A. D. Roy

Andrew Donald Roy was born 28 June 1920. His father, Donald Whatley Roy, was a physician. A. D. Roy began studies in mathematics at Sidney Sussex College, Cambridge, in 1938. He won the distinguished Tripos award in 1939 in mathematics. His studies were interrupted by the outbreak of World War II, and he eventually served in the Fourteenth Army in India. He fought in the Battle of Imphal which stemmed the Japanese invasion of India in 1944. During his service, Roy contracted jaundice and suffered a nervous collapse, which lingered in the form of depression. After the war, he returned to Cambridge to study economics and history and was awarded a second Tripos award in economics in 1948. He later married Katherine Juliet Grove-White, and the pair had a son, Donald James Roy, and two daughters. He completed his Master of Arts in Economics at Cambridge in 1950, reading under Professor Edward Austin Gossage Robinson. Roy died on 12 March 2003 of heart disease. (See Sullivan, 2011{{cite book|first=Edward J. |last=Sullivan |year=2011 |url=https://books.google.com/books?id=uPRleZinTCoC&pg=PA73 |title=A.D. Roy: The Forgotten Father of Portfolio Theory Part 1|editor-first1= Jeff E. |editor-last=Biddle |editor-first2=Ross B. |editor-last2=Emmett |journal=Research in the History of Economic Thought and Methodology|volume=29 |publisher=Emerald Group Publishing Limited|pages=73–82|isbn=9781780520070 |doi=10.1108/S0743-4154(2011)000029A008 }} for a more complete biography and Heckman and Sattinger, 2015{{cite journal|last1=Heckman|first1=J. J.|last2=Sattinger|first2=M.|title=Introduction to 'The Distribution of Earnings and of Individual Output,' by A.D. Roy|journal=Economic Journal|date=2015|volume=125|issue=583|pages=378–402|doi=10.1111/ecoj.12226|pmid=25892742|pmc=4399962}} for an intellectual biography.)

Roy was appointed Faculty Assistant Lecturer in Statistics at Cambridge University in 1949. In 1950, Roy was appointed Director of Economic Studies at Cambridge and then University Lecturer in Economics and Politics at Sidney Sussex College in 1951. While at Cambridge, Roy wrote an influential paper on productivity and the shape of the distribution of earnings{{cite journal|last1=Roy|first1=A. D.|title=The Distribution of Earnings and of Individual Output|journal=Economic Journal|date=1950|volume=60|issue=239|pages=489–505|doi=10.2307/2226792|jstor=2226792}} which he substantially generalized in his seminal 1951 article on self-selection and income inequality (Roy, 1951).{{cite journal|last1=Roy|first1=A. D.|title=Some Thoughts on the Distribution of Earnings|journal=Oxford Economic Papers|date=1951|volume=3|issue=2|pages=135–146|doi=10.1093/oxfordjournals.oep.a041827}} In addition, Roy made a fundamental contribution to portfolio theory in his paper 'Safety First and the Holding of Assets' (1952).{{cite journal|last1=Roy|first1=A. D.|title=Safety First and the Holding of Assets|journal=Econometrica|date=1952|volume=20|issue=3|pages=431–449|doi=10.2307/1907413|jstor=1907413}}

Roy left Sidney Sussex in 1962 to serve as Economic Consultant and later Senior Economic Advisor to the Treasury. In 1964, Roy entered civil service, and worked for the Treasury, Department of Trade and Industry, Ministry of Defence, and Department of Health and Social Security. During this time, Roy addressed issues more closely related to macroeconomics such as labor productivity (Roy, 1982;{{cite journal|last1=Roy|first1=A. D.|title=Labour Productivity in 1980: An International Comparison|journal=National Institute Economic Review|date=1982|volume=101|issue=1|pages=26–37|doi=10.1177/002795018210100104|s2cid=154862307 }} Roy and Wenban-Smith, 1983{{cite book|last1=Roy|first1=A. D.|last2=Wenban-Smith|first2=G.|title=Trends in UK Productivity: A Production Function Approach|date=1983|publisher=National Institute of Economic and Social Research|location=London, UK}}).

