Article(id=1315693773091352577, tenantId=1146029695717560320, journalId=1308397381743640680, issueId=1315693724970103290, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1747065600000, receivedDateStr=2025-05-13, revisedDate=1751212800000, revisedDateStr=2025-06-30, acceptedDate=null, acceptedDateStr=null, onlineDate=1791615439912, onlineDateStr=2026-10-10, pubDate=1791993600000, pubDateStr=2026-10-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1791615439912, onlineIssueDateStr=2026-10-10, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1791615439912, creator=13701087609, updateTime=1791615439912, updator=13701087609, issue=Issue{id=1315693724970103290, tenantId=1146029695717560320, journalId=1308397381743640680, year='2026', volume='44', issue='10', pageStart='2017', pageEnd='2240', issueExtLink='null', onlineDate='null', pubDate='1791993600000', pubDateStr='2026-10-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1791615428440, creator='13701087609', updateTime=1791615454688, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1315693835188031766, tenantId=1146029695717560320, journalId=1308397381743640680, issueId=1315693724970103290, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1315693835188031767, tenantId=1146029695717560320, journalId=1308397381743640680, issueId=1315693724970103290, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=2207, endPage=2217, ext={EN=ArticleExt(id=1315693773405925378, articleId=1315693773091352577, tenantId=1146029695717560320, journalId=1308397381743640680, language=EN, title=The driving role of technological innovation in the development of small and medium-sized industrial enterprises in China, columnId=1309226375089840648, journalTitle=Studies in Science of Science, columnName=Frontiers and Opinions, runingTitle=null, highlight=null, articleAbstract=

Against the backdrop of global economic integration and rapid technological advancement, small and medium-sized industrial enterprises (SMEIs) have emerged as a crucial force in the national economy, with technological innovation serving as the core driving force for their development. Exploring the driving effects between the two is of great significance for policy formulation and enterprise development. This study constructs an indicator system for evaluating the technological innovation and development level of SMEIs. It employs classical cycle theory and the growth rate cycle composite index to quantitatively assess their capabilities and levels, and utilizes impulse response function analysis and variance decomposition to dissect the driving mechanisms. The findings are as follows: (1) In the classical cycle, both the technological innovation input and output indices exhibit an overall upward trend, with the output index growing at a faster pace. After a brief decline in the enterprise scale index from 2017 to 2018, growth resumed due to policy support. (2) The growth rate cycle reveals that there is a lag effect in the fluctuations of the growth rate cycle indices for input and output. The fluctuation trends of enterprise scale and innovation capability are consistent, but the scale fluctuations are more pronounced. (3) Impulse response analysis indicates that the initial impact of technological innovation input is moderate. An initial increase in the output index leads to a temporary fluctuation in enterprise development followed by an upward trend and can promote the formation of a virtuous cycle in the input index. (4) Variance decomposition shows that both the input and output indices have a four-period lag effect on enterprise development. The variance contribution rate of the output index (approximately 28%) is higher than that of the input index (6%), indicating a more significant driving role of output. Both governments and enterprises should attach great importance to technological innovation. While increasing investment, they should strengthen the monitoring of technological achievement transformation, promote technological innovation output, and drive the steady development of SMEIs.

, authors=Wu YANG, Yuan YUAN, Kun WANG, authorsList=Wu YANG, Yuan YUAN, Kun WANG, authorCompany=null, correspAuthors=Yuan YUAN, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1315693774882320401, articleId=1315693773091352577, tenantId=1146029695717560320, journalId=1308397381743640680, language=CN, title=科技创新对中国中小工业企业发展的驱动研究, columnId=1309226375303750154, journalTitle=科学学研究, columnName=前沿与观点, runingTitle=null, highlight=null, articleAbstract=

在全球经济一体化与技术快速进步背景下,中小工业企业成为国民经济关键力量,科技创新是其发展核心驱动力。探究二者驱动效应对政策制定与企业发展意义重大。本研究构建中小工业企业科技创新与发展水平指标体系,运用古典循环理论、增长率循环合成指数定量评估其能力与水平,并借助脉冲响应函数分析和方差分解剖析驱动机制。研究发现:(1)古典循环中,科技创新投入与产出指数整体上升,产出指数增速更快。2017-2018年企业规模指数短暂下滑后因政策支持恢复增长。(2)增长率循环显示,投入和产出指数增长率循环指数波动有滞后效应,企业规模与创新能力波动趋势一致,但规模波动更明显。(3)脉冲响应分析表明,科技创新投入初期影响温和,产出指数初期增加会使企业发展短暂波动后上升,而且能促进投入指数形成良性循环。(4)方差分解显示,投入和产出指数对企业发展有4期滞后效应,产出指数方差贡献率(约28%)高于投入指数(6%),产出驱动作用更显著。政府和企业应高度重视科技创新,加大投入的同时强化成果转化监测,促进科技创新产出,推动中小工业企业稳健发展。

, authors=杨武, 袁媛, 王坤, authorsList=杨武, 袁媛, 王坤, authorCompany=null, correspAuthors=袁媛, authorNote=

杨武(1961-),男,教授、博士生导师。

王坤(2001-),女,硕士研究生。

, correspAuthorsNote=
袁媛(2001-),女,满族,硕士研究生,E-mail:。
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杨武(1961-),男,教授、博士生导师。

