\xi_\tau} + \delta /\sqrt n} \right) - \tau \left({1 - F\left({{\xi_\tau} + \delta /\sqrt n} \right)} \right)} \hfill \cr {} \hfill & {= F\left({{\xi_\tau} + \delta /\sqrt n} \right) - \tau = {{F\left({{\xi_\tau} + \delta /\sqrt n} \right) - F\left({{\xi_\tau}} \right)} \over {\delta i\sqrt n}} \cdot \delta /\sqrt n \to f\left({{\xi_\tau}} \right)\delta /\sqrt n} \hfill \cr}

The variance of $g_{n} (ξ_{τ} + δ / \sqrt{n})$ {g_n}\left({{\xi_\tau} + \delta /\sqrt n} \right) is as follows: (12) $\begin{array}{l} D (g_{n} (ξ_{τ} + δ / \sqrt{n}) = D n^{- 1} (\sum_{i = 1}^{n} I) (< ξ_{τ} + δ \sqrt{n} / - τ)) & = n^{- 2} D \sum_{i = 1}^{n} (I (Y < ξ_{τ} + δ \sqrt{n}) - τ \\ = n^{- 2} \sum_{i = 1}^{n} DI (Y < ξ_{τ} + δ / \sqrt{n}) - τ \end{array}$ \matrix{{D\left({{g_n}\left({{\xi_\tau} + \delta /\sqrt n} \right) = D{n^{- 1}}\left({\sum\limits_{i = 1}^n I} \right)} \right.\left({< {\xi_\tau} + \delta \sqrt n / - \tau)} \right)} \hfill & {= {n^{- 2}}D\sum\limits_{i = 1}^n \left({I\left({Y < {\xi_\tau} + \delta \sqrt n} \right) - \tau} \right.} \hfill \cr {} \hfill & {= {n^{- 2}}\sum\limits_{i = 1}^n DI\left({Y < {\xi_\tau} + \delta /\sqrt n} \right) - \tau} \hfill \cr}

According to the definition of variance [22]: (13) $\begin{array}{l} D (I (Y < ξ) - τ & = (- 1 τ - I ξ_{τ} - (δ \sqrt{n} - τ (\sqrt{n} + (- τ - {(F (ξ_{τ} + δ / \sqrt{n}) - τ)}^{2} (1 - F (ξ_{τ} + δ / \sqrt{n})) \\ = (1 - F {(ξ_{τ} + δ \sqrt{n})}^{2}) F ξ_{τ} - (δ \sqrt{n} + (F {(ξ_{τ} + δ / \sqrt{n})}^{2}) - (1 F (ξ_{τ} + δ \sqrt{n})) \\ = (F (ξ_{τ} + δ / \sqrt{n})) - (1 F ξ_{τ} + (δ \sqrt{n})) \end{array}$ \matrix{{D(I(Y < \xi) - \tau} \hfill & {= (- 1\tau - I{\xi_\tau} - (\delta \sqrt n - \tau (\sqrt n + (- \tau - {{(F({\xi_\tau} + \delta /\sqrt n) - \tau)}^2}\left({1 - F({\xi_\tau} + \delta /\sqrt n)} \right)} \hfill \cr {} \hfill & {= (1 - F{{({\xi_\tau} + \delta \sqrt n)}^2})F{\xi_\tau} - (\delta \sqrt n + (F{{({\xi_\tau} + \delta /\sqrt n)}^2}) - \left({1F\left({{\xi_\tau} + \delta \sqrt n} \right)} \right)} \hfill \cr {} \hfill & {= \left({F\left({{\xi_\tau} + \delta \;/\sqrt n} \right)} \right) - \left({1F{\xi_\tau} + \left({\delta \sqrt n} \right)} \right)} \hfill \cr}

So there are: (14) $\begin{array}{l} D (g_{n} (ξ_{τ} + δ / \sqrt{n})) & = n^{- 2} \sum_{t = 1}^{n} F (ξ_{τ} + δ / \sqrt{n}) (1 - F (ξ_{t} + δ / \sqrt{n})) \\ = F (ξ_{τ} + δ / \sqrt{n}) (- 1 F ξ_{τ} (+ δ / \sqrt{n})) / τ - (1 - τ) \end{array}$ \matrix{{D\left({{g_n}\left({{\xi_\tau} + \delta /\sqrt n} \right)} \right)} \hfill & {= {n^{- 2}}\sum\limits_{t = 1}^n F\left({{\xi_\tau} + \delta /\sqrt n} \right)\left({1 - F\left({{\xi_t} + \delta /\sqrt n} \right)} \right)} \hfill \cr {} \hfill & {= F\left({{\xi_\tau} + \delta /\sqrt n} \right)\left({- 1F{\xi_\tau}(+ \delta /\sqrt n))/\tau -} \right.\left({1 - \tau} \right)} \hfill \cr}

