# Research on the Dynamic Interrelationship among R&D Investment, Technological Innovation, and Economic Growth in China

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methodology and Materials

#### 3.1. Methodology

#### 3.1.1. Entropy Method

_{ij})

_{m}

_{×n}. For an indicator x

_{j}, the larger the difference between indicator values x

_{ij}is, the greater impact it has on the comprehensive evaluation. If the values of an indicator are all equal, then this indicator has no impact on the comprehensive evaluation. The specific calculation process is as follows.

- In order to avoid the case in which data for the entropy value does not exist, a data shift is performed.For positive indicators (a larger value is better):$${X}_{ij}^{\prime}=\frac{{X}_{ij}-\mathrm{min}\left({X}_{1j},{X}_{2j},\dots ,{X}_{nj}\right)}{\mathrm{max}\left({X}_{1j},{X}_{2j},\dots ,{X}_{nj}\right)-\mathrm{min}\left({X}_{1j},{X}_{2j},\dots ,{X}_{nj}\right)}+1,\text{}i=1,2,\dots ,n;j=1,2,\dots ,m$$For negative indicators (a smaller value is better):$${X}_{ij}^{\prime}=\frac{\mathrm{max}\left({X}_{1j},{X}_{2j},\dots ,{X}_{nj}\right)-{X}_{ij}}{\mathrm{max}\left({X}_{1j},{X}_{2j},\dots ,{X}_{nj}\right)-\mathrm{min}\left({X}_{1j},{X}_{2j},\dots ,{X}_{nj}\right)}+1,\text{}i=1,2,\dots ,n;j=1,2,\dots ,m$$
- Calculate the ratio of the jth indicator in the ith plan to the sum of the jth indicator.$$\text{}{P}_{ij}=\frac{{X}_{ij}}{{{\displaystyle \sum}}_{i=1}^{n}{X}_{ij}}\text{\hspace{1em}}\left(j=1,2,\dots m\right)$$
- Calculate the entropy of the jth indicator.$${e}_{j}=-k{{\displaystyle \sum}}_{i=1}^{n}{p}_{ij}\mathrm{ln}\left({p}_{ij}\right),\text{}\mathrm{where}\text{}\mathrm{k}0,\text{}\mathrm{k}=1/\mathrm{ln}\left(\mathrm{n}\right),\text{}{e}_{j}\ge 0$$
- Calculate the coefficient of variation of the jth indicator. The coefficient of variation is defined as$${\mathrm{g}}_{\mathrm{j}}=\frac{1-{\mathrm{e}}_{\mathrm{j}}}{\mathrm{m}-{\mathrm{E}}_{\mathrm{e}}},\text{}\mathrm{where}\text{}{\mathrm{E}}_{\mathrm{e}}={{\displaystyle \sum}}_{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{e}}_{\mathrm{j}\text{}},0\le {\mathrm{g}}_{\mathrm{i}}\le 1,{{\displaystyle \sum}}_{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{g}}_{\mathrm{j}}=1$$
- Determine the weight of each coefficient of variation:$${\omega}_{j}=\frac{{g}_{j}}{{{\displaystyle \sum}}_{j=1}^{m}{g}_{j}}$$
- Calculate the level of development of each variable:$${s}_{i}={\displaystyle \sum}_{j=1}^{m}{\omega}_{j}\ast {p}_{ij}$$

#### 3.1.2. Vector Autoregression Model

_{t}is an m-dimensional endogenous variable vector; x

_{t}is a d-dimensional exogenous variable vector; A

_{1}…A

_{P}and B

_{1}…B

_{t}are matrixes to be evaluated, and the endogenous variable and exogenous variable have p and r order lag periods, respectively; and ε

_{t}is the random disturbance term.

#### 3.1.3. Impulse Response Function

_{t}

_{−1}represents all the available information when an impact occurs; I

_{Y}is the impulse response value of the nth period; and E is the expected value.

#### 3.1.4. Variance Decomposition

#### 3.2. Materials

#### 3.2.1. Input Indicator

#### 3.2.2. Output Indicator

#### 3.2.3. Variable Selection

_{1}. The number of patent applications and the number of patent grants were fitted to obtain the value of the technological innovation level, which was recorded as F

_{2}. GDP (unit: 100 million yuan) and residents’ consumption level (unit: yuan) were fitted to obtain the value of the economic growth level, which was recorded as F

_{3}. In order to make the data comparable and to reflect the actual growth effect of each indicator, the year 1995 was used as the base period. The expenditure portion of R&D investment, GDP, and residents’ consumption level over the years were adjusted according to the consumer price index in the corresponding year.

_{1}, LNF

_{2}and LNF

_{3}, respectively.

