1932

Abstract

The constant-elasticity-of-substitution (CES) aggregator and its demand system are ubiquitous in business cycles theory, macroeconomic growth and development, international trade and other general equilibrium fields; this is because the CES aggregator has many knife-edge properties that help to keep the analysis tractable in the presence of many goods and factors. However, this also makes it hard to tell which properties of CES are responsible for certain results. Furthermore, it is necessary to relax some of those properties for certain applications. In this article, I review several classes of non-CES aggregators, each of which removes some properties of CES and keeps the rest to introduce some flexibility while retaining the tractability of CES as much as possible. These classes are named after the properties of CES they keep. I explain how these classes are related to each other and discuss their relative strengths and weaknesses to indicate which classes are suited for which applications.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-economics-082322-013910
2023-09-13
2024-05-07
Loading full text...

Full text loading...

/deliver/fulltext/economics/15/1/annurev-economics-082322-013910.html?itemId=/content/journals/10.1146/annurev-economics-082322-013910&mimeType=html&fmt=ahah

Literature Cited

  1. Antonelli GB. 1971 (1886). Sulla teoria matematica della economia politica [On the mathematical theory of political economy]. Preferences, Utility, and Demand: A Minnesota Symposium JS Chipman pp. 333–46 New York: Harcourt Brace Jovanovich
    [Google Scholar]
  2. Arkolakis K, Costinot A, Rodriguez-Clare A. 2012. New trade models, same old gains?. Am. Econ. Rev. 102:194–130
    [Google Scholar]
  3. Arrow KJ, Chenery HB, Minhas BS, Solow RM. 1961. Capital-labor substitution and economic efficiency. Rev. Econ. Stat. 43:3225–50
    [Google Scholar]
  4. Auer R, Burstein A, Lein S, Vogel J. 2022. Unequal expenditure switching: evidence from Switzerland NBER Work. Pap. 29757
  5. Auerbach AJ. 1985. The theory of excess burden and optimal taxation. Handbook of Public Economics Vol. 1, ed. AJ Auerbach, M Feldstein 61–127. Amsterdam: North-Holland
    [Google Scholar]
  6. Banks J, Blundell R, Lewbel A. 1997. Quadratic Engel curves and consumer demand. Rev. Econ. Stat. 79:4527–39
    [Google Scholar]
  7. Baqaee DR, Burstein A. 2022. Welfare and output with income effects and taste shocks Work. Pap. Univ. Calif. Los Angeles:
  8. Berlingieri G, Boeri F, Lashkari D, Vogel J 2022. Capital-skill complementarity in firms and in the aggregate economy. Unpublished manuscript, Univ. Calif., Los Angeles
    [Google Scholar]
  9. Berndt ER, Christensen LR. 1973. The internal structure of functional relationships: separability, substitution, and aggregation. Rev. Econ. Stud. 40:3403–10
    [Google Scholar]
  10. Blackorby C, Russell RR. 1981. The Morishima elasticity of substitution: symmetry, constancy, separability, and its relationship to the Hicks and Allen elasticities. Rev. Econ. Stud. 48:1147–58
    [Google Scholar]
  11. Blackorby C, Russell RR. 1989. Will the real elasticity of substitution please stand up? (A comparison of the Allen/Uzawa and Morishima elasticities). Am. Econ. Rev. 79:4882–88
    [Google Scholar]
  12. Bohr C, Mestieri M, Yavuz