$I (Y_{i} < ξ_{τ} + δ / \sqrt{n}) - τ (i = 1, \dots, n)$ I\left({{Y_i} < {\xi_\tau} + \delta /\sqrt n} \right) - \tau (i = 1, \cdots,n) as an independent binomial distribution sequence, the probability $F (ξ_{τ} + δ / \sqrt{n})$ F({\xi_\tau} + \delta /\sqrt n) and $1 - F (ξ_{τ} + δ / \sqrt{n})$ 1 - F\left({{\xi_\tau} + \delta /\sqrt n} \right) get values τ and 1 −τ. According to the Moivre–Laplace limit theorem, $g_{n} (ξ_{τ} + δ / \sqrt{n}) = n^{- 1} \sum_{i = 1}^{n} (I (Y_{i} < ξ_{τ} + δ / \sqrt{n}) - τ)$ {g_n}\left({{\xi_\tau} + \delta /\sqrt n} \right) = {n^{- 1}}\sum\limits_{i = 1}^n \left({I\left({{Y_i} < {\xi_\tau} + \delta /\sqrt n} \right) - \tau} \right) The distribution is asymptotically normal [23].

If ω² = τ(1 −τ)/f² (ξ_τ) the formula is: (15) $\begin{array}{l} P (\sqrt{n} ({\hat{ξ}}_{t} - ξ_{τ}) > δ) & = P (g_{n} (ξ_{τ} + δ / \sqrt{n}) < 0) \\ = P (\frac{g_{n} (ξ_{τ} + δ / \sqrt{n}) - f (ξ_{τ}) δ / \sqrt{n}}{\sqrt{τ (1 - τ) / n}} < \frac{- f (ξ_{τ}) δ / \sqrt{n}}{\sqrt{τ (1 - τ) / n}}) \\ = P (\frac{g_{n} (ξ_{τ} + δ / \sqrt{n}) - f (ξ_{τ}) δ / \sqrt{n}}{\sqrt{τ (1 - τ) / n}} < - \frac{δ}{ω}) \to 1 - Φ (δ / ω) \end{array}$ \matrix{{P\left({\sqrt n \left({{{\hat \xi}_t} - {\xi_\tau}} \right) > \delta} \right)} \hfill & {= P\left({{g_n}\left({{\xi_\tau} + \delta /\sqrt n} \right) < 0} \right)} \hfill \cr {} \hfill & {= P\left({{{{g_n}\left({{\xi_\tau} + \delta /\sqrt n} \right) - f\left({{\xi_\tau}} \right)\delta /\sqrt n} \over {\sqrt {\tau (1 - \tau)/n}}} < {{- f\left({{\xi_\tau}} \right)\delta /\sqrt n} \over {\sqrt {\tau (1 - \tau)/n}}}} \right)} \hfill \cr {} \hfill & {= P\left({{{{g_n}\left({{\xi_\tau} + \delta /\sqrt n} \right) - f\left({{\xi_\tau}} \right)\delta /\sqrt n} \over {\sqrt {\tau (1 - \tau)/n}}} < - {\delta \over \omega}} \right) \to 1 - \Phi (\delta /\omega)} \hfill \cr}

It can be concluded that: (16) $\sqrt{n} ({\hat{ξ}}_{τ} - ξ_{τ}) \sim N (0, ω^{2})$ \sqrt n \left({{{\hat \xi}_\tau} - {\xi_\tau}} \right) \sim N\left({0,{\omega ^2}} \right)

Assume ω² = τ(1 −τ)/f² (ξ_τ). It is clear that there are two factors that affect the estimation accuracy of samples: on the one hand, in the tail τ(1 −τ) tend to get smaller values, and get higher estimation accuracy; on the other hand f (ξ_τ) small variance can be obtained in the high-density region, and the estimation accuracy is high, while in the low-density region, the estimation accuracy is relatively low.

Considering the linear regression model [24], the expression is: (17) $y_{i} = x_{i}^{'} β + ε_{i}, i = 1, \dots, n$ {y_i} = x_i^{'}\beta + {\varepsilon_i},i = 1, \cdots,n where ɛ_i(i = 1, ⋯, n) as i.i.d. Sequence, F the distribution function is described, f it describes the density function. If f (F⁻¹(x)) > 0, j = 1, ⋯, m, and $n^{- 1} \sum_{i = 1}^{n} x_{i} x_{i}^{'} \equiv Q_{n} \to Q_{0}$ {n^{- 1}}\sum\limits_{i = 1}^n {x_i}x_i^{'} \equiv {Q_n} \to {Q_0} , Q₀ is a positive definite matrix, MP dimensional vector estimation of multiple quantile regression ${\hat{β}}_{n} = ({\hat{β}}_{n}^{'} (τ_{1}), \dots, {\hat{β}}_{n}^{'} (τ_{m}))$ {\hat \beta_n} = \left({\hat \beta_n^{'}\left({{\tau_1}} \right), \cdots,\hat \beta_n^{'}\left({{\tau_m}} \right)} \right) has the following form: (18) $\sqrt{n} ({\hat{β}}_{n} - β) = {(\sqrt{n} ({\hat{β}}_{n} (τ_{,}) - β (τ_{j})))}_{j = 1}^{m} \sim N (0, Ω \otimes Q_{0}^{- 1})$ \sqrt n \left({{{\hat \beta}_n} - \beta} \right) = \left({\sqrt n \left({{{\hat \beta}_n}\left({{\tau_,}} \right) - \beta \left({{\tau_j}} \right)} \right)} \right)_{j = 1}^m \sim N\left({0,\Omega \otimes Q_0^{- 1}} \right)