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杨武(1961-),男,教授、博士生导师。

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王坤(2001-),女,硕士研究生。

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王坤(2001-),女,硕士研究生。

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figureFileSmall=4ftgRBnFey+8nKgJRAS4Ng==, figureFileBig=gvg4KBgEwP0JD3VnnKBb2g==, tableContent=null), ArticleFig(id=1315693777126273074, tenantId=1146029695717560320, journalId=1308397381743640680, articleId=1315693773091352577, language=EN, label=Figure 5, caption=Unit root test of VAR model, figureFileSmall=Mmi89Zwiri8p1rrC7bYHiA==, figureFileBig=uWfc/jpvsq08umnFoWwWDg==, tableContent=null), ArticleFig(id=1315693777184993331, tenantId=1146029695717560320, journalId=1308397381743640680, articleId=1315693773091352577, language=CN, label=图5, caption=VAR模型的单位根检验, figureFileSmall=Mmi89Zwiri8p1rrC7bYHiA==, figureFileBig=uWfc/jpvsq08umnFoWwWDg==, tableContent=null), ArticleFig(id=1315693777281462324, tenantId=1146029695717560320, journalId=1308397381743640680, articleId=1315693773091352577, language=EN, label=Figure 6, caption=Impulse response diagram, figureFileSmall=ijt5CJ9K31+c8sadqVgzAg==, figureFileBig=yAYXqwHm0pgHM8ZxrqWSig==, tableContent=null), ArticleFig(id=1315693777352765493, tenantId=1146029695717560320, journalId=1308397381743640680, articleId=1315693773091352577, language=CN, label=图6, caption=脉冲响应图

注:横轴代表冲击作用的滞后期数,最大滞后期设定为20期;纵轴代表被解释变量对冲击的响应程度;中间的实线表示各期内对冲击反应的大小,两侧的虚线表示偏离带。在分析过程中,主要关注实线曲线的变化趋势,以反映在给予解释变量一个冲击后,被解释变量的变化程度。

, figureFileSmall=ijt5CJ9K31+c8sadqVgzAg==, figureFileBig=yAYXqwHm0pgHM8ZxrqWSig==, tableContent=null), ArticleFig(id=1315693777419874358, tenantId=1146029695717560320, journalId=1308397381743640680, articleId=1315693773091352577, language=EN, label=Figure 7, caption=Variance decomposition chart, figureFileSmall=IHcQ1MGZud7n+boaTrNiQQ==, figureFileBig=e/SuSo+X8v+7O2qToqzNSg==, tableContent=null), ArticleFig(id=1315693777482788919, tenantId=1146029695717560320, journalId=1308397381743640680, articleId=1315693773091352577, language=CN, label=图7, caption=方差分解图

注:横轴代表冲击作用的滞后期数,最大滞后期设定为20期;纵轴代表被解释变量对冲击的响应程度;中间的实线表示各期内对冲击反应的大小,纵轴表示某个冲击对这个变量波动的贡献。

, figureFileSmall=IHcQ1MGZud7n+boaTrNiQQ==, figureFileBig=e/SuSo+X8v+7O2qToqzNSg==, tableContent=null), ArticleFig(id=1315693777558286392, tenantId=1146029695717560320, journalId=1308397381743640680, articleId=1315693773091352577, language=EN, label=Table 1, caption=

Index system of scientific and technological innovation and enterprise development level of small and medium-sized industrial enterprises

, figureFileSmall=null, figureFileBig=null, tableContent=
第一层指标 第二层指标 第三层指标体系 基本指标单位
企业科技创新 科技创新投入 R&D经费内部支出 万元
R&D经费外部支出 万元
技术改造经费支出 万元
新产品开发经费支出 万元
R&D研究人员折合全时当量 人年
科技创新产出 R&D项目数 项
新产品开发项目数 项
发明专利申请数 件
有效发明专利数 件
企业发展水平 企业创新发展 新产品销售收入 万元
新产品出口收入 万元
有R&D活动的企业数 个
有研发机构的企业数 个
企业规模发展 机构硕博人数 人
机构人员 人
企业单位数 个
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中小工业企业科技创新与企业发展水平指标体系

, figureFileSmall=null, figureFileBig=null, tableContent=
第一层指标 第二层指标 第三层指标体系 基本指标单位
企业科技创新 科技创新投入 R&D经费内部支出 万元
R&D经费外部支出 万元
技术改造经费支出 万元
新产品开发经费支出 万元
R&D研究人员折合全时当量 人年
科技创新产出 R&D项目数 项
新产品开发项目数 项
发明专利申请数 件
有效发明专利数 件
企业发展水平 企业创新发展 新产品销售收入 万元
新产品出口收入 万元
有R&D活动的企业数 个
有研发机构的企业数 个
企业规模发展 机构硕博人数 人
机构人员 人
企业单位数 个
), ArticleFig(id=1315693777738641466, tenantId=1146029695717560320, journalId=1308397381743640680, articleId=1315693773091352577, language=EN, label=Table 2, caption=

The results of the ADF unit root test

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变量 ADF值 Z(t) 检验结果
lnA1 0.311 0.978 不平稳
DlnA1 -2.695 0.075 平稳
lnA2 -1.627 0.469 不平稳
DlnA2 -3.29 0.0153 平稳
lnB -1.323 0.6187 不平稳
DlnB -2.896 0.0458 平稳
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ADF单位根检验结果

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变量 ADF值 Z(t) 检验结果
lnA1 0.311 0.978 不平稳
DlnA1 -2.695 0.075 平稳
lnA2 -1.627 0.469 不平稳
DlnA2 -3.29 0.0153 平稳
lnB -1.323 0.6187 不平稳
DlnB -2.896 0.0458 平稳
), ArticleFig(id=1315693777885442108, tenantId=1146029695717560320, journalId=1308397381743640680, articleId=1315693773091352577, language=EN, label=Table 3, caption=