Roy (1951) recognized that a major mechanism guiding assignment in the labor market is David Ricardo's principle of comparative advantage. A worker choosing an occupation will compare the income from one occupation with the income from another occupation. To use the example provided by Roy in his 1951 paper, a person who chose trout fishing would have a comparative advantage at that activity compared to a person who chose rabbit catching. A second consequence of the choice of occupations is that the distribution of earnings is built up from the distributions of earnings in individual occupations. The distribution of earnings within an occupation is affected by the selection of workers into that occupation, as determined by 'the association existing between any individual's performance in the two occupations' (Roy, 1951, p. 494). Roy considers both positive and negative correlation between performances. As a result of the selection, the aggregate distribution of earnings depends on the occupations available to workers and their performances in different occupations.

Selection among alternative occupations, as described by Roy, draws on notions of potential outcomes used in the literature on the design of experiments (Neyman, 1923;{{cite journal|last1=Neyman|first1=J.|title=On the Application of Probability Theory to Agricultural Experiments|journal=Roczniki Nauk Rolniczych|date=1923|volume=10|pages=1–51}} Cox, 1958{{cite book|last1=Cox|first1=D. R.|title=Planning of Experiments|date=1958|publisher=Wiley|location=New York}}). Like later work by Quandt (1972),{{cite journal|last1=Quandt|first1=R.|title=A New Approach to Estimating Switching Regressions|journal=Journal of the American Statistical Association|date=1972|volume=67|issue=338|pages=306–310|doi=10.2307/2284373|jstor=2284373}} Gronau (1974){{cite journal|last1=Gronau|first1=R.|title=Wage Comparisons–A Selectivity Bias|journal=Journal of Political Economy|date=1974|volume=82|issue=6|pages=1119–1143|doi=10.1086/260267|s2cid=153856057}} and Heckman (1974,{{cite journal|last1=Heckman|first1=J. J.|title=Shadow Prices, Market Wages, and Labor Supply|journal=Econometrica|date=1974|volume=42|issue=4|pages=679–694|doi=10.2307/1913937|jstor=1913937}} 1976{{cite journal|last1=Heckman|first1=J. J.|title=The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables|journal=Annals of Economic and Social Measurement|date=1976|volume=5|issue=4|pages=475–492}}), he added a choice mechanism to the model of potential outcomes in the statistical literature determining allocations of individuals across sectors associated with outcomes.Heckman, 2008 discusses the contribution of economists to the Neyman–Fisher–Rubin literature on potential outcomes.{{cite journal|last1=Heckman|first1=J. J.|title=Econometric Causality|journal=International Statistical Review|date=2008|volume=76|issue=1|pages=1–27|doi=10.1111/j.1751-5823.2007.00024.x|s2cid=14318481 }} Roy introduced economic decision-making into the determination of occupations and earnings and thereby anticipated procedures later used for the rigorous analysis of earnings data.