If error term ɛ_i(i = 1, ⋯, n) is i.i.d. Sequence, strictly speaking, is an independent but inconsistent sequence, so the parameter limit distribution of a single quantile is: (19) $\sqrt{n} (\hat{β} (τ) - β (τ)) \sim N (0, τ (1 - τ) H_{n}^{- 1} \cdot J_{n} H_{n}^{- 1})$ \sqrt n (\hat \beta (\tau) - \beta (\tau)) \sim N\left({0,\tau (1 - \tau)H_n^{- 1} \cdot {J_n}H_n^{- 1}} \right) where, $J_{n} (τ) = n^{- 1} \sum_{i = 1}^{n} x_{i} x_{i}^{'}$ {J_n}(\tau) = {n^{- 1}}\sum\limits_{i = 1}^n {x_i}x_i^{'} , $H_{n} (τ) = lim_{n \to \infty} n^{- 1} \sum_{i = 1}^{n} x_{i} x_{i}^{'} f_{i} (ξ_{i} (τ))$ {H_n}(\tau) = \mathop {\lim}\limits_{n \to \infty} {n^{- 1}}\sum\limits_{i = 1}^n {x_i}x_i^{'}{f_i}\left({{\xi_i}(\tau)} \right) .

3.3

Estimation of asymptotic covariance matrix

ω² = τ(1−τ)/f² (ξ_τ) It is clear that the asymptotic accuracy of quantile regression depends on the derivative of the density function at the estimated quantile, that is, s(τ) = (f (F⁻¹(τ)))⁻¹. It can be called quantile density function [25]. Knowable F(F⁻¹(τ)) = t, bilateral pair t the derivation leads to: (20) $\frac{dF (F^{- 1} (τ))}{dt} = f (F^{- 1} (t)) \frac{d (F^{- 1} (t))}{dt} = 1$ {{dF\left({{F^{- 1}}(\tau)} \right)} \over {dt}} = f\left({{F^{- 1}}(t)} \right){{d\left({{F^{- 1}}(t)} \right)} \over {dt}} = 1 (21) $\frac{d (F^{- 1} (t))}{dt} = {(f (F^{- 1} (t)))}^{- 1} = s (t)$ {{d\left({{F^{- 1}}(t)} \right)} \over {dt}} = {\left({f\left({{F^{- 1}}(t)} \right)} \right)^{- 1}} = s(t)

So the sparse function is a quantile function F⁻¹(t) derivative. By performing a difference on the empirical quantile function, s(t) is estimated as: (22) ${\hat{s}}_{n} (t) = ({\hat{F}}_{n}^{1} (t + h_{n}) - {\hat{F}}_{n}^{- 1} (t - h_{n})) / (2 h_{n})$ {\hat s_n}(t) = \left({{{\hat F}_n}^1\left({t + {h_n}} \right) - \hat F_n^{- 1}\left({t - {h_n}} \right)} \right)/\left({2{h_n}} \right) where, ${\hat{F}}^{- 1}$ {\hat F^{- 1}} is representative of F⁻¹ experience estimates, h_n represents the window width, and when n → ∞ when, h_n → 0. Through the standard asymptotic property of density estimation [26], the optimal window width with the minimum mean square error is obtained as follows: (23) $h_{n} = n^{1 / 5} {(4.5 {(s (τ) / s^{''} (τ))}^{2})}^{1 / 5}$ {h_n} = {n^{1/5}}{\left({4.5{{\left({s(\tau)/{s^{''}}(\tau)} \right)}^2}} \right)^{1/5}}

Usually, s(τ)/s″(τ) pair distribution function F is insensitive, if the normal distribution is used, the substitution error is very small [27]. Namely: (24) $\frac{s (τ)}{s^{''} (τ)} = \frac{f^{2}}{2 {(f^{'} / f)}^{2} + (f^{'} / f - f^{''} / f)}$ {{s(\tau)} \over {{s^{''}}(\tau)}} = {{{f^2}} \over {2{{\left({{f^{'}}/f} \right)}^2} + \left({{f^{'}}/f - {f^{''}}/f} \right)}}