Variance decomposition table

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期数 DlnB方差分解 DlnA1方差分解 DlnA2方差分解
DlnA1 DlnA2 DlnB DlnA1 DlnA2 DlnB DlnA1 DlnA2 DlnB
1 0.00 0.00 100.00 74.13 22.99 2.88 0.00 99.70 0.30
2 0.49 23.33 76.18 71.45 25.54 3.01 12.21 84.85 2.94
3 0.48 23.92 75.60 38.98 24.28 36.74 12.78 82.85 4.37
4 5.25 27.12 67.63 40.44 22.95 36.61 20.28 66.28 13.44
5 5.64 27.83 66.53 36.94 21.03 42.03 19.41 64.43 16.15
6 6.52 28.69 64.79 35.41 20.81 43.78 17.34 61.22 21.44
7 6.67 28.84 64.49 35.51 20.84 43.64 18.08 58.46 23.47
8 6.59 28.29 65.12 33.94 21.16 44.90 18.17 58.53 23.31
9 7.12 28.04 64.84 33.88 20.89 45.23 17.90 57.89 24.21
10 7.12 28.06 64.82 33.94 20.89 45.17 17.84 57.35 24.81
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方差分解表

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期数 DlnB方差分解 DlnA1方差分解 DlnA2方差分解
DlnA1 DlnA2 DlnB DlnA1 DlnA2 DlnB DlnA1 DlnA2 DlnB
1 0.00 0.00 100.00 74.13 22.99 2.88 0.00 99.70 0.30
2 0.49 23.33 76.18 71.45 25.54 3.01 12.21 84.85 2.94
3 0.48 23.92 75.60 38.98 24.28 36.74 12.78 82.85 4.37
4 5.25 27.12 67.63 40.44 22.95 36.61 20.28 66.28 13.44
5 5.64 27.83 66.53 36.94 21.03 42.03 19.41 64.43 16.15
6 6.52 28.69 64.79 35.41 20.81 43.78 17.34 61.22 21.44
7 6.67 28.84 64.49 35.51 20.84 43.64 18.08 58.46 23.47
8 6.59 28.29 65.12 33.94 21.16 44.90 18.17 58.53 23.31
9 7.12 28.04 64.84 33.88 20.89 45.23 17.90 57.89 24.21
10 7.12 28.06 64.82 33.94 20.89 45.17 17.84 57.35 24.81
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科技创新对中国中小工业企业发展的驱动研究
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杨武 , 袁媛 , 王坤
科学学研究 | 前沿与观点 2026,44(10): 2207-2217
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科学学研究 |前沿与观点 2026 , 44 (10) : 2207 -2217
科技创新对中国中小工业企业发展的驱动研究
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[Author(id=1315693775180115990, tenantId=1146029695717560320, journalId=1308397381743640680, articleId=1315693773091352577, orderNo=0, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=null, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1315693775251419160, tenantId=1146029695717560320, journalId=1308397381743640680, articleId=1315693773091352577, authorId=1315693775180115990, language=EN, stringName=Wu YANG, firstName=Wu, middleName=null, lastName=YANG, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=null, address=School of Economics and Management, University of Science and Technology Beijing, Beijing 100083, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1315693775322722329, tenantId=1146029695717560320, journalId=1308397381743640680, articleId=1315693773091352577, authorId=1315693775180115990, language=CN, stringName=杨武, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=null, address=北京科技大学经济管理学院, 北京 100083, bio={"content":"

杨武(1961-),男,教授、博士生导师。

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杨武(1961-),男,教授、博士生导师。

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杨武, 袁媛 , 王坤
作者信息
  • 北京科技大学经济管理学院, 北京 100083
通讯作者:
袁媛(2001-),女,满族,硕士研究生,E-mail:。
作者简介:

杨武(1961-),男,教授、博士生导师。

王坤(2001-),女,硕士研究生。

The driving role of technological innovation in the development of small and medium-sized industrial enterprises in China
Wu YANG, Yuan YUAN , Kun WANG
Affiliations
  • School of Economics and Management, University of Science and Technology Beijing, Beijing 100083
出版时间: 2026-10-15
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在全球经济一体化与技术快速进步背景下,中小工业企业成为国民经济关键力量,科技创新是其发展核心驱动力。探究二者驱动效应对政策制定与企业发展意义重大。本研究构建中小工业企业科技创新与发展水平指标体系,运用古典循环理论、增长率循环合成指数定量评估其能力与水平,并借助脉冲响应函数分析和方差分解剖析驱动机制。研究发现:(1)古典循环中,科技创新投入与产出指数整体上升,产出指数增速更快。2017-2018年企业规模指数短暂下滑后因政策支持恢复增长。(2)增长率循环显示,投入和产出指数增长率循环指数波动有滞后效应,企业规模与创新能力波动趋势一致,但规模波动更明显。(3)脉冲响应分析表明,科技创新投入初期影响温和,产出指数初期增加会使企业发展短暂波动后上升,而且能促进投入指数形成良性循环。(4)方差分解显示,投入和产出指数对企业发展有4期滞后效应,产出指数方差贡献率(约28%)高于投入指数(6%),产出驱动作用更显著。政府和企业应高度重视科技创新,加大投入的同时强化成果转化监测,促进科技创新产出,推动中小工业企业稳健发展。

