由“P值困境”引发对“不育的”经济学反思
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摘要
美国《政治分析》杂志2018年初突然宣布禁用P值,由于P值应用广泛,事件使得社会科学研究者陷入"P值困境"。P值作为重要的统计变量,若此变量不值得信赖,那么现代以数学或统计为基础的社会科学理论都值得怀疑,尤以经济学为最。事实上经济学家在"数学是一门语言"的掩护下引入数学,其背后不乏深层次原因,有科学革命的影响,政治规避的动机及路径依赖的无奈。但数学在经济学的应用超越了语言的范畴,导致"数学谬误"的产生,进一步导致"不育的"经济学。从历史来看,数学在经济学中的应用大体可分为三个阶段,每个阶段都争议不断,"P值困境"的出现再次引发对经济学的反思,考查其哲学属性,价值取向及人本特征,是避免"数学滥用"并走出"P值困境"的必经之路。
In early 2018,American Journal " Political Analysis"abruptly banned the p-value in regression table. Due to the wide application of this statistic variable,social science researchers fell into the"p-value dilemma". As an important statistical variable,if P-value is not trustworthy,the whole modern social science theory which are based on mathematics or statistics became doubtful,especially economics. Actually,economists introduced mathematics under the cover of "mathematics is a language". However,There were many deep reasons behind,including the influence of the scientific revolution,the motive of political evasion and the helplessness of path dependence. Unfortunately,the application of mathematics in economics goes beyond the scope of language,and resulting in "mathiness"and further leading to "infertile"economics. Historically,the application of mathematics in economics can be roughly divided into three periods,each period are full of controversy,nowadays,the emergence of "p-value dilemma"triggers reflection on economics once again,examining its philosophical attributes,research objects and value orientation became the only way to avoid "mathiness"and the "p-value dilemma"in the future.
In early 2018,American Journal " Political Analysis"abruptly banned the p-value in regression table. Due to the wide application of this statistic variable,social science researchers fell into the"p-value dilemma". As an important statistical variable,if P-value is not trustworthy,the whole modern social science theory which are based on mathematics or statistics became doubtful,especially economics. Actually,economists introduced mathematics under the cover of "mathematics is a language". However,There were many deep reasons behind,including the influence of the scientific revolution,the motive of political evasion and the helplessness of path dependence. Unfortunately,the application of mathematics in economics goes beyond the scope of language,and resulting in "mathiness"and further leading to "infertile"economics. Historically,the application of mathematics in economics can be roughly divided into three periods,each period are full of controversy,nowadays,the emergence of "p-value dilemma"triggers reflection on economics once again,examining its philosophical attributes,research objects and value orientation became the only way to avoid "mathiness"and the "p-value dilemma"in the future.
引文
[1]GILL J. Comments from the new editor[J]. Political Analysis,2018,26(1):1-2.
[2]NUZZO R. Scientific method:Statistical errors[J]. Nature,2014,506(7487):150-152.
[3]DEBREU G. The mathematization of economic theory[J].American Economic Review,1991,81(1):1-7.
[4]HAHN F. Reflections[J]. Royal Economics Society Newsletter,1992(77):11-17.
[5]杨小凯.经济学——新兴古典与新古典框架[M].北京:社会科学文献出版社,2003:6-7.
[6]阿弗里德·马歇尔.经济学原理[M].北京:华夏出版社,2010:6.
[7]PIGOU A C. Memorials of Alfred Marshall[M]. London:Macmillan,1925:427.
[8]DEBREU G. Theoretic models:Mathematical form and economic content[J]. Econometrica,1986,54(6):1259-1270.
[9]陈彦斌.经济学研究的范式导向[N].光明日报(理论版),2015-05-21(16).
[10]MIROWSKI P. More heat than light:Economics as social physics,physics as nature's economics[M]. Cambridge:Cambridge University Press,1989.
[11]ANDERSON P W,ARROW K J,PINES D. The economy as an evolving complex system:The proceedings of the evolutionary paths of the global economy[M]. California:Addison-Wesley,1988.
[12]ARTHUR W B,DURLAUF S N,LANE D A. The economy as an evolving complex system II[M]. Calif.:Addison-Wesley,1997.
[13]BLUME L E,DURLAUF S N. The economy as an evolving complex system III:Current perspectives and future directions[M]. Oxford:Oxford University Press,2005.
[14]琼·罗宾逊,约翰·伊特韦尔.现代经济学导论[M].北京:商务印书馆,2005:6-7.
[15]罗伊·温特罗伯.一个历史学家的视角:罗伊·温特罗伯访谈[A].经济学家之经济学家——与诺贝尔奖获得者和候选者的对话[C].北京:北京大学出版社,2008:31-39.