Send f = ϕ, (f′ / f) (F⁻¹(t)) = Φ⁻¹ (t) then: (25) $h_{n} = n^{- 1 / 5} (\frac{4.5 ϕ^{4} (Φ^{- 1} (t))}{{(2 Φ^{- 1} {(t)}^{2} + 1)}^{2}})$ {h_n} = {n^{- 1/5}}\left({{{4.5{\phi ^4}\left({{\Phi ^{- 1}}(t)} \right)} \over {{{\left({2{\Phi ^{- 1}}{{(t)}^2} + 1} \right)}^2}}}} \right)

Quantile function for sample $F_{n}^{- 1}$ F_n^{- 1} calculate by using the fitting residual of quantile regression, and the formula is: (26) ${\hat{u}}_{i} = y_{i} - x_{i}^{'} \hat{β} (τ), i = 1, \dots, n$ {\hat u_i} = {y_i} - x_i^{'}\hat \beta (\tau),\quad \quad i = 1, \cdots,n

The empirical quantile function is: (27) $F_{n}^{- 1} (t) = {\hat{u}}_{\infty}, t \in ((i - 1) / n, i / n)$ F_n^{- 1}(t) = {\hat u_\infty},\quad \quad t \in ((i - 1)/n,i/n)

In general, the number of zero residuals in quantile regression is exactly $\hat{β}$ \hat \beta number of parameters for p. Therefore, according to the residual estimation F⁻¹ the potential factor in the approach is the need to ensure adequate window width [28]. Obviously, when p/n relative h_n this phenomenon is more important when it is large, and can be reduced through strict implementation. Another estimate F⁻¹ the method is: (28) $F_{n}^{- 1} (τ) = \bar{x} {\hat{β}}_{n} (τ)$ F_n^{- 1}(\tau) = \bar x{\hat \beta_n}(\tau) where, $\bar{x} = n^{- 1} \sum_{i = 1}^{n} x_{i}$ \bar x = {n^{- 1}}\sum\limits_{i = 1}^n {x_i} .

Existence i.i.d. the limit form of the parameter covariance matrix of the error term model is: (29) $\sqrt{n} ({\hat{β}}_{n} (τ) - β (τ)) \sim N (0, ω^{2} (τ) D_{0}^{- 1})$ \sqrt n \left({{{\hat \beta}_n}(\tau) - \beta (\tau)} \right) \sim N\left({0,{\omega ^2}(\tau)D_0^{- 1}} \right)

Of which, ω²(τ) = τ(1 −τ)/f² (F⁻¹(τ)) $D_{0} = lim_{n \to \infty} n^{- 1} \sum_{i = 1}^{n} x_{i} x_{i}^{'}$ {D_0} = \mathop {\lim}\limits_{n \to \infty} {n^{- 1}}\sum\limits_{i = 1}^n {x_i}x_i^{'}

3.4

Diagnostic test of model

According to the traditional regression analysis R² a goodness-of-fit statistic [29], the scoring function is: (30) $Q (τ / X_{1}, β (τ)) = β_{0} (τ) + X_{1}^{'} β_{1} (τ)$ Q\left({\tau /{X_1},\beta (\tau)} \right) = {\beta_0}(\tau) + X_1^{'}{\beta_1}(\tau)

The optimal value of the objective function with unconstrained parameters is: (31) $\hat{V} (τ) = min_{β_{(τ)}} \sum_{i} ρ_{τ} (Y_{i} - β_{0} (τ) - X_{i}^{'} β_{1} (τ))$ \hat V(\tau) = \mathop {\min}\limits_{{\beta_{(\tau)}}} \sum\limits_i {\rho_\tau}\left({{Y_i} - {\beta_0}(\tau) - X_i^{'}{\beta_1}(\tau)} \right)

Null hypothesis H₀ : β₁(τ) = 0, optimal value of objective function with intercept only: (32) $\tilde{V} (τ) = min_{β_{0} (τ)} \sum_{i} ρ_{τ} (Y_{i} - β_{0} (τ))$ \tilde V(\tau) = \mathop {\min}\limits_{{\beta_0}(\tau)} \sum\limits_i {\rho_\tau}\left({{Y_i} - {\beta_0}(\tau)} \right)

According to the goodness-of-fit criterion, the formula is: (33) $R^{\} (τ) = 1 - \hat{V} (τ) / \tilde{V} (τ)$ {R^\backslash}(\tau) = 1 - \hat V(\tau)/\tilde V(\tau)

R¹ (τ) Within (0.1), the larger the value, the better the fitting effect in the quantile [30].

