Abstract
Although Terence Gorman was the greatest Irish economist of the twentieth century, he was totally unknown to the general public. He was the purest of pure theorists, whose life was devoted to scholarship and teaching, and whose work of forbidding technical difficulty was incomprehensible to most of his contemporaries. Yet, paradoxically, he was always concerned with applied issues, and the tools and theorems he developed, notably those dealing with aggregation, separability, duality and hedonic models, have had a lasting influence on empirical work.
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Notes
- 1.
Gorman always spoke fondly of the then Whately Professor in Trinity, George Duncan. In a late paper on the Le Chatelier Principle, which appeared in a Festschrift for Ivor Pearce, Gorman wrote: ‘I would like to praise George Duncan…who introduced me to economics as an engine of thought, and who, in particular, taught me to expect the result that I will attempt to prove, and that in one of the first lectures of the first term of my first year in Trinity College Dublin’. Gorman continued, with his characteristic bluntness, that Duncan was ‘a man in many ways like Ivor [Pearce] who might have become just as distinguished had he known more mathematics. He could not make head nor tail of the accelerator: but taught us about what have come to be known as Arrow-Debreu goods in one of his first lectures’ (Gorman 1984: 1 and 16).
- 2.
- 3.
Blackorby et al. (1978) appear to have been the first to refer to it as such.
- 4.
See Neary (1997) for further discussion and references.
- 5.
- 6.
More precisely, the condition is that the utility function must be expressible in one of the following three forms, where f is homogeneous of degree one:
-
(1)
u = F (v1, v2) (the case where there are only two classes)
-
(2)
u = F [v1, f (v2, …, vn)] (all but one class can be grouped into a homogeneous function)
-
(3)
u = F [v1 + … + vd + f (vd+1, …, vn)] (classes 1 to d and a homogeneous function grou** the remaining classes all enter additively).
-
(1)
- 7.
The weights are usually interpreted as subjective probabilities, an interpretation which Gorman found unhelpful: ‘Frequently they seem to me to obscure, rather than enlighten’ (Gorman 1982: 215).
- 8.
We often make the further simplification fst(yst) = δsrtyst, where δ is a probability and r a discount factor, but Gorman does not force such an interpretation.
- 9.
That is, considers only its own consumption; this is what gives separability or independence in the additional dimension.
- 10.
The theorem states that if two separable sets overlap in their membership, then their intersection and differences are also separable. In the social welfare case, the overlap** arises because the separable (self-regarding) individuals are all involved in states of the world to which Samuelson’s weak independence axiom applies; in the intertemporal choice case the separability is induced by the partial myopia mentioned below.
- 11.
He was of course fully aware of the continuing controversy over the weak independence axiom for choice under uncertainty and the fact that it has been rejected by many empirical experiments.
- 12.
Determined by the tangent of the consumer’s indifference curve with the convex hull of the affordable combinations of the two characteristics.
- 13.
- 14.
It has also been applied in a great variety of other fields, notably through the later work of Lancaster (1966).
- 15.
Muellbauer (1974) independently rederived Barten’s results using the dual approach.
- 16.
Articles denoted with an asterisk are included in Blackorby and Shorrocks (1995).
- 17.
As explained in the text, much of Gorman’s work was never published, although many previously unpublished papers were collected in Blackorby and Shorrocks (1995). This brief selection includes only those papers which he included in his curriculum vitae of 1985 or which are discussed in the text.
References
Main Works by W.M. Gorman
Collected Works
Blackorby, C. and A.F. Shorrocks (eds) (1995). Separability and Aggregation: Collected Works of W.M.Gorman. Volume 1. Oxford: Clarendon Press.
Other
Boyle, J.R., W.M. Gorman, and S.E. Pudney (1977). ‘The Demand for Related Goods: A Progress Report’. Chapter 2c in M.D. Intriligator (ed.) Frontiers of Quantitative Economics. Volume IIIA. Amsterdam: North–Holland: 87–101. Invited paper at the Third World Congress of the Econometric Society.
*Gorman, W.M. (1953). ‘Community Preference Fields’. Econometrica, 21(1): 63–80.
Gorman, W.M. (1955). ‘The Intransitivity of Certain Criteria Used in Welfare Economics’. Oxford Economic Papers, New Series, 7(1): 23–35.
Gorman, W.M. (1957). ‘Convex Indifference Curves and Diminishing Marginal Utility’. Journal of Political Economy, 65(1): 40–50.
Gorman, W.M. (1957). ‘How Surprising is a Chain of Coincidences?’. Metroeconomica, 9(2): 112–115.
Gorman, W.M. (1957). ‘A Note on “A Revised Theory of Expectations”’. Economic Journal, 67(267): 549–551.
Gorman, W.M. (1957). ‘Some Comments on Professor Hicks’ Revision of Demand Theory’. Metroeconomica, 9(3): 167–180.
Gorman, W.M. (1958). ‘Tariffs, Retaliation, and the Elasticity of Demand for Imports’. Review of Economic Studies, 25(3): 133–162. Reprinted as Chapter 12 in M.J. Farrell (ed.) (1973) Readings in Welfare Economics. London: Macmillan: 167–196.