[16]STREETEN P P. What's wrong with contemporary economics[J]. The Pakistan Development Review,2000,39(3):191-211.
[17]KATZNER D W. Why Mathematics in Economics?[J].Journal of Post Keynesian Economics,2003,25(4):561-574.
[18]李子奈.关于现代计量经济学的研究方法[J].清华大学学报(哲学社会科学版),1995(3):25-34.
[19]约瑟夫·熊彼特.从马克思到凯恩斯的十大经济学家[M].北京:电子工业出版社,2013:82.
[20]SAMUELSON P A. Economic theory and mathematics:An appraisal[J]. The American Economic Review,1952,42(2):56-66.
[21]李子奈,齐良书.计量经济学模型的功能与局限[J].数量经济技术经济研究,2010(9):133-146. 2015.
[22]ROMER P M. Mathiness in the theory of economic growth[J]. American Economic Review,2015,105(5):89-93.
[23]NOVICK D. Mathematics:Logic,quantity,and method[J]. Review of Economics&Statistics,1954,36(4):357-358.
[24]SAMUELSON P A. Introduction:Mathematics in economics——no,no or yes,yes,yes?[J]. Review of Economics&Statistics,1954,36(4):359.
[25]WILSON E B,STIGLER G. Mathematics in economics:Further comment[J]. Review of Economics&Statistics,1955,37(3):297-300.
[26]KLEIN L R. The contributions of mathematics in economics[J]. Review of Economics&Statistics,1954,36(4):359-361.
[27]DUESENBERRY J S. The methodological basis of economic theory[J]. The Review of Economics and Statistics,1954,36(4):361-363.
[28]CHIPMAN J S. Empirical testing and mathematical models[J]. Review of Economics&Statistics,1954,36(4):363-365.
[29]TINBERGEN J. The functions of mathematical treatment[J]. Review of Economics&Statistics,1954,36(4):365-369.
[30]CHAMPERNOWNE D G. On the use and misuse of mathematics in presenting economic theory[J]. Review of Economics&Statistics,1954(4):369-372.
[31]DORFMAN R. A catechism:Mathematics in social science[J]. Review of Economics&Statistics,1954,36(4):374-377.
[32]KOOPMANS T C. On the use of mathematics in economics[J]. The Review of Economics&Statistics,1954,36(4):377-379.
[33]SOLOW R. The survival of mathematical economics[J].The Review of Economics&Statistics,1954,36(4):372-374.
[34]DADAYAN V,CHERNYAK Y. Mathematical methods in economics[J]. Management science,1961,7(4):323-334.
[35]HURWICZ L. Mathematics in Economics:Language and Instrument[A]. Mathematics and the Social Sciences[M]. PA:The American Academy of Political Science.1963:158.
[36]本耐特·迈考卢姆.罗伯特·卢卡斯访谈录[A].经济学家之经济学家——与诺贝尔奖获得者和候选者的对话[C].北京:北京大学出版社,2008:44-53.
[37]DEBREU G. Economic theory in the mathematical mode[J]. The American Economic Review,1984,74(3):267-278.
[38]田国强.现代经济学的基本分析框架与研究方法[J].经济研究,2005(2):113-125.
[39]BOULDING K E. Samuelson's foundations:The role of mathematics in economics[J]. Journal of Political Economy,1948,56(3):187-199.
[40]MENARD C. Three forms of resistance to statistics:Say,cournot,walras[J]. History of Political Economy,1980,12(4):524-541.
[41]WEINTRAUB R. How economics became a mathematical science?[M]. Durham:Duke University Press,2002.
[42]QUDDUS M,RASHID S. The overuse of mathematics in economics:Nobel resistance[J]. Eastern Economic Journal,1994,20(3):251-265.
[43]KANTOROVICH L V. Mathematics in economics:Achievements,difficulties,perspectives[J]. Mathematical Programming,1976,11(1):204-211.
[44]约翰·梅纳德·凯恩斯.就业、利息和货币通论[M].北京:商务印书馆,2013:309.
[45]LEONTIEF W. Academic economics[J]. Science,1982,217(4555):104-107.
[46]ENKE S. More on the misuse of mathematics in economics:A rejoinder[J]. Review of Economics&Statistics,1955,37(2):131-133.
[47]PANI N. On subjectivity in mathematical economics[J].Economic&Political Weekly,2003,38(35):3686-3693.
[48]HAAVELMO T. Prize Lecture[R]. Sveriges riksbank:Prize in economic sciences in memory of alfred nobel,1989.