Set vector ς = (β^′ (τ₁), ⋯ β^′ (τ_m))′, the linear zero assumption is: (34) $H_{0} : R_{ς} = r$ {H_0}:{R_\varsigma} = r

The statistics of Wald test are: (35) $T_{n} = n {(R \hat{ς} - r)}^{'} {[R V_{n}^{- 1} R^{'}]}^{- 1} (R \hat{ς} - r) \sim χ_{q}^{2}$ {T_n} = n{(R\hat \varsigma - r)^{'}}{\left[ {RV_n^{- 1}{R^{'}}} \right]^{- 1}}(R\hat \varsigma - r) \sim \chi_q^2 where, q is a representative matrix of R rank, V_n is a representative of mp × mp matrix, middle (i, j) and the sub matrix is: (36) $V_{n} (τ_{i}, τ_{j}) = (τ_{i} \land τ_{j} - τ_{i} τ_{j}) H_{n} {(τ_{i})}^{- 1} J_{n} (τ_{i}, τ_{j}) H_{n} {(τ_{j})}^{- 1}$ {V_n}\left({{\tau_i},{\tau_j}} \right) = \left({{\tau_i} \wedge {\tau_j} - {\tau_i}{\tau_j}} \right){H_n}{\left({{\tau_i}} \right)^{- 1}}{J_n}\left({{\tau_i},{\tau_j}} \right){H_n}{\left({{\tau_j}} \right)^{- 1}}

Compared with the general least square method, it can only show the influence of independent variable parameters on the partial change of variables [31]. Quantile regression can more accurately show the variable transformation category of independent variables and the harm of independent variables to the standard spread pattern. It can capture various features of the spread. When the main parameters cause different harm to the spread of variables in different parts (such as left or right), it can more comprehensively describe the features of the spread, and then obtain comprehensive results.

Empirical results and analysis

The variables to consider the compressive strength of enterprises' independent innovation investment are basically the expenditure on innovation activities or the investment in independent innovation human resources [32]. The variables to consider the size of enterprises include the number of employees, sales, and property. When setting up the entity model, this paper selects the compressive strength of the budget input of the enterprise's independent innovation funds (the ratio of the internal structure expenditure of the enterprise's activity funds budget to the sales volume) as the expression variable [33]. Taking full account of the independent innovation budget input, the compressive strength variable is applied to the enterprise sales. The enterprise scale variable set here will select the total number of employees in the enterprise. In addition to the scale of the enterprise, there are also many manipulation variables added to the presentation variables.

Schumpeter's economic growth theory holds that enterprises pursuing perfect monopoly rights and interests are the main energy to promote independent innovation and technological progress. Therefore, the acquisition of enterprise profits at this stage, that is, enterprise profitability will do great harm to the next innovation technology. It is also effective to select the early operating profit margin as the expression variable [34].

In order to better determine whether there is an optimal control correlation between the enterprise scale and the compressive strength of independent innovation investment, the quadratic term of enterprise scale is also added to the entity model as an expression variable [35].

As the main body of innovation activities, its expenditure cost immediately affects the transformation of enterprise product cost. On the one hand, the rise of labour cost has increased the working pressure of enterprise management, on the other hand, it has driven enterprises to adopt proactive methods, select innovative technology capabilities and maintain the continuous development trend of enterprises. Here, we choose the average salary as the key variable to consider the labour cost.

The level of independent innovation equity financing ability can directly harm the independent innovation investment of enterprises. Because of the high risk of innovation activities and the difficulty of enterprise equity financing, enterprises with strong equity financing ability also relatively increase the innovation activity investment. Therefore, the variable of total amount of equity financing in the creative industry was selected to clarify the relationship between equity financing ability and R&D investigated the compressive strength of investment.

For many years, enterprises have been harmed by various national economic policies, rules and regulations, environmental damage and other complex reasons, and the compressive strength of independent innovation investment will vary. Therefore, the variable duration can be added to get the harm to enterprise innovation activities for many years. Based on the above comprehensive analysis and demonstration, the definition of entity model variables is shown in Table 1.

Table 1

Variable definition

Variable	Unit	Definition

Innovation spending intensity	%	Internal expenditure of scientific and technological activity funds/sales income
Last period sales profit margin	%	Profit/Sales Revenue
Salary per capita	Million	Total salary/number of employees
Years	Year	2013–2020
Enterprise size	People	Number of employees
Size	Big	>1000
	Small	>1000

The data used in this paper are the 8-year data of large, medium and small industrial production enterprises in Shanghai from 2014 to 2021 [36]. In the sample selection process, some enterprises were removed according to the database security and reliability standards. Finally, the year-end data information (mixed cross-sectional data) of 1308 enterprises was selected as the analysis sample. The mixed cross-section data obtains several random samples from a population at different points to carry out mixing. Therefore, while increasing the number of samples, more accurate prediction values can be obtained, thus giving resource advantages to the determination and analysis in this paper.

As shown in Table 2, descriptive statistical analysis is carried out on the sample information expressed as independent innovation expenditure variables in the sample.

Table 2

Statistical description of explained variables

Statistics	Innovation spending intensity

Mean	0.025
Median	0.002
Maximum	0.796
Minimum	0.000
Std.Dev	0.042
Skewness	6.73
Kurtosis	77.65
JB	3.12 + E05
Sample size	1280

According to Table 2, this variable is not normal, and JB statistics greatly exceed the threshold, which fully tests the non-normality and asymmetry of sample information. Therefore, the possible multiple regression analysis with OLS may lead to serious deviation of the index, which is unfavourable for further analysis based on the reversion conclusion. Therefore, in order to get a more effective and efficient conclusion, quantile regression is used.