Roy's selection phenomenon has been applied and extended to a wide range of other contexts, including: choice of market versus non-market work and wage comparisons (Gronau, 1974; Heckman, 1974, 1976; Lewis, 1974{{cite journal|last1=Lewis|first1=H. G.|title=Comments on Selectivity Bias in Wage Comparisons|journal=Journal of Political Economy|date=1974|volume=82|issue=6|pages=1145–1155|doi=10.1086/260268|s2cid=154754879}}); and more general decision rules (see the survey in Heckman and Vytlacil, 2007a{{cite journal|last1=Heckman|first1=J. J.|last2=Vytlacil|first2=E.|title=Econometric Evaluation of Social Programs, Part I: Causal Models, Structural Models and Econometric Policy Evaluation|journal=Handbook of Econometrics|date=2007a|volume=6B|pages=4779–4874|publisher=Elsevier|location=Amsterdam|doi=10.1016/S1573-4412(07)06070-9}}). His work also affected analysis of choice in: union versus non-union sectors (Lee, 1978{{cite journal|last1=Lee|first1=L. F.|title=Unionism and Wage Rates: A Simultaneous Equation Model with Qualitative and Limited Dependent Variables|journal=International Economic Review|date=1978|volume=19|issue=2|pages=415–433|doi=10.2307/2526310|jstor=2526310}}); levels of education (Willis and Rosen, 1979{{cite journal|last1=Willis|first1=R.|last2=Rosen|first2=S.|title=Education and Self-Selection|journal=Journal of Political Economy|date=1979|volume=87|issue=5|pages=S7–S36|doi=10.1086/260821 |citeseerx=10.1.1.160.3842}}); geographical region (Robinson and Tomes, 1982{{cite journal|last1=Robinson|first1=C.|last2=Tomes|first2=N.|title=Self Selection and Interprovincial Migration in Canada|journal=Journal of Economics|date=1982|volume=15|issue=3|pages=474–502|doi=10.2307/134762|jstor=134762|url=https://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=1719&context=economicsresrpt}}); marital status (McElroy and Horney, 1981{{cite journal|last1=McElroy|first1=M.|last2=Horney|first2=M.|title=Nash Bargained Household Decisions: Toward a Generalization of the Theory of Demand|journal=International Economic Review|date=1981|volume=22|issue=2|pages=333–349|doi=10.2307/2526280|jstor=2526280}}); occupational choice (Miller, 1984{{cite journal|last1=Miller|first1=R.|title=Job Matching and Occupational Choice|journal=Journal of Political Economy|date=1984|volume=92|issue=6|pages=1086–1120|doi=10.1086/261276|citeseerx=10.1.1.560.905|s2cid=154097300}}); piece rate versus salary pay structures (Lazear, 1986{{cite journal|last1=Lazear|first1=E.|title=Salaries and Piece Rates|journal=Journal of Business|date=1986|volume=106|issue=1|pages=405–431|doi=10.1086/296345}}); industry changers (Solon, 1988;{{cite journal|last1=Solon|first1=G.|title=Self-Selection Bias in Longitudinal Estimation of Wage Gaps|journal=Economics Letters|date=1988|volume=28|issue=3|pages=285–290|doi=10.1016/0165-1765(88)90133-4|hdl=2027.42/27523|hdl-access=free}} Gibbons and Katz, 1992{{cite journal|last1=Gibbons|first1=R.|last2=Katz|first2=L.|title=Does Unmeasured Ability Explain Inter-Industry Wage Differentials?|journal=Review of Economic Studies|date=1992|volume=59|issue=3|pages=515–535|doi=10.2307/2297862|jstor=2297862|s2cid=55469856 |url=http://www.nber.org/papers/w3182.pdf}}); immigration (Borjas, 1990{{cite book|last1=Borjas|first1=G.|title=Friends or Strangers: The Impact of Immigrants on the US Economy|url=https://archive.org/details/friendsorstrange00borj|url-access=registration|date=1990|publisher=Basic Books|location=New York|isbn=9780465025671}}); and segmented labor markets (Magnac, 1991{{cite journal|last1=Magnac|first1=T.|title=Segmented or Competitive Labor Markets?|journal=Econometrica|date=1991|volume=59|issue=1|pages=165–187|doi=10.2307/2938245|jstor=2938245}}). Flinn and Heckman (1982){{cite journal|last1=Flinn|first1=C.|last2=Heckman|first2=J. J.|title=New Methods for Analyzing Structural Models of Labor Force Dynamics|journal=Journal of Econometrics|date=1982|volume=18|issue=1|pages=115–168|doi=10.1016/0304-4076(82)90097-5|s2cid=16100294|url=http://www.nber.org/papers/w0856.pdf}} extend Roy's selection model by incorporating choices based on search. See French and Taber (2011){{cite journal|last1=French|first1=E.|last2=Taber|first2=C.|editor1-last=Ashenfelter|editor1-first=O.|editor2-last=Card|editor2-first=D.|title=Identification of models of the labor market|journal=Handbook of Labour Econometrics|series=Handbook of Labor Economics|date=2011|volume=4A|pages=537–618|publisher=Elsevier|location=Amsterdam|doi=10.1016/S0169-7218(11)00412-6|isbn=9780444534507|citeseerx=10.1.1.725.5094}} for a comprehensive discussion of the use of the Roy model in labor economics.