[49]STIGLER G J. The mathematical method in economicsthe fourth of five lectures on economic problems[M]. London:London School of Economics,1949.
[50]ALIIS M. My life philosophy[J]. The American Economist,1989,33(2):3-17.
[51]SCHOEFFLER S. Mathematics in economics:Some dangers[J]. Review of Economics&Statistics,1956,38(1):88-90.
[52]BOULDING K E. Economics as an Institution[R]. The Fifth Annual Kenneth Parsons Lecture Series,IBS,Boulder,Colorado,1989.
[53]BUCHANAN J. Liberty,market,and state[M]. NY:New York University Press,1985:15.
[54]HAAVELMO T. The role of the econometrician in the advancement of economic theory[J]. Econometrica,1958,26(3):351-357.
[55]张金清,李徐.经济学中的“数学困惑”及其解析[J].经济学家,2007(3):29-37.
[56]马克思.数学手稿[M].北京:人民出版社,1975.
[57]约瑟夫·熊彼特.经济分析史[M].北京:商务印书馆,1996.
[58]萨缪尔森.中间道路经济学[M].北京:首都经济贸易大学出版社,2000.
[59]马歇尔.经济学原理[M].北京:华夏出版社,2010:22.
[60]约翰·梅纳德·凯恩斯.艾尔弗雷德·马歇尔传[M].北京:商务印书馆,1990:8-9.
[61]BESLEY T,PAXSON C. Angus deaton symposium-Introduction[J]. Economic Journal,2011,121(554):F119-F122.
(1)大统一理论是物理学概念,德布鲁曾提出这种设想,同时指出经济学离构建大统一理论还为时尚早。
(2)此处采用杨小凯关于主流经济学的定义,即所谓的主流经济学就是在世界范围内的大学课堂上被讲授得最多的、应用最广泛的经济学。
(3)享德森认为配第和格朗特发表的经济学小册子应当是数学与经济学最早的结合;杰文斯、费雪认为最早的应当是意大利人塞瓦,他于1711年发表了《论货币,只限于在几何学上加以论述》;熊彼特认为数理经济学的起点是伯努利;德布鲁则认为1826年屠能的著作中已经有数学的应用,可以放在古诺之前。
(4)这五种刊物分别是:《经济计量学》《经济研究评论》《国际经济评论》《经济理论杂志》和《数理经济学杂志》。
(5)美国的经济史学家米洛斯基详细论证了新古典经济学中价值理论是如何效仿物理学中能量理论的。
(6)经济物理学是由美国波士顿大学物理学教授Eugene Stanley等人于20世纪90年代初首次提出、用以描述物理学家在20世纪最后二十多年中对股票市场、公司成长以及相关的经济问题所作出的研究成果。详细会议内容可参见Blume和Durlauf(2005)。
(7)马克思在19世纪60年代以后阅读了大量的数学书籍,尤其是微积分方面的书籍,并做了详细的手稿,这些手稿一直保存在阿姆斯特丹的国际社会史研究所的档案馆中。伊丽莎白·熊彼特则证实熊彼特在晚年经常研习数学,尤其是对瓦尔拉斯一般均衡原理的推导。
(8)萨缪尔森晚年一直倡导其中间道路经济学,其中随处可见他对于历史哲学的引用和评论。而德布鲁在1991年的发言中说:“我们的学科以丰富的知识多样化为荣,但这种多样化受到越来越多的占绝大多数的数学成员所压制。”
(9)马歇尔在晚年的回忆录中写到:“在假期,我访问了几个城市的最贫穷的人聚居的地方,沿路走过一条又一条街道,察看了最贫穷的人的脸色。接着,我就决心尽我所能,要对政治经济学作一番彻底研究。”
[2]NUZZO R. Scientific method:Statistical errors[J]. Nature,2014,506(7487):150-152.
[3]DEBREU G. The mathematization of economic theory[J].American Economic Review,1991,81(1):1-7.
[4]HAHN F. Reflections[J]. Royal Economics Society Newsletter,1992(77):11-17.
[5]杨小凯.经济学——新兴古典与新古典框架[M].北京:社会科学文献出版社,2003:6-7.
[6]阿弗里德·马歇尔.经济学原理[M].北京:华夏出版社,2010:6.
[7]PIGOU A C. Memorials of Alfred Marshall[M]. London:Macmillan,1925:427.
[8]DEBREU G. Theoretic models:Mathematical form and economic content[J]. Econometrica,1986,54(6):1259-1270.
[9]陈彦斌.经济学研究的范式导向[N].光明日报(理论版),2015-05-21(16).