Quantile regression was carried out on the constructed detection entity model using the R software, and the corresponding regression estimation conclusions shown in Table 3 were obtained.

Table 3

Quantile regression results

Variable	OLS	Quan20	Quan40	Quan50	Quan60	Quan80

ren	6.78E−06 (0.874)	5.73E−09^″ (1.303)	1.34E−08 (0.012)	4.99E−06^** (1.342)	1.46E−05^*** (2.503)	7.67E−07 (0.098)
ren2	6.03E−11 (0.438)	5.21E−11^** (1.668)	1.44E−10^*** (9.997)	1.29E−10^*** (4.744)	9.12E−11^*** (2.097)	−7.53E−41^*** (−2.925)
wage	−5.59E−05^** (−1.874)	2.43E−08^″ (1.392)	6.82E−08 (0.023)	−9.35E−07 (−0.086)	1.12E−06 (0.058)	−1.12E−05 (−0.749)
pr-1	8.98E −04 (0.294)	−1.12E−06 (−1.233)	−3.361E−06 (−0.005)	−1.26E−04 (−0.12)	8.44E−04 (0.212)	4.72E−03 (0.683)
big	1.51E−02^*** (2.217)	3.73E−06 (0.698)	1.44E −05 (0.014)	4.82E−03^* (1.489)	9.23E−03^** (2.007)	9.91E−03 (1.010)
big Xren	−9.03E−06 (−1.106)	−5.86E−09′ (−1.314)	−1.54E−08 (−0.104)	−5.59E−06 (−1.491)	−1.54E−05^*** (−2.614)	−4.01E−06 (−0.476)
big Xren2	−1.26E −10 (−0.383)	2.85E−11 (0.913)	1.49E −11 (0.122)	−6.67E−11 (−0.100)	−1.12E −10 (−0.602)	−9.33E−11 (−0.868)
Yoo	−3.61E −03 (−0.539)	−4.55E−06′ (−1.409)	−6.68E−06 (−0.005)	−2.21E −04 (−0.062)	3.94E −04 (0.094)	7.8E −03 (0.864)
Yor	−3.45E −03 (−0.518)	−2.56E−06 (−0.805)	−5.18E −07 (−0.0003)	3.03E−03 (0.828)	4.13E−03 (1.038)	3.18E−03 (0.380)
Y02	−2.01E −03 (−0.294)	−1.03E−06 (−0.268)	3.87E −03^* (1.615)	5.22E−03^* (1.417)	5.82E−03^* (1.439)	9.06E−03 (1.106)
Y03	3.18E −03 (0.463)	7.28E−07 (0.173)	1.58E−03 (1.189)	−8.85E−04 (−0.255)	2.7E−03 (0.596)	I.IIE−02 (1.128)
You	2.36E−03 (0.341)	−2.95E−06 (−0.737)	−7.35E−06 (−0.007)	−4.01E−03^* (−1.523)	−2.99E−03 (−0.582)	1.11E−02 (1.309)
Yo (pseudo)	2.14E−03 (0.300)	−7.23E −06′ (−1.274)	−1.24E−05 (−0.013)	−4.28E−03^** (−1.800)	−6.59E−03^* (−1.338)	115E−02^* (1.404)
R-squared	0.684	7.03	14.08	17.25	19.26	19.40

Table 3 sets the price index as the weighted average value of consumer price index and fixed asset investment price index, with weights of 0.55 and 0.45, respectively, so as to obtain the actual value.

It can be seen that the regression conclusion of OLS is only 0.684, the goodness of linear fitting is extremely low, only the average salary and the type of enterprise scale are prominent at the level of 5% and 1%, respectively, and the necessity of some independent variables is low. This means that because of the non-regular expression and asymmetry of sample information, the application of OLS method has an important harm to the determination results. In OLS mode, there is no ‘U’ or ‘inverted U’ correlation between enterprise size and expenditure intensity, so large enterprises exceed the innovation expenditure intensity of key companies. However, with increase of the company's total volume, its effect is very different. The increase in scale of large enterprises will reduce the intensity of expenditure, and increase in the scale of small- and medium-sized enterprises will increase the intensity of expenditure. At the same time, the increase in average salary is likely to significantly reduce the intensity of capital investment.