科技创新  /  创新驱动  /  中小工业企业

Against the backdrop of global economic integration and rapid technological advancement, small and medium-sized industrial enterprises (SMEIs) have emerged as a crucial force in the national economy, with technological innovation serving as the core driving force for their development. Exploring the driving effects between the two is of great significance for policy formulation and enterprise development. This study constructs an indicator system for evaluating the technological innovation and development level of SMEIs. It employs classical cycle theory and the growth rate cycle composite index to quantitatively assess their capabilities and levels, and utilizes impulse response function analysis and variance decomposition to dissect the driving mechanisms. The findings are as follows: (1) In the classical cycle, both the technological innovation input and output indices exhibit an overall upward trend, with the output index growing at a faster pace. After a brief decline in the enterprise scale index from 2017 to 2018, growth resumed due to policy support. (2) The growth rate cycle reveals that there is a lag effect in the fluctuations of the growth rate cycle indices for input and output. The fluctuation trends of enterprise scale and innovation capability are consistent, but the scale fluctuations are more pronounced. (3) Impulse response analysis indicates that the initial impact of technological innovation input is moderate. An initial increase in the output index leads to a temporary fluctuation in enterprise development followed by an upward trend and can promote the formation of a virtuous cycle in the input index. (4) Variance decomposition shows that both the input and output indices have a four-period lag effect on enterprise development. The variance contribution rate of the output index (approximately 28%) is higher than that of the input index (6%), indicating a more significant driving role of output. Both governments and enterprises should attach great importance to technological innovation. While increasing investment, they should strengthen the monitoring of technological achievement transformation, promote technological innovation output, and drive the steady development of SMEIs.