## 4. Results

#### 4.1. Development Level of R&D Investment, Technological Innovation, and Economic Growth

#### 4.1.1. Development Level Trend

#### 4.1.2. Growth Rate Fluctuation of Development Levels

#### 4.2. VAR Model for R&D Investment, Technological Innovation, and Economic Growth

_{1}, LNF

_{2}and LNF

_{3}had all passed the significance test, and hencerejected the presence of a unit root at a a significance level of 5%. Therefore, all these three variables are stationary time series.

_{1}, LNF

_{2}and LNF

_{3}. According to information criteria (AIC and SC), and take the limit of time series lengthen into consideration, the optimal lag period of the model was chosen to be 3. The results are shown in Table 4. The VAR (3) model was established.

#### 4.3. Impulse Response Analysis

#### 4.3.1. Analysis of Impulse response function results

#### 4.3.2. Cumulative Effect of Impulse Response

#### 4.4. Variance Decomposition Analysis

#### 4.4.1. Analysis of Variance Decomposition Results

#### 4.4.2. Mean Value Analysis of Variance Decomposition

#### 4.5. Robustness Examination

## 5. Discussion of Empirical Results

## 6. Concluding Remarks

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Mechanism of influence among R&D investment, technological innovation, and economic growth.

**Figure 2.**Development level curves of China’s R&D investment (F

_{1}), technological innovation (F

_{2}), and economic growth (F

_{3}) from 1995 to 2016.

**Figure 3.**Growth rate of China’s R&D investment, technological innovation, and economic growth development level from 1996 to 2016.

Target Layer | System Layer | Indicator Layer | Unit |
---|---|---|---|

R&D investment, technological innovation, and economic growth evaluation system | R&D investment | R&D expenditure | 10,000 yuan |

Full-time equivalent of personnel | People/year | ||

Technological innovation | Number of patent applications | ||

Number of patent grants | |||

Total number of Chinese papers collected by major foreign search engines | |||

Number of papers published by Chinese researchers in domestic and foreign journals collected by major foreign search engines | |||

Economic growth | GDP | 100 million yuan | |

Residents’ consumption level | Yuan |

Variables | Max | Min | Mean | Std.Dev |
---|---|---|---|---|

F_{1} | 0.8240 | 0.0140 | 0.3132 | 0.2752 |

F_{2} | 0.8300 | 0.0052 | 0.2459 | 0.2570 |

F_{3} | 0.8145 | 0.0282 | 0.3181 | 0.2583 |

**Table 3.**Augmented Dickey–Fuller (ADF) test results of the vector autoregression (VAR) model for R&D investment, technological innovation, and economic growth development levels.

Variable Sequence | ADF Test | Significance Level of 5% | Lag Period | Conclusion |
---|---|---|---|---|

LNF_{1} | −7.3572 | −3.0123 | 0 | Stationary |

LNF_{2} | −4.0971 | −3.0300 | 2 | Stationary |

LNF_{3} | −7.2375 | −3.0124 | 0 | Stationary |

Lag | LogL | LR | FPE | AIC | SC | HQ |
---|---|---|---|---|---|---|

0 | 32.9390 | NA | 8.59e−06 | −3.1515 | −3.0024 | −3.1262 |

1 | 107.4460 | 117.6426 | 8.86e−09 | −10.0470 | −9.4505 | −9.9460 |

2 | 121.1941 | 17.3660 | 5.88e−090 | −10.5467 | −9.5029 | −10.3701 |

3 | 147.3018 | 24.73368 * | 1.24e−09 * | −12.34756 * | −10.85634 * | −12.09519 * |

Variable Sequence | LNF3 | LNF1 | LNF2 |
---|---|---|---|

LNF_{1} (−1) | 0.8073 | 0.0173 | 0.0798 |

−0.4777 | −0.6390 | −0.1819 | |

LNF_{1} (−2) | 0.0236 | −0.5369 | 0.2287 |

−0.4531 | −0.6060 | −0.1725 | |

LNF_{1} (−3) | −0.4314 | −0.0358 | −0.4148 |

−0.2742 | −0.3668 | −0.1044 | |

LNF_{2} (−1) | −0.0531 | −0.1782 | 0.0935 |

−0.1972 | −0.2638 | −0.0751 | |

LNF_{2} (−2) | −0.0337 | 0.3752 | 0.1024 |

−0.1525 | −0.2040 | −0.0581 | |

LNF_{2} (−3) | 0.2293 | 0.3217 | 0.1873 |

−0.2145 | −0.2869 | −0.0817 | |

LNF_{3} (−1) | 0.4097 | 1.0976 | 0.7403 |

−0.7775 | −1.0400 | −0.2960 | |

LNF_{3} (−2) | −0.4485 | −1.6277 | −0.7119 |

−0.7115 | −0.9518 | −0.2709 | |

LNF_{3} (−3) | 0.4343 | 1.6144 | 0.4729 |

−0.4594 | −0.6145 | −0.1749 | |

C | 0.1205 | 0.3758 | 0.0788 |

−0.0593 | −0.0794 | −0.0226 | |

R-squared | 0.9988 | 0.9988 | 0.9998 |

Period | Response of LNF_{1} to LNF_{2} | Response of LNF_{2} to LNF_{1} | Response of LNF_{2} to LNF_{3} | Response of LNF_{3} to LNF_{2} | Response of LNF_{1} to LNF_{3} | Response of LNF_{3} to LNF_{1} |
---|---|---|---|---|---|---|