According to the quantile regression data, the overall innovation expenditure intensity of large enterprises is higher than that of small- and medium-sized enterprises, and the regression coefficient is positive. With the increase of stores, it slowly expands. Among them, the coefficient conclusion is more significant at 0.5 and 0.6 loci. This shows that when the innovation expenditure intensity is at the medium level, large enterprises can have stronger innovation ability than the backbone companies with the relatively sufficient fund utilisation and good reputation. Here, the key factors are the high level of asset concentration in the internal structure of large enterprises, the strong overall strength of innovative talents, and the strong immunity to the hidden dangers of unsuccessful product research and development. Therefore, the diligence of innovation expenditure is generally very large. Backbone companies encounter practical problems of enterprise scale expansion, take out part of internal structure assets to expand production scale, and the innovation expenditure is less than that of large enterprises. The details are shown in Figures 1 and 2.

Impact of enterprises of different sizes and types on expenditure intensity. (a) Large enterprises. (b) Medium-sized enterprises

Relationship between the scale of different types of enterprises and the intensity of expenditure. (a) Large enterprises appropriation expenditure. (b) Large enterprises appropriation expenditure. (c) Medium-sized enterprises appropriation expenditure. (d) Medium-sized enterprises appropriation expenditure

It can be seen from Figure 1 that the total number of employees of the enterprise scale has also changed greatly with the type of business scale. The marks of the first and second reversion coefficients of small and medium-sized enterprises are basically positive. Only when the score is high (0.8), the primary and secondary new project coefficients are obviously negative from the 1% level, but the key new project coefficients are significantly reduced, and there is a less significant ‘inverted U’ type correlation on the whole. On the other hand, apart from 0.8 points, between 0.2 and 0.6 points, the first coefficient shows a relatively significant growth trend, and the second coefficient shows the characteristic of first adjustment. The higher the expenditure intensity, the higher the total amount of the company, indicating a stronger active effect. However, the ‘rate’ of this increase increased again at the bottom point, and the high score in the middle gradually decreased. On the other hand, large enterprises have obtained quite different conclusions in the chain stores. The coefficient mark of key new items is negative from beginning to end. The coefficient mark of primary and secondary new items changes from low scores (0.2–0.5) to positive numbers, and from higher scores (0.6–0.8) to negative numbers.

Based on the conclusion in Table 3, it can be found that large enterprises have a significant ‘U’ correlation between the low quantile (0.2–0.5) and enterprise size and innovation expenditure intensity. However, at high score points, this kind of correlation disappears, and the order coefficient may be marked as all negative numbers, resulting in lower data. This is not a simple linear correlation between the change in business scale and expenditure intensity of large enterprises at the middle score of low expenditure intensity. On the contrary, the larger the enterprise size, the less the innovation expenditure. However, after exceeding a certain threshold, the company's innovative product R&D shows that the theme activities increase with the increase in business scale. However, from a high score (0.6–0.8), if large enterprises expand again, it will have an important adverse impact on the intensity of innovation expenditure. The primary factor is that the larger the enterprise scale, the greater the operation and management ability, the slower the reaction rate of the operation leaders, the more traditional the company's innovation concept, the larger the operation scale, the greater the company's operation cost and the lower the management decision-making efficiency.

Figure 2(a) and 2(b) describes large enterprises. The increase in their scale will reduce the intensity of expenditure. Figure 2(c) and 2(d) describes small- and medium-sized enterprises. The increase in their scale will increase the intensity of expenditure. At the same time, the increase in average salary is likely to significantly reduce the intensity of capital investment.

It can be seen that in the adjustment variables, the independent variable of average salary is repeatedly marked by the correlation coefficient in each branch, but only in the low branch, there is a need for a 10% level. In general, the low index is positive, and the higher in the middle is negative. Because the low budget expenditure has low compressive strength, the company introduces high-tech talents, offers high salary positions, and increases investment in innovation and R&D. Therefore, increasing the average salary can improve the compressive strength of expenditure. However, with increase in high scores and the continuous growth of labour costs, the manufacturing industry must take all kinds of restrictions into account. Only by reducing the expenditure on independent innovation can the additional expenditure of costs be filled.

The coefficient estimates were not significant at each quantile, and the estimated values were only 10% significant at 0.4 quantile. The coefficient estimates were only significantly lower at the low quantile (0.2), and there were significant positive correlations in different degrees at the other quantiles. Except for the 0.9 quantile, in other quantiles, the manufacturing industry will increase R&D investment as time changes.

Conclusion

This paper makes an in-depth study on the relationship between government subsidies, R&D investment and high-quality development of the manufacturing industry. The quantile regression entity model is created, and the asymmetric linear loss function is introduced to obtain the point estimation of quantile. The asymptotic distribution is obtained according to the Moivre–Laplace limit value law. The sample quantile function is calculated, and the asymptotic covariance matrix is estimated by the fitting residual of quantile regression. The solid model is tested according to the goodness-of-fit specification. The experimental results show that the coefficient conclusion is more significant at the 0.5 and 0.6 quantiles, and this method is efficient and widely applicable.