[10]MIROWSKI P. More heat than light:Economics as social physics,physics as nature's economics[M]. Cambridge:Cambridge University Press,1989.
[11]ANDERSON P W,ARROW K J,PINES D. The economy as an evolving complex system:The proceedings of the evolutionary paths of the global economy[M]. California:Addison-Wesley,1988.
[12]ARTHUR W B,DURLAUF S N,LANE D A. The economy as an evolving complex system II[M]. Calif.:Addison-Wesley,1997.
[13]BLUME L E,DURLAUF S N. The economy as an evolving complex system III:Current perspectives and future directions[M]. Oxford:Oxford University Press,2005.
[14]琼·罗宾逊,约翰·伊特韦尔.现代经济学导论[M].北京:商务印书馆,2005:6-7.
[15]罗伊·温特罗伯.一个历史学家的视角:罗伊·温特罗伯访谈[A].经济学家之经济学家——与诺贝尔奖获得者和候选者的对话[C].北京:北京大学出版社,2008:31-39.
[16]STREETEN P P. What's wrong with contemporary economics[J]. The Pakistan Development Review,2000,39(3):191-211.
[17]KATZNER D W. Why Mathematics in Economics?[J].Journal of Post Keynesian Economics,2003,25(4):561-574.
[18]李子奈.关于现代计量经济学的研究方法[J].清华大学学报(哲学社会科学版),1995(3):25-34.
[19]约瑟夫·熊彼特.从马克思到凯恩斯的十大经济学家[M].北京:电子工业出版社,2013:82.
[20]SAMUELSON P A. Economic theory and mathematics:An appraisal[J]. The American Economic Review,1952,42(2):56-66.
[21]李子奈,齐良书.计量经济学模型的功能与局限[J].数量经济技术经济研究,2010(9):133-146. 2015.
[22]ROMER P M. Mathiness in the theory of economic growth[J]. American Economic Review,2015,105(5):89-93.
[23]NOVICK D. Mathematics:Logic,quantity,and method[J]. Review of Economics&Statistics,1954,36(4):357-358.
[24]SAMUELSON P A. Introduction:Mathematics in economics——no,no or yes,yes,yes?[J]. Review of Economics&Statistics,1954,36(4):359.
[25]WILSON E B,STIGLER G. Mathematics in economics:Further comment[J]. Review of Economics&Statistics,1955,37(3):297-300.
[26]KLEIN L R. The contributions of mathematics in economics[J]. Review of Economics&Statistics,1954,36(4):359-361.
[27]DUESENBERRY J S. The methodological basis of economic theory[J]. The Review of Economics and Statistics,1954,36(4):361-363.
[28]CHIPMAN J S. Empirical testing and mathematical models[J]. Review of Economics&Statistics,1954,36(4):363-365.
[29]TINBERGEN J. The functions of mathematical treatment[J]. Review of Economics&Statistics,1954,36(4):365-369.
[30]CHAMPERNOWNE D G. On the use and misuse of mathematics in presenting economic theory[J]. Review of Economics&Statistics,1954(4):369-372.
[31]DORFMAN R. A catechism:Mathematics in social science[J]. Review of Economics&Statistics,1954,36(4):374-377.
[32]KOOPMANS T C. On the use of mathematics in economics[J]. The Review of Economics&Statistics,1954,36(4):377-379.
[33]SOLOW R. The survival of mathematical economics[J].The Review of Economics&Statistics,1954,36(4):372-374.
[34]DADAYAN V,CHERNYAK Y. Mathematical methods in economics[J]. Management science,1961,7(4):323-334.
[35]HURWICZ L. Mathematics in Economics:Language and Instrument[A]. Mathematics and the Social Sciences[M]. PA:The American Academy of Political Science.1963:158.
[36]本耐特·迈考卢姆.罗伯特·卢卡斯访谈录[A].经济学家之经济学家——与诺贝尔奖获得者和候选者的对话[C].北京:北京大学出版社,2008:44-53.
[37]DEBREU G. Economic theory in the mathematical mode[J]. The American Economic Review,1984,74(3):267-278.
[38]田国强.现代经济学的基本分析框架与研究方法[J].经济研究,2005(2):113-125.
[39]BOULDING K E. Samuelson's foundations:The role of mathematics in economics[J]. Journal of Political Economy,1948,56(3):187-199.
[40]MENARD C. Three forms of resistance to statistics:Say,cournot,walras[J]. History of Political Economy,1980,12(4):524-541.
[41]WEINTRAUB R. How economics became a mathematical science?[M]. Durham:Duke University Press,2002.