*Gorman, W.M. (1959a). ‘Separable Utility and Aggregation’. Econometrica, 27(3): 469–481. Reprinted as Chapter 16 in K.J. Arrow (ed.) (1971) Selected Readings in Economic Theory from Econometrica. Cambridge, MA: MIT Press: 326–338.
Gorman, W.M. (1959). ‘The Effect of Tariffs on the Level and Terms of Trade’. Journal of Political Economy, 67(3): 246–265.
Gorman, W.M. (1959). ‘Are Social Indifference Curves Convex?’. Quarterly Journal of Economics, 73(3): 485–496.
Gorman, W.M. (1960). ‘Tariffs and Trade in a Two-Good World’. International Economic Review, 1(3): 223–229.
*Gorman, W.M. (1961). ‘On a Class of Preference Fields’. Metroeconomica, 13(2): 53–56.
Gorman, W.M. (1961). ‘Elasticity of Demand for Imports with Close, but Imperfect Substitutes’. International Economic Review, 2(3): 371–376.
Gorman, W.M. (1963). ‘Additive Logarithmic Preferences, A Further Note’. Review of Economic Studies, 30(1): 56–62.
*Gorman, W.M. (1964). ‘More Scope for Qualitative Economics’. Review of Economic Studies, 31(1): 65–68.
Gorman, W.M. (1965a). ‘Production Functions in Which the Elasticities of Substitution Stand in Fixed Proportions to Each Other’. Review of Economic Studies, 32(3): 217–224.
Gorman, W.M. (1965). ‘Professor Friedman’s Consumption Function and the Theory of Choice’. Econometrica, 32(1/2): 189–197.
Gorman, W.M. (1967). ‘Tastes, Habits and Choices’. International Economic Review, 8(2): 218–222.
*Gorman, W.M. (1968a). ‘Measuring the Quantities of Fixed Factors’. Chapter 5 in J.N. Wolfe (ed.) Value, Capital and Growth: Papers in Honour of Sir John Hicks. Edinburgh: Edinburgh University Press: 141–172.
*Gorman, W.M. (1968b). ‘The Structure of Utility Functions’. Review of Economic Studies, 35(4): 367–390.
*Gorman, W.M. (1968). ‘Conditions for Additive Separability’. Econometrica, 36(3/4): 605–609.
Gorman, W.M. (1971). ‘Preference, Revealed Preference, and Indifference’. Chapter 5 in J.S. Chipman, L. Hurwicz, M.K. Richter and H.F. Sonnenschein (eds) Preferences, Utility and Demand: A Minnesota Symposium. New York: Harcourt Brace Jovanovich: 81–113.
Gorman, W.M. (1976). ‘Tricks with Utility Functions’. Chapter 11 in M.J. Artis and A.R. Nobay (eds) Essays in Economic Analysis. Cambridge: Cambridge University Press: 211–243. Invited address to the 1975 Association of University Teachers in Economics Conference.
Gorman, W.M. (1980). ‘A Possible Procedure for Analysing Quality Differentials in the Egg Market’. Review of Economic Studies, 47(5): 843–856. First circulated as Journal Paper No. 2319, Iowa Agricultural Experiment Station, November 1956.
*Gorman, W.M. (1981). ‘Some Engel Curves’. Chapter 1 in A. Deaton (ed.) Essays on the Theory and Measurement of Demand in Honour of Sir Richard Stone. Cambridge: Cambridge University Press: 7–30.
Gorman, W.M. (1984). ‘Le Chatelier and General Equilibrium’. Chapter 1 in A. Ingham and A. Ulph (eds) Demand, Equilibrium and Trade: Essays in Honour of Ivor F. Pearce. London: Macmillan: 1–18.
*Gorman, W.M. (1986). ‘Assembling Efficient Organizations?’. Chapter 8 in W.P. Heller, R.M. Starr and D.A. Starrett (eds) Uncertainty, Information and Communication: Essays in Honor of Kenneth J. Arrow. Volume III. Cambridge: Cambridge University Press: 213–228.
*Gorman, W.M. (1987). ‘Separability’. In J. Eatwell, M. Milgate and P. Newman (eds) The New Palgrave: A Dictionary of Economics. Volume 4. London: Macmillan: 305–311.
*Gorman, W.M. (1990). ‘More Measures for Fixed Factors’. In G.D. Myles (ed.) Measurement and Modelling in Economics. Amsterdam: North–Holland: 381–409.
Gorman, W.M. and G.D. Myles (1987). ‘Characteristics’. In J. Eatwell, M. Milgate and P. Newman (eds) The New Palgrave: A Dictionary of Economics. Volume 1. London: Macmillan: 403–406.
Unpublished Works
Gorman, W.M. (1959c). ‘The Demand for Fish: An Application of Factor Analysis’. Paper read to the Amsterdam meeting of the Econometric Society; Discussion Paper A.6, Faculty of Commerce and Social Science, Birmingham University, September.