Figures et tableaux

Quantile regression results

Variable	OLS	Quan20	Quan40	Quan50	Quan60	Quan80

ren	6.78E−06 (0.874)	5.73E−09^″ (1.303)	1.34E−08 (0.012)	4.99E−06^** (1.342)	1.46E−05^*** (2.503)	7.67E−07 (0.098)
ren2	6.03E−11 (0.438)	5.21E−11^** (1.668)	1.44E−10^*** (9.997)	1.29E−10^*** (4.744)	9.12E−11^*** (2.097)	−7.53E−41^*** (−2.925)
wage	−5.59E−05^** (−1.874)	2.43E−08^″ (1.392)	6.82E−08 (0.023)	−9.35E−07 (−0.086)	1.12E−06 (0.058)	−1.12E−05 (−0.749)
pr-1	8.98E −04 (0.294)	−1.12E−06 (−1.233)	−3.361E−06 (−0.005)	−1.26E−04 (−0.12)	8.44E−04 (0.212)	4.72E−03 (0.683)
big	1.51E−02^*** (2.217)	3.73E−06 (0.698)	1.44E −05 (0.014)	4.82E−03^* (1.489)	9.23E−03^** (2.007)	9.91E−03 (1.010)
big Xren	−9.03E−06 (−1.106)	−5.86E−09′ (−1.314)	−1.54E−08 (−0.104)	−5.59E−06 (−1.491)	−1.54E−05^*** (−2.614)	−4.01E−06 (−0.476)
big Xren2	−1.26E −10 (−0.383)	2.85E−11 (0.913)	1.49E −11 (0.122)	−6.67E−11 (−0.100)	−1.12E −10 (−0.602)	−9.33E−11 (−0.868)
Yoo	−3.61E −03 (−0.539)	−4.55E−06′ (−1.409)	−6.68E−06 (−0.005)	−2.21E −04 (−0.062)	3.94E −04 (0.094)	7.8E −03 (0.864)
Yor	−3.45E −03 (−0.518)	−2.56E−06 (−0.805)	−5.18E −07 (−0.0003)	3.03E−03 (0.828)	4.13E−03 (1.038)	3.18E−03 (0.380)
Y02	−2.01E −03 (−0.294)	−1.03E−06 (−0.268)	3.87E −03^* (1.615)	5.22E−03^* (1.417)	5.82E−03^* (1.439)	9.06E−03 (1.106)
Y03	3.18E −03 (0.463)	7.28E−07 (0.173)	1.58E−03 (1.189)	−8.85E−04 (−0.255)	2.7E−03 (0.596)	I.IIE−02 (1.128)
You	2.36E−03 (0.341)	−2.95E−06 (−0.737)	−7.35E−06 (−0.007)	−4.01E−03^* (−1.523)	−2.99E−03 (−0.582)	1.11E−02 (1.309)
Yo (pseudo)	2.14E−03 (0.300)	−7.23E −06′ (−1.274)	−1.24E−05 (−0.013)	−4.28E−03^** (−1.800)	−6.59E−03^* (−1.338)	115E−02^* (1.404)
R-squared	0.684	7.03	14.08	17.25	19.26	19.40

Variable definition

Variable	Unit	Definition

Innovation spending intensity	%	Internal expenditure of scientific and technological activity funds/sales income
Last period sales profit margin	%	Profit/Sales Revenue
Salary per capita	Million	Total salary/number of employees
Years	Year	2013–2020
Enterprise size	People	Number of employees
Size	Big	>1000
	Small	>1000

Statistical description of explained variables

Statistics	Innovation spending intensity

Mean	0.025
Median	0.002
Maximum	0.796
Minimum	0.000
Std.Dev	0.042
Skewness	6.73
Kurtosis	77.65
JB	3.12 + E05
Sample size	1280

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Applied Mathematics and Nonlinear Sciences

Research on the relationship between government subsidies, R&D investment and high-quality development of manufacturing industry

Yu Guan
Yu Guan

Publié en ligne: 30 Nov 2022

Volume & Edition: AHEAD OF PRINT

Pages: -

Reçu: 01 Jun 2022

Accepté: 08 Aug 2022

Détails du journal et du numéro

Applied Mathematics and Nonlinear Sciences

Aperçu PDF

Article

Fig. 1

Fig. 2

Figures et tableaux

Fig. 1

Fig. 2

Quantile regression results

Variable definition

Statistical description of explained variables

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Applied Mathematics and Nonlinear Sciences

Research on the relationship between government subsidies, R&D investment and high-quality development of manufacturing industry

Yu GuanYu Guan

Publié en ligne: 30 Nov 2022

Volume & Edition: AHEAD OF PRINT

Pages: -

Reçu: 01 Jun 2022

Accepté: 08 Aug 2022

Détails du journal et du numéro

Applied Mathematics and Nonlinear Sciences

Aperçu PDF

Article

Fig. 1

Fig. 2

Figures et tableaux

Fig. 1

Fig. 2

Quantile regression results

Variable definition

Statistical description of explained variables

Références

Articles récents

Planifiez votre conférence à distance avec Sciendo

Yu Guan
Yu Guan