[42]QUDDUS M,RASHID S. The overuse of mathematics in economics:Nobel resistance[J]. Eastern Economic Journal,1994,20(3):251-265.
[43]KANTOROVICH L V. Mathematics in economics:Achievements,difficulties,perspectives[J]. Mathematical Programming,1976,11(1):204-211.
[44]约翰·梅纳德·凯恩斯.就业、利息和货币通论[M].北京:商务印书馆,2013:309.
[45]LEONTIEF W. Academic economics[J]. Science,1982,217(4555):104-107.
[46]ENKE S. More on the misuse of mathematics in economics:A rejoinder[J]. Review of Economics&Statistics,1955,37(2):131-133.
[47]PANI N. On subjectivity in mathematical economics[J].Economic&Political Weekly,2003,38(35):3686-3693.
[48]HAAVELMO T. Prize Lecture[R]. Sveriges riksbank:Prize in economic sciences in memory of alfred nobel,1989.
[49]STIGLER G J. The mathematical method in economicsthe fourth of five lectures on economic problems[M]. London:London School of Economics,1949.
[50]ALIIS M. My life philosophy[J]. The American Economist,1989,33(2):3-17.
[51]SCHOEFFLER S. Mathematics in economics:Some dangers[J]. Review of Economics&Statistics,1956,38(1):88-90.
[52]BOULDING K E. Economics as an Institution[R]. The Fifth Annual Kenneth Parsons Lecture Series,IBS,Boulder,Colorado,1989.
[53]BUCHANAN J. Liberty,market,and state[M]. NY:New York University Press,1985:15.
[54]HAAVELMO T. The role of the econometrician in the advancement of economic theory[J]. Econometrica,1958,26(3):351-357.
[55]张金清,李徐.经济学中的“数学困惑”及其解析[J].经济学家,2007(3):29-37.
[56]马克思.数学手稿[M].北京:人民出版社,1975.
[57]约瑟夫·熊彼特.经济分析史[M].北京:商务印书馆,1996.
[58]萨缪尔森.中间道路经济学[M].北京:首都经济贸易大学出版社,2000.
[59]马歇尔.经济学原理[M].北京:华夏出版社,2010:22.
[60]约翰·梅纳德·凯恩斯.艾尔弗雷德·马歇尔传[M].北京:商务印书馆,1990:8-9.
[61]BESLEY T,PAXSON C. Angus deaton symposium-Introduction[J]. Economic Journal,2011,121(554):F119-F122.
(1)大统一理论是物理学概念,德布鲁曾提出这种设想,同时指出经济学离构建大统一理论还为时尚早。
(2)此处采用杨小凯关于主流经济学的定义,即所谓的主流经济学就是在世界范围内的大学课堂上被讲授得最多的、应用最广泛的经济学。
(3)享德森认为配第和格朗特发表的经济学小册子应当是数学与经济学最早的结合;杰文斯、费雪认为最早的应当是意大利人塞瓦,他于1711年发表了《论货币,只限于在几何学上加以论述》;熊彼特认为数理经济学的起点是伯努利;德布鲁则认为1826年屠能的著作中已经有数学的应用,可以放在古诺之前。
(4)这五种刊物分别是:《经济计量学》《经济研究评论》《国际经济评论》《经济理论杂志》和《数理经济学杂志》。
(5)美国的经济史学家米洛斯基详细论证了新古典经济学中价值理论是如何效仿物理学中能量理论的。
(6)经济物理学是由美国波士顿大学物理学教授Eugene Stanley等人于20世纪90年代初首次提出、用以描述物理学家在20世纪最后二十多年中对股票市场、公司成长以及相关的经济问题所作出的研究成果。详细会议内容可参见Blume和Durlauf(2005)。
(7)马克思在19世纪60年代以后阅读了大量的数学书籍,尤其是微积分方面的书籍,并做了详细的手稿,这些手稿一直保存在阿姆斯特丹的国际社会史研究所的档案馆中。伊丽莎白·熊彼特则证实熊彼特在晚年经常研习数学,尤其是对瓦尔拉斯一般均衡原理的推导。
(8)萨缪尔森晚年一直倡导其中间道路经济学,其中随处可见他对于历史哲学的引用和评论。而德布鲁在1991年的发言中说:“我们的学科以丰富的知识多样化为荣,但这种多样化受到越来越多的占绝大多数的数学成员所压制。”
(9)马歇尔在晚年的回忆录中写到:“在假期,我访问了几个城市的最贫穷的人聚居的地方,沿路走过一条又一条街道,察看了最贫穷的人的脸色。接着,我就决心尽我所能,要对政治经济学作一番彻底研究。”