technological innovation  /  innovation-driven development  /  small and medium-sized industrial enterprises
杨武, 袁媛, 王坤. 科技创新对中国中小工业企业发展的驱动研究. 科学学研究, 2026 , 44 (10) : 2207 -2217 .
Wu YANG, Yuan YUAN, Kun WANG. The driving role of technological innovation in the development of small and medium-sized industrial enterprises in China[J]. Studies in Science of Science, 2026 , 44 (10) : 2207 -2217 .
在全球化和技术革新的持续推动下,科技创新已经成为经济增长的主要驱动力。中小工业企业作为中国经济体系的关键构成要素,其发展状况直接决定了国家经济的活力与竞争力。据国家统计局数据,中国中小工业企业数量占全国工业企业总数的99%以上,贡献了超过60%的工业增加值,提供了约80%的城镇就业岗位。中小工业企业产值和产量远远超过大型企业,却常常受到忽视。
在当前经济新常态下,中国政府高度重视中小工业企业的科技创新能力提升,相继出台了一系列扶持政策,旨在通过科技创新驱动中小工业企业转型升级,增强其核心竞争力。2021年,国家科技型中小企业技术创新基金支持项目超过1.5万个,资助金额超过100亿元人民币。中国中小工业企业研发投入强度逐年增加,2022年全国规模以上工业企业研发投入强度达到1.56%,其中中小工业企业研发投入占比逐年上升。探讨科技创新如何驱动中小工业企业发展,对于促进中小工业企业转型升级、实现可持续发展具有重要的理论和实践意义。本研究旨在深入分析科技创新对中小工业企业发展的影响机制,构建科学合理的测度体系,并建立向量自回归模型(VAR),分析科技创新和中小工业企业发展的双向驱动关系。
中小工业企业在经济体系中占据着举足轻重的地位,其科技创新能力与经济增长的关系日益受到关注,但针对驱动机制的系统研究仍显不足。学者从多维度构建了中小企业发展评价框架。Singh等聚焦可持续制造性能评估[1];Zotova则探讨了战略发展有效性评估方法[2]。在创新评价方面,谢延钊等将科技型中小企业创新指数分为投入、过程、产出和环境4个维度[3];陈云等进一步细化了技术创新能力指标体系[4]。然而,这些研究较少从专利视角分析中小工业企业的科技创新,存在一定局限性。现有研究普遍认同科技创新对经济的促进作用,但对双向驱动机制的探讨不足。刘建明等实证分析了科技创新对区域经济的单向推动作用[5];孙娜等强调科技创新是产业升级的核心动力,但未深入分析经济反哺创新的路径[6]。部分学者开始关注互动关系,如张艳丽等利用系统动力学模型发现科技创新与经济发展存在协同效应,但研究局限于绿色创新领域[7];郑威等揭示了财政科技政策的调节作用,但仍未全面刻画动态关联[8]。杨武等进一步量化了科技创新与高技术产业发展的耦合关系,证实其对经济增长和结构优化的显著影响[9-11]。
以上研究在中小企业科技创新领域取得了重要进展,但仍存在三个关键局限:第一,研究对象泛化,缺乏对中小工业企业的针对性研究,特别是基于专利指标的创新评价体系尚未建立;第二,理论框架不完整,多数研究仅关注科技创新对经济的单向影响,对双向互动机制的系统性研究不足;第三,方法论层面呈现静态化特征,传统计量模型难以捕捉创新要素与经济变量间的双向驱动关系。基于此,本研究通过构建包含专利质量维度的多维评价体系,并运用向量自回归模型,旨在揭示中小工业企业科技创新与发展的双向动态驱动机制。
目前,不同学者基于各自研究视角与目标,在科技创新方面围绕研发资金、创新产出[12,13]等选取指标,在企业发展方面则从经济效益[14]、研发能力[15]、财务状况[16,17]等多维度选取指标来评估企业状况。本文通过对学者研究成果的总结并借鉴杨武和田雪姣[9]、张鑫和陶化冶等[12]学者的研究成果,构建了中小工业企业科技创新与企业发展水平指标体系,综合涵盖科技创新的投入、产出及效益等多个层面,确保全面反映中小工业企业的科技创新实力和发展状况,具体见表1。
为构建科学的评价体系指数,本研究选取规模以上中小工业企业2011年至2022年间的科技创新与企业发展水平相关指标的原始数据,运用基于古典循环和增长率循环的合成指数方法,对相关指标进行合成,权重的确定采用变异系数法。所有原始数据均来源于《中国统计年鉴》以及《中国工业统计年鉴》,缺失数据采用线性趋势法补足。
(1)数据的标准化处理
在数据的标准化处理过程中,首先需要明确各项评价指标的性质和量纲。由于科技创新与企业发展的各项指标可能存在单位和量纲上的差异,直接进行合成分析会导致结果失真。因此,需要对原始数据进行标准化处理,消除单位和量纲的影响,使得各项指标能够在同一尺度上进行比较和合成。本研究采用均值标准化的方法对数据进行处理,其中$\overline{{\mathit{X}}_{\mathit{i}}}$为指标Xi的平均值,i为2011-2022,公式如下:
${\mathit{X}}_{\mathit{t}}={\mathit{X}}_{\mathit{i}}/{\overline{\mathit{X}}}_{\mathit{i}}$
(2)古典循环法合成指数
①求单个指标的对称变化率。设Cit表示第i个指标第t年的对称变化率,其中Xit和Xit-1分别表示第i个指标第t年和第t-1年的原始数据,对称变化率的计算公式如下:
${\mathit{C}}_{\mathit{i}\mathit{t}}=\frac{{\mathit{X}}_{\mathit{i}\mathit{t}}-{\mathit{X}}_{\mathit{i}\mathit{t}-1}}{\frac{{\mathit{X}}_{\mathit{i}\mathit{t}}+{\mathit{X}}_{\mathit{i}\mathit{t}-1}}{2}}\times 100=200\times \frac{{\mathit{X}}_{\mathit{i}\mathit{t}}-{\mathit{X}}_{\mathit{i}\mathit{t}-1}}{{\mathit{X}}_{\mathit{i}\mathit{t}}+{\mathit{X}}_{\mathit{i}\mathit{t}-1}},\mathit{t}=\mathrm{2,3},\dots,\mathit{n}$
当Xit=0或为负值或者为比例序列时,对称变化率取一阶差分:
${\mathit{C}}_{\mathit{i}\mathit{t}}={\mathit{X}}_{\mathit{i}\mathit{t}}-{\mathit{X}}_{\mathit{i}\mathit{t}-1}$