1 | 0.0000 | 0.0448 | 0.0000 | 0.0030 | 0.0000 | 0.0122 |

2 | −0.0008 | 0.0062 | 0.0122 | 0.0058 | 0.0045 | 0.0167 |

3 | −0.0007 | −0.0088 | −0.0111 | 0.0057 | 0.0014 | 0.0220 |

4 | 0.0085 | 0.0134 | 0.0083 | 0.0096 | 0.0024 | 0.0113 |

5 | 0.0092 | −0.0178 | 0.0117 | 0.0086 | 0.0067 | −0.0045 |

6 | 0.0123 | 0.0033 | 0.0004 | 0.0107 | 0.0031 | −0.0098 |

7 | 0.0127 | 0.0071 | −0.0001 | 0.0097 | 0.0025 | −0.0067 |

8 | 0.0118 | −0.0017 | 0.0075 | 0.0084 | 0.0037 | −0.0076 |

9 | 0.0087 | −0.0044 | 0.0010 | 0.0061 | 0.0026 | −0.0050 |

10 | 0.0077 | 0.0067 | 0.0034 | 0.0057 | 0.0017 | −0.0017 |

Total | 0.0694 | 0.0487 | 0.0333 | 0.0734 | 0.0286 | 0.0269 |

Period | LNF_{1} | LNF_{2} | LNF_{3} | ||||||
---|---|---|---|---|---|---|---|---|---|

LNF_{1} | LNF_{2} | LNF_{3} | LNF_{1} | LNF_{2} | LNF_{3} | LNF_{1} | LNF_{2} | LNF_{3} | |

1 | 100.0000 | 0.0000 | 0.0000 | 57.8430 | 42.1570 | 0.0000 | 53.0622 | 3.2976 | 43.6403 |

2 | 99.3798 | 0.0179 | 0.6022 | 55.7617 | 40.2097 | 4.0286 | 64.8165 | 6.5300 | 28.6535 |

3 | 99.4624 | 0.0254 | 0.5122 | 51.2951 | 42.1476 | 6.5573 | 77.4696 | 6.4086 | 16.1218 |

4 | 98.0133 | 1.4273 | 0.5595 | 51.2640 | 41.1490 | 7.5869 | 74.4088 | 11.9885 | 13.6027 |

5 | 95.6369 | 2.9776 | 1.3855 | 50.8200 | 39.9140 | 9.2661 | 69.8604 | 15.9454 | 14.1943 |

6 | 92.8682 | 5.6226 | 1.5091 | 50.6582 | 40.1397 | 9.2021 | 66.4384 | 20.4470 | 13.1147 |

7 | 90.2417 | 8.2033 | 1.5550 | 48.7739 | 42.5325 | 8.6936 | 63.6262 | 23.8531 | 12.5207 |

8 | 88.3484 | 9.9763 | 1.6753 | 48.1410 | 42.2698 | 9.5893 | 62.2537 | 25.7878 | 11.9585 |

9 | 87.5475 | 10.7426 | 1.7099 | 47.3860 | 43.2247 | 9.3893 | 61.5001 | 26.7733 | 11.7266 |

10 | 86.8029 | 11.4736 | 1.7236 | 47.3117 | 43.2730 | 9.4154 | 60.5232 | 27.8018 | 11.6750 |

Mean | 93.8301 | 5.0467 | 1.1232 | 50.9255 | 41.7017 | 7.3729 | 65.3959 | 16.8833 | 17.7208 |

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## Share and Cite

**MDPI and ACS Style**

Liu, C.; Xia, G.
Research on the Dynamic Interrelationship among R&D Investment, Technological Innovation, and Economic Growth in China. *Sustainability* **2018**, *10*, 4260.
https://doi.org/10.3390/su10114260

**AMA Style**

Liu C, Xia G.
Research on the Dynamic Interrelationship among R&D Investment, Technological Innovation, and Economic Growth in China. *Sustainability*. 2018; 10(11):4260.
https://doi.org/10.3390/su10114260

**Chicago/Turabian Style**

Liu, Chao, and Guanjun Xia.
2018. "Research on the Dynamic Interrelationship among R&D Investment, Technological Innovation, and Economic Growth in China" *Sustainability* 10, no. 11: 4260.
https://doi.org/10.3390/su10114260