Analysis of selection bias has led to substantial improvements in the evaluation of social programs (Heckman et al., 1996,{{cite journal|last1=Heckman|first1=J. J.|last2=Ichimura|first2=H.|last3=Smith|first3=J.|last4=Todd|first4=P.|title=Sources of selection bias in evaluating social programs: An interpretation of conventional measures and evidence on the effectiveness of matching as a program evaluation method|journal=Proceedings of the National Academy of Sciences|date=1996|volume=93|issue=23|pages=13416–13420|doi=10.1073/pnas.93.23.13416|pmid=8917606|pmc=24108|bibcode=1996PNAS...9313416H|doi-access=free}} 1997;{{cite journal|last1=Heckman|first1=J. J.|last2=Ichimura|first2=H.|last3=Todd|first3=P.|title=Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme|journal=Review of Economic Studies|date=1997|volume=64|issue=4|pages=605–654|doi=10.2307/2971733|jstor=2971733}} Abbring and Heckman, 2007;{{cite journal|last1=Aabring|first1=J.|last2=Heckman|first2=J. J.|title=Econometric Evaluation of Social Programs, Part III: Distributional Treatment Effects, Dynamic Treatment Effects, Dynamic Discrete Choice, and General Equilibrium Policy Evaluation|journal=Handbook of Econometrics|date=2007|volume=6B|pages=5145–5303|publisher=Elsevier|location=Amsterdam|doi=10.1016/S1573-4412(07)06072-2}} Heckman and Vytlacil, 2007a, b{{cite journal|last1=Heckman|first1=J. J.|last2=Vytlacil|first2=E.|title=Econometric Evaluation of Social Programs, Part II: Using the Marginal Treatment Effect to Organize Alternative Economic Estimators to Evaluate Social Programs and to Forecast Their Effects in New Environments|journal=Handbook of Econometrics|date=2007b|volume=6B|pages=4875–5143|publisher=Elsevier|location=Amsterdam|doi=10.1016/S1573-4412(07)06071-0}}). A further extension considers general equilibrium models of income distribution and treatment effects (Heckman et al., 1998;{{cite journal|last1=Heckman|first1=J. J.|last2=Lochner|first2=L.|last3=Taber|first3=C.|title=General-Equilibrium Treatment Effects: A Study of Tuition Policy|journal=American Economic Review|date=1998|volume=88|issue=2|pages=381–386}} Abbring and Heckman, 2007). The Roy (1951) model which analyzes potential outcomes using a choice mechanism improves on later, less clearly formulated work exposited in statistics under the rubric of the "Rubin model". See Heckman (2008) and Heckman and Sattinger (2015).

Roy also made a fundamental contribution to finance. His (1952) paper is widely regarded as a contribution to portfolio theory co-equal with that of the Nobel-Prize winning analysis of Harry Markowitz (1952).{{cite journal|last1=Markowitz|first1=H. M.|title=Portfolio Selection|journal=Journal of Finance|date=1952|volume=7|issue=1|pages=77–91|doi= 10.1111/j.1540-6261.1952.tb01525.x |s2cid=7492997 }} Both developed the mean-variance trade-off for a portfolio of correlated assets (Markowitz, 1991).{{cite journal|last1=Markowitz|first1=H. M.|title=Foundations of Portfolio Theory|journal=Journal of Finance|date=1991|volume=46|issue=2|pages=469–477|doi=10.1111/j.1540-6261.1991.tb02669.x}} Reflecting on his 1952 work and Roy's (1952) paper, Markowitz wrote: 'On the basis of Markowitz (1952), I am often called the father of modern portfolio theory (MPT), but Roy can claim an equal share of this honor'. (Markowitz, 1999, p. 6){{cite journal|last1=Markowitz|first1=H. M.|title=The Early History of Portfolio Theory|journal=Financial Analysts Journal|date=1999|volume=55|issue=4|pages=5–16|doi=10.2469/faj.v55.n4.2281}} For a more extensive discussion of Roy's contribution to portfolio theory, see Bernstein (1992){{cite book|last1=Bernstein|first1=P.|title=Capital Ideas|date=1992|publisher=John Wiley & Sons|location=Hoboken, NJ}} and Sullivan (2011).

• [https://www.jstor.org/stable/2226792? The distribution of earnings and of individual output] {{subscription required}} Economic Journal, vol. 60(239), pp. 489–505. (1950).
• [https://www.jstor.org/discover/10.2307/2662082? Some Thoughts on the Distribution of Earnings] {{subscription required}} Oxford Economic Papers, New Series, Vol. 3, No. 2 (1951).
• [https://www.jstor.org/discover/10.2307/1907413? Safety First and the Holding of Assets] {{subscription required}} Econometrica Vol. 20, No. 3 (1952).
• [https://www.jstor.org/stable/23875548? Labour productivity in 1980: an international comparison] {{subscription required}} National Institute Economic Review, vol. 101(1), pp. 26–37. (1982).
• [http://sabre.sussex.ac.uk/vufindsmu/Record/susx566783? Trends in UK Productivity: A Production Function Approach] Roy, A. D.; Wenban-Smith, G. London, UK: National Institute of Economic and Social Research. (1983).

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Category:1920 births

Category:2003 deaths

Category:Alumni of Sidney Sussex College, Cambridge

Category:20th-century British economists