②求指标标准化平均变化率Sit。首先求标准化因子,用Ai表示第i个指标对称变化率时间序列的序时平均数,n表示标准化的期数:
${\mathit{A}}_{\mathit{i}}=\stackrel{\mathit{n}}{\sum _{\mathit{t}=2}}\frac{\left|{\mathit{C}}_{\mathit{i}\mathit{t}}\right|}{\mathit{n}-1}$
则第i个指标第t期标准化平均变化率为:
${\mathit{S}}_{\mathit{i}\mathit{t}}={\mathit{C}}_{\mathit{i}\mathit{t}}/{\mathit{A}}_{\mathit{i}},\mathit{t}=\mathrm{2,3},\dots,\mathit{n}$
③计算多指标对称变化率标准化后的加权平均数Rt,其中ωi表示权数:
${\mathit{R}}_{\mathit{t}}=\stackrel{\mathit{k}}{\sum _{\mathit{i}=1}}{\mathit{S}}_{\mathit{i}\mathit{t}}{\mathit{\omega }}_{\mathit{i}}/\stackrel{\mathit{k}}{\sum _{\mathit{i}=1}}{\mathit{\omega }}_{\mathit{i}}$
④计算合成指数It,令I(1)=100
${\mathit{I}}_{\mathit{t}}={\mathit{I}}_{\mathit{t}-1}\times \frac{200+{\mathit{R}}_{\mathit{t}}}{200-{\mathit{R}}_{\mathit{t}}},\mathit{t}=\mathrm{2,3},\dots,\mathit{n}$
(3)增长率循环法合成指数
求单个指标的同比增长率Ri:
${\mathit{R}}_{\mathit{i}}=\frac{{\mathit{X}}_{\mathit{i}\mathit{t}}-{\mathit{X}}_{\mathit{i}\mathit{t}-1}}{{\mathit{X}}_{\mathit{i}\mathit{t}-1}}\times 100\mathrm{\%},\mathit{t}=\mathrm{2,3},\dots,\mathit{n}$
其余计算步骤同古典循环方法,不再赘述。
(4)指标赋权
运用变异系数法对指标进行赋权,计算步骤如下:
①计算第i个指标的变异系数,其中CVi表示第i项指标的变异系数,u表示第i项指标的平均值。
$\mathit{C}{\mathit{V}}_{\mathit{i}}={\mathit{\sigma }}_{\mathit{i}}/\mathit{u}$
${\mathit{\sigma }}_{\mathit{i}}=\sqrt{\frac{1}{\mathit{n}}\stackrel{\mathit{n}}{\sum _{\mathit{i}=1}}({\mathit{X}}_{\mathit{i}}{-\mathit{\mu })}^{2}}$
②计算第i个评价指标的权重
${\mathit{\omega }}_{\mathit{i}}=\mathit{C}{\mathit{V}}_{\mathit{i}}/\stackrel{\mathit{n}}{\sum _{\mathit{i}=1}}\mathit{C}{\mathit{V}}_{\mathit{i}}$
通过对规模以上中小工业企业2011年至2022年间企业科技创新与企业发展水平相关指标的测度,我们运用古典循环法合成了科技创新投入指数、科技创新产出指数、企业创新发展指数以及企业规模发展指数。这些指数为我们提供了对中小工业企业科技创新与企业发展水平动态关系的深入理解,具体测度结果分别见图1和图2。
由图1可知,2011年至2022年期间,科技创新投入指数与科技创新产出指数均呈现出持续上升的趋势。科技创新产出指数在2014年至2015年期间增长速度有所减缓,这与全球经济形势的不稳定、投资环境的不利以及中国在该时期对科技创新投入政策的相对保守态度有关。在此背景下,科研经费投入增长放缓,进而对科技创新领域的资金投入造成了一定的限制,导致创新产出增长速度下降。相对而言,科技创新投入指数在2019年至2020年期间增长幅度较大,主要得益于中国在该阶段对科技创新支持力度的加大,以及一系列鼓励科技创新政策的出台。“十三五”国家科技创新规划的实施,强调了创新驱动发展战略,推动了以科技创新为核心的全面创新,为科技创新提供了坚实的政策支持。此外,中国还增强了对科研机构和企业的研发支持,提升了科研人员的待遇,并优化了科技创新环境。并且中国创新产出指数持续高于创新投入指数。这一现象的原因在于,中国在科技创新方面具有较高的转化效率和创新能力。一方面,中国科研机构和企业在技术创新方面具备较强的实力,能够迅速将科研成果转化为实际应用,从而推动创新产出的提升。另一方面,中国政府对科技创新的支持政策也起到了积极的推动作用,通过提供资金、人才等资源支持,促进了科技创新活动的持续开展和创新成果的不断涌现。因此,尽管在某些年份增速有所波动,但中小工业企业在科技创新方面的投入与产出均表现出积极的增长趋势。科技创新投入的增加,包括研发经费、人员投入等,为企业的科技创新活动提供了有力支持,推动了科技创新产出的不断提升。
由图2可知,企业创新发展指数和企业规模发展指数的变化情况。企业创新发展指数在考察期间内总体呈现上升趋势,表明中小工业企业在通过科技创新提升市场竞争力和盈利能力方面取得了显著成效。同时,企业规模发展指数也呈现出稳步增长的趋势,说明中小工业企业在规模上实现了扩张和成长。但企业发展规模在2017年至2018年有明显的下降趋势,与当时全球经济形势和国内政策调整有关。在此期间,全球经济面临诸多挑战,包括贸易保护主义抬头、国际市场需求疲软等因素,对中小工业企业的发展产生了不利影响。同时,国内经济结构调整和环保政策的加强,也对部分中小工业企业造成了短期压力,导致在规模扩张方面遇到困难。然而,2018年之后,企业规模发展指数逐渐回升,这与国家出台的一系列扶持政策密切相关。政府加大了对中小企业的财政支持和税收优惠力度,推动了科技创新和产业升级。同时,国家还实施了简政放权、优化营商环境的改革措施,降低了企业的运营成本和市场准入门槛,激发了中小企业的活力和创新能力。此外,国家还特别强调了对中小工业企业技术改造和创新的支持,通过设立专项基金、提供研发补贴等方式,鼓励企业加大研发投入,提升产品和服务的附加值。这些政策的实施有效缓解了中小工业企业面临的困境,促进了规模发展上的持续进步。
基于古典循环的测度结果分析表明,中小工业企业在科技创新与企业发展方面取得了积极进展。科技创新投入与产出的不断增长,以及企业创新发展和规模发展的稳步提升,共同构成了中小工业企业持续健康发展的坚实基础。然而,面对日益激烈的市场竞争和不断变化的外部环境,中小工业企业仍需不断加大科技创新投入,优化创新资源配置,提升创新能力和水平,以实现更高质量、更可持续的发展。