Gorman, W.M. (1960b). ‘A Note on Hotelling’s Method of Extracting the Latent Roots and Vectors of a Matrix’. Discussion Paper A.12, Faculty of Commerce and Social Science, Birmingham University, September.
*Gorman, W.M. (1965). ‘Consumer Budgets and Price Indices’. Unpublished typescript.
*Gorman, W.M. (1970a). ‘Conditions for Generalised Additive Separability’. Discussion Paper No. 9, Department of Economics, London School of Economics, September.
*Gorman, W.M. (1970). ‘Quasi Separable Preferences, Costs and Technologies’. Paper read at Harvard University, November.
Gorman, W.M. (1972). ‘Sketch for the Demand for Related Goods’. Presidential Address to the Econometric Society.
*Gorman, W.M. (1982). ‘Facing an Uncertain Future’. Technical Report No. 359, Institute for Mathematical Studies in the Social Sciences, Stanford University, January.
Gorman, W.M. (1986a). ‘Unpublished Notes for a Seminar at University College Dublin’. 12 March.
Other Works Referred To
Antonelli, G.B. (1886). Sulla Teoria Matematica dell’Economia Politica. Pisa: Tipografia del Folchetto. English translation, ‘On the Mathematical Theory of Political Economy’, Chapter 16 in J.S. Chipman, L. Hurwicz, M.K. Richter and H.F. Sonnenschein (eds) (1971) Preferences, Utility and Demand: A Minnesota Symposium. New York: Harcourt Brace Jovanovich: 333–360.
Barten, A.P. (1964). ‘Family Composition, Prices and Expenditure Patterns’. In P.E. Hart, G. Mills and J.K. Whitaker (eds) Econometric Analysis for National Economic Planning. London: Butterworth: 277–292.
Black, F. and M. Scholes (1972). ‘The Valuation of Option Contracts and a Test of Market Efficiency’. Journal of Finance, Papers and Proceedings, 27(2): 399–417.
Blackorby, C., R. Boyce and R.R. Russell (1978). ‘Estimation of Demand Systems Generated by the Gorman Polar Form: A Generalization of the S-Branch Utility Tree’. Econometrica, 46(2): 345–363.
Blaug, M. (1986). Who’s Who in Economics: A Biographical Dictionary of Major Economists 1799–1986. Second edition. Sussex: Wheatsheaf Books.
Campbell, J.Y., A.W. Lo and A.C. Mackinlay (1997). The Econometrics of Financial Markets. Princeton, NJ: Princeton University Press.
Deaton, A.S. and J. Muellbauer (1980). ‘An Almost Ideal Demand System’. American Economic Review, 70(3): 312–326.
Debreu, G. (1951). ‘The Coefficient of Resource Allocation’. Econometrica, 19(3): 273–292.
Griliches, Z. (1961). ‘Hedonic Price Indexes for Automobiles: An Econometric Analysis of Quality Change’. In The Price Statistics of the Federal Government. Report No. 3, General Series, No. 73. New York: National Bureau of Economic Research: 173–196.
Honohan, P. and J.P. Neary (2003). ‘W.M. Gorman (1923–2003)’. The Economic and Social Review, 34(2): 195–209.
Lancaster, K.J. (1966). ‘A New Approach to Consumer Theory’. Journal of Political Economy, 74(2): 132–157.
Malmquist, S. (1953). ‘Index Numbers and Indifference Surfaces’. Trabajos de Estadistica, 4(2): 209–242.
Markowitz, H. (1959). Portfolio Selection: Efficient Diversification of Investments. New York: John Wiley.
Merton, R.C. (1973). ‘Theory of Rational Option Pricing’. Bell Journal of Economics and Management Science, 4(1): 141–183.
Muellbauer, J. (1974). ‘Household Composition, Engel Curves and Welfare Comparisons Between Households: A Duality Approach’. European Economic Review, 5(2): 103–122.
Muellbauer, J. (1975). ‘Aggregation, Income Distribution and Consumer Demand’. Review of Economic Studies, 42(4): 525–543.
Nataf, A. (1953). ‘Sur des Questions d’Agrégation en Économétrie’. Publications de l’Institut de Statistique de l’Université de Paris, 2, Fasc., 4: 5–61.
Neary, J.P. (1997). ‘R.C. Geary’s Contributions to Economic Theory’. Chapter 3 in D. Conniffe (ed.) Roy Geary, 1896–1983: Irish Statistician. Dublin: Oak Tree Press and The Economic and Social Research Institute: 93–118.
Strotz, R.H. (1957). ‘The Empirical Implications of a Utility Tree’. Econometrica, 25(2): 269–280.
Waugh, F.W. (1928). ‘Quality Factors Influencing Vegetable Prices’. Journal of Farm Economics, 10(2): 185–196.
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Honohan, P., Neary, P. (2021). W.M. Gorman (1923–2003). In: Cord, R.A. (eds) The Palgrave Companion to Oxford Economics. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-58471-9_21
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