Philip and Sewall Wright: The Inven5on of Instrumental Variables Regression

Transcription

1 Philip and Sewall Wright: The Inven5on of Instrumental Variables Regression Philip Wright Sewall Wright

2 Bachelor degree from 1884 MA in economics from Harvard 1887 Professor Lombard College Instructor at Harvard under Professor W. Taussig US Tariff Commission Ins5tute of Economics Philip Wright

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4 Sewall Wright ( ) Famous Gene5cist Dept. of Zoology at the University of Chicago (1925 to 1955) Undergrad: Lombard College ScD Harvard, Biology, 1915 Philip Wright s oldest son Sewall Wright Pictured 1928

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6 The Wright Family: Apprx 1910

7 Inven5ng IV Regression Big break through: Instrumental variables can be used to es5mate the coefficient on an endogenous variable. Appendix B of 1928 book, The Tariff on Animal and Vegetable Oils, by Philip Wright, US Tariff Commission

8 Who authored Appendix B?

9 From Stock and Trebbi (2003) stylometric analysis, we know Philip wrote the actual text for appendix B.

10 Even if Philip wrote appendix B, who was responsible for the main ideas?

11 Case for Philip He authored Appendix B and he was deeply invested in the ques5on as it was vital to his work at the 5me. He also had a deep understanding of the iden5fica5on problem.

12 Case for Sewall all, Sewall was the sta5s5cal mastermind he had published Correla5on and Causa5on in 1921 he also published a 1925 paper on corn and hog cycles. In this paper the variables are all exogenous and not simultaneous. Sewall had said that he did not know how to manage endogenous variables and simultaneous equa5ons.

13 Who Invented IV Regression? The lefers that Philip and Sewall exchanged from late 1925 to 1926 shows the development of ideas. Who invented IV Regression?

14 Collabora5ve.

15 Diagrams using factors Below are Phillip s Jan 26, 1926 rendi5on of diagrams Sewall introduced to him on Dec.28, 1925

16 Basics of Path Analysis Path Analysis X=aA+U σ x =1, σ A =1 ; a=r XA In Modern Nota5on X a A β = a σ A /σ X β= (Σax)/ (Σa 2 Σx 2 ) * (Σa 2 /Σx 2 ) β= Σax/Σx 2

17 Applying Path Analysis to Philip s work: Inven5ng the Method of Addi5onal Factors From Correla5on and Causa5on : a diagram when variables are not independent

18 The link between 1921 and 1926 But, Sewall never solved this equa5on instead he simplified it It was simply an example of what could exists in a system of correla5ons. Sewall finally solves the diagram to the le@ because Philip prompt the ques5on

19 Deriva5on of the IV regressor with Path Analysis By defini5on of elas5city e=(o/p)*(σ O /σ p )= (r AO1 /r AP1 )*(σ O /σ p ) To get O/P, apply path coefficients Thus e=(r AO1 /r AP1 )*(σ O /σ p )

20 Philip s Response I expect I am stupid but I don t seem to be able to pick up a new branch of mathema?cs or quickly, as I could once. Feb. 13, 1926: Philip to Sewall

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22 Philip s Deriva5on I have worked out for your math of es?ma?ng supply and demand curves without reference to the theory of path coefficients.

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24 I discovered it by a singularly round about process.

25 Introducing Error I should suppose with a finite number of observa?ons [ΣAS] would seldom be precisely 0. If an expression could be developed showing the value of the most probable devia?on from 0 if this product it would be of the nature of a probable error. March 6, 1926: Philip to Sewall e= (ΣAO probable error)/(σap)

26 Tes5ng his method March 4: a simula5on for known elas5ci5es to test his formula basically a one draw Monte Carlo Simula5on. March 15: Es5mate elas5city of demand for spring wheat Finds elas5city of demand of 0.88 Uses building permits as the instrument Concludes this a result obviously absurd

27 Philip s Data 22 observa5ons: years 1903 to 1924 Real Price, Wheat Output (millions of bushels) Variables: Acreage, yield per acre, rainfall (inches), ra5o of harvest of flaxseed to spring wheat, building permits Uses devia5ons of data from straight line trends.

28 Philip s Test Output_Dev= 0.72 price_dev (0.96) Instrument: building permits First stage F sta5s5c: 1.31 A weak instrument by modern standards

29 In the case of any specific commodity is it possible to find factors which have such dis?nct caused rela?ons with output or demand condi?ons? Such factors, I fear, especially in the case of demand condi?ons, are not easy to find. Philip: March 15, 1926

30 Using one of Philip s different variables Output_Dev= 0.48 price_dev (0.74) Instrument: rainfall First stage F sta5s5c: Not a weak instrument by modern standards

31 Addi5onal Diagrams

32 2SLS Ideological groundwork for 2SLS Second Stage of 2SLS First Stage of 2SLS

33 Summary: Philip and Sewall s Contribu5on Introduced the idea of addi5onal factors 2 separate deriva5ons that lead to the IV es5mator Ideological framework for 2SLS A first draw Monte Carlo simula5on Empirical Applica5ons Further discussion of weak variables

34 What Next?

35 What next? When I was in Cambridge, I spoke to Dr. Taussig about my study of supply and demand curves and he suggested that I prepare an ar?cle for the Quarterly. I hope I can handle it so as to do jus?ce to your analysis I think it will prove the most valuable part of the ar?cle. Philip to Sewall, February 9, 1926

36 Philip s submission for the Aug edi5on was rejected. Taussig was the editor at the 5me.

37 Conclusions Philip used the IV es5mator in his work for his 1928 book and included the findings on IV regression in Appendix B. He included both Sewall s and his own deriva5ons. They never solved a mul5ple factor of variables diagram to get the 2SLS equa5on, though the ideological framework was present and understood in the 1926 correspondence.

38 Philip to Sewall: March 15, 1926 With all your anxie?es and problems connected with your new posi?on I am afraid I have been asking too much.

39 My only excuse is that it is a mathema?cal problem which interests me very much and which I have thought you also might find not without interest.

40 I hope all this work you have put into it is not going to prove obsolete. I hope we shall be able to see some results in prac?cal applica?on.