增长率循环指数可以更好地反映中小工业企业科技创新与企业发展水平之间的相对波动趋势。该指数着重强调两者之间的相对变化趋势,使我们能够更准确地理解企业在科技创新和整体发展方面的周期性波动,具体结果如图3和图4所示。
由图3可知,基于增长率循环的科技创新投入指数和科技创新产出指数都呈现出一种波动性的相对变化趋势。这两个指数的曲线不仅在形态上具有一定的相似性,而且在时间序列上也表现出一定的滞后效应。具体来看,科技创新投入指数在2012年至2014年间增长相对放缓,这与当时中国经济结构调整、经济转型以及科技创新投入政策的调整紧密相关。在此期间,政府更加注重科技创新的质量而非数量,导致投入增长放缓。而科技创新产出指数在滞后一段时间后,于2012年至2015年间呈现逐步下降趋势,这一变化与科技创新成果转化所需时间、市场需求的变动以及国际竞争的加剧等因素有关。同时,国内政策环境亦对科技创新产出产生影响,科技创新政策的调整、知识产权保护力度的加强,导致成果转化放缓。进一步观察,科技创新投入指数在2014年至2015年间呈现下降趋势,此现象与经济下行压力的增大、企业研发投入的减少有关。而科技创新产出指数在滞后效应的作用下,于2016年至2017年间增长率逐步下降,这一变化是科技创新投入转化为产出的滞后效应、市场需求变化以及国际竞争环境等因素共同作用的结果。在此期间,中国政府亦推出了一系列旨在鼓励科技创新的政策,如增加科技研发投入、优化科技创新环境、加强知识产权保护等,以期提升科技创新的能力与水平。
由图4可知,中小工业企业基于增长率循环的发展水平、企业创新能力和企业发展规模均呈现出持续变化的相对波动趋势。进一步地,企业发展规模相较于企业创新能力的相对波动趋势更为显著,并且两者之间存在趋势的一致性。这种波动在很大程度上受到了中国宏观经济政策以及产业政策的调整影响。在2012年至2018年期间,随着中国经济进入新常态,产业结构调整和优化升级成为主基调,这导致部分传统中小工业企业面临转型升级的压力,进而使得企业创新水平和企业发展规模指数增长率水平出现不同程度的下降。特别是在2018年,受到环保政策趋严、去产能政策等因素的影响,许多中小企业面临生存困境,企业发展规模指数因此跌破100。然而,随着国家对中小企业创新发展的支持力度不断加大,出台一系列减税降费政策、优化营商环境等,2018年之后,企业创新水平和企业发展规模指数开始回升,显示出中小企业在转型升级过程中逐渐找到新的发展路径。
向量自回归模型(VAR模型)是一种基于多变量时间序列数据的统计模型,旨在捕捉各变量之间的动态交互关系。该模型允许所有变量互为解释变量和因变量,从而能够全面分析系统内各变量间的相互影响。本文采用VAR模型,旨在精确量化中小工业企业科技创新与企业发展水平之间的驱动效应。在具体应用中,由于古典循环指数是一个绝对数值,能够直观反映经济活动的总量变化;而增长率循环指数则体现相对变化趋势,更多地反映经济活动的增速变化。鉴于本文关注的是科技创新对企业发展水平的驱动效应,因此选择古典循环指数进行VAR模型的构建,以更准确地揭示两者之间的动态关系。由上文,企业创新水平和企业发展规模曲线体现出一致性,这种一致性表明两者之间存在密切的关联或相互依存关系。因此,在探究它们与其他变量的相互作用时,为了简化模型并突出主要关系,我们将其视为一个整体进行分析。故在建立VAR模型时,将企业创新水平和企业发展规模视为整体,研究科技创新投入、科技创新产出以及这一整体即企业发展水平的驱动效应。
平稳性检验是时间序列分析中的一项基础性工作,它旨在确保数据序列在统计上具有稳定性,从而避免伪回归等问题。在构建VAR模型之前,对所有参与模型构建的时间序列数据进行平稳性检验是至关重要的。因此,本文采用ADF(Augmented Dickey-Fuller)单位根检验法对科技创新投入指数、科技创新产出指数以及企业发展水平综合指数进行平稳性检验。若原始数据序列未通过平稳性检验,则需对其进行差分处理,直至序列变为平稳,以满足VAR模型构建的要求。为消除异方差,首先对数据进行对数处理。A1表示科技创新投入,A2表示科技创新产出,B表示企业发展水平。由表2可知lnA1、lnA2、lnB的Z值均大于0.01显著性水平下的临界值,这表明lnA1、lnA2、lnB序列均存在单位根,即原始数据序列为非平稳序列。为了将非平稳序列转化为平稳序列,我们对lnA1、lnA2、lnB序列分别进行一阶差分处理,得到DlnA1、DlnA2、DlnB序列。再次利用ADF单位根检验法对一阶差分后的序列进行平稳性检验,结果显示DlnA1、DlnA2、DlnB的Z值均小于0.01显著性水平下的临界值,说明一阶差分后的序列已经变为平稳序列,满足VAR模型构建的要求。将一阶差分后的数据意义上解释为指标的增量,即科技创新投入、科技创新产出以及企业发展水平的变动情况。这一处理不仅符合经济学中对变量增量的关注,也便于后续分析各变量间的动态关系。
本研究综合运用多种滞后阶数筛选方法,旨在精确确定向量自回归(VAR)模型的最优滞后阶数。通过对四项评价指标进行深入分析与比较,研究结果一致指向滞后阶数为2的最优选择。基于此,本研究决定采用滞后阶数为2的VAR(2)模型。在构建的向量自回归VAR(2)模型中,为了验证模型的稳定性,本研究采用了Stata软件进行单位根检验,并生成了相应的图表。由图5可知,所有单位根均位于单位圆内部,从而确认了所估计的模型的收敛稳定性。这一结果进一步揭示了所选变量之间存在长期稳定的关联性,为后续的脉冲响应函数分析和方差分解提供了坚实的基础。
脉冲响应函数分析能够直观展现某一变量受到冲击后对其他变量的动态影响。在中小工业企业科技创新与企业发展水平的VAR(2)模型中,我们分别给科技创新投入指数、科技创新产出指数一个正向冲击,观察这两个冲击对企业发展水平综合指数的影响。
如图6所示,对科技创新投入指数施加正向冲击后,企业发展水平综合指数在短期内表现出正向反应,然而总体波动幅度有限,大约在10期后达到稳定状态。这一结果表明,科技创新投入的增加在初期能够对企业发展水平产生积极的推动作用,但这种推动作用相对温和,并未引发剧烈的波动。随着时间的推移,这种正向影响逐渐趋于平稳,显示出科技创新投入对企业发展的长期稳健性。
而当给予科技创新产出指数一个正向冲击后,企业发展水平综合指数的响应先下降后上升,是由于科技创新产出的初期增加需要企业投入更多的资源和精力进行新技术的推广和应用,从而暂时性地增加了企业的运营成本,导致企业发展水平综合指数出现短暂下降。但随后,随着新技术的逐渐成熟和应用效果的显现,科技创新产出开始为企业带来实际的经济效益和竞争优势,企业发展水平综合指数随之上升,并且波动较为明显。这种波动反映了科技创新产出对企业发展影响的复杂性和动态性,可能受到市场环境、政策调整等多种因素的共同作用。最终,随着各种因素的逐渐稳定,以及企业对新技术应用的不断熟练和优化,科技创新产出对企业发展的正向推动作用也趋于平稳,企业发展水平综合指数逐渐趋于0,进入一个相对稳定的发展阶段。
进一步分析发现,科技创新投入指数和科技创新产出指数的冲击对企业发展水平综合指数的影响存在交互效应。即科技创新投入的增加不仅能够直接提升企业发展水平,还能够通过促进科技创新产出的增加来间接推动企业发展。当给科技创新投入指数一个正向冲击后,科技创新产出指数呈现短暂下降之后迅速回升,并呈现不断波动状态,直至15期左右趋近于0。这种先降后升并伴随波动的现象,是由于科技创新投入初期往往需要大量资金、人力等资源的集中投入,而这些资源的即时转化效率并不高,可能导致短期内科技创新产出的暂时减少。然而,随着投入的持续增加和资源的有效整合,科技创新活动逐渐进入正轨,产出效率开始提升,科技创新产出指数因此迅速回升。此后的波动状态则可能源于科技创新过程中的不确定性,如技术难题的攻克、市场需求的变化等,这些因素都可能影响科技创新产出的稳定性和持续性。而到15期左右趋近于0,则表明随着科技创新活动的深入和稳定,以及企业对新技术应用的不断熟练和优化,科技创新投入对科技创新产出的直接影响逐渐减弱,进入一个相对平稳的发展阶段。这种交互效应的存在,进一步强调了科技创新投入和产出在推动企业发展中的重要作用,也为企业制定科技创新战略提供了重要参考。同样地,科技创新产出的增加也能够反馈作用于科技创新投入,形成良性循环,共同推动中小工业企业科技创新与企业发展水平的持续提升。
方差分解旨在进一步解析VAR模型中各变量波动性的来源,以及各变量冲击对特定变量预测误差的贡献度。通过方差分解,更深入地了解中小工业企业科技创新与企业发展水平之间动态关系的内在机制。
在针对中小工业企业科技创新与企业发展水平的向量自回归(VAR)模型分析中,本研究对企业发展水平综合指数的预测误差进行了方差分解,旨在深入探究科技创新投入指数与科技创新产出指数对企业发展水平波动性的影响。如图7所示,科技创新投入指数与科技创新产出指数对企业发展水平综合指数的预测误差均具有显著的贡献效应,并且这种贡献效应随时间的演进呈现出特定的变化趋势。具体而言,在预测的初期阶段,企业发展水平综合指数的波动性主要受到其自身惯性的影响,即前期波动对当前波动具有显著的滞后效应。然而,随着时间的推移,科技创新投入指数与科技创新产出指数的贡献效应逐渐增强,成为影响企业发展水平波动性的重要因素。如表3所示,科技创新投入指数与科技创新产出指数在约4期后达到稳定状态,揭示了存在约4期的滞后效应。这种滞后效应可能是由于科技创新活动本身需要一定的时间来实施和产生效果,同时企业也需要一定的时间来适应和调整科技创新带来的变化。因此,在科技创新投入和产出对企业发展水平产生影响的过程中,会存在一定的时间滞后。一步分析显示,科技创新产出指数的方差贡献率稳定在约28%,显著高于科技创新投入指数约6%的方差贡献率。是由于科技创新产出指数更能直接反映企业的创新能力和市场竞争力,而科技创新投入指数虽然反映了企业的创新投入情况,但并不一定能够直接转化为有效的创新产出。因此,科技创新产出指数对企业发展水平的影响更为显著。
方差分解的结果揭示了中小工业企业科技创新与企业发展水平之间动态关系的内在机制。科技创新投入和产出不仅直接影响企业发展水平,还通过交互效应共同推动企业发展。因此,在制定科技创新战略时,企业应充分考虑科技创新投入和产出的协同作用,以实现科技创新与企业发展的良性循环。同时,政府也应加大对中小工业企业科技创新的支持力度,优化科技创新环境,提升科技创新转化能力和水平,重视科技创新产出,为中小工业企业的持续健康发展提供有力保障。
本研究通过对中小工业企业科技创新与企业发展水平的深入探究,结合古典循环和增长率循环的测度分析以及脉冲响应和方差分解的视角,得出了以下重要结论:
(1)古典循环测度结果。科技创新投入指数与科技创新产出指数整体上表现出积极的增长趋势,并且创新产出指数持续高于创新投入指数。尽管在2017年至2018年期间,企业发展规模指数有所下降,但随后在政府扶持政策的推动下,企业规模发展指数逐渐回升。
(2)增长率循环测度结果。科技创新投入指数和科技创新产出指数都呈现出波动性的相对变化趋势,且两者之间存在滞后效应。企业发展规模相较于企业创新能力的相对波动趋势更为显著,并且两者之间存在趋势的一致性。
(3)脉冲响应分析结果。科技创新投入的增加在初期能够对企业发展水平产生积极的推动作用,但这种推动作用相对温和,并未引发剧烈的波动。科技创新产出指数的增加导致企业发展水平综合指数的响应先下降后上升,科技创新产出的初期增加需要企业投入更多的资源和精力进行新技术的推广和应用,从而暂时性地增加了企业的运营成本,导致企业发展水平综合指数出现短暂下降。并且科技创新产出的增加则能够反馈作用于科技创新投入,形成良性循环,共同推动中小工业企业科技创新与企业发展水平的持续提升。
(4)方差分解分析结果。科技创新投入指数和科技创新产出指数对企业发展水平综合指数的影响存在4期滞后效应。科技创新产出指数的方差贡献率稳定在约28%,显著高于科技创新投入指数约6%的方差贡献率。科技创新投入和产出不仅直接影响企业发展水平,还通过交互效应共同推动企业发展。
因此,本文认为,在推动中小工业企业科技创新发展的过程中,不能仅仅聚焦于加大创新投入力度,更要高度重视创新产出以及投入向产出的转化率。创新投入能够高效转化为实际产出,以提升中小工业企业的创新能力和市场竞争力,实现可持续发展。此外,企业规模的发展也会反作用于企业创新产出,二者相互促进,形成良性循环机制,助力中小工业企业实现高质量发展。
  • 国家自然科学基金面上项目(72074019)
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2026年第44卷第10期
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  • 接收时间:2025-05-13
  • 首发时间:2026-10-10
  • 出版时间:2026-10-15
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  • 收稿日期:2025-05-13
  • 修回日期:2025-06-30
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国家自然科学基金面上项目(72074019)
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    北京科技大学经济管理学院, 北京 100083

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袁媛(2001-),女,满族,硕士研究生,E-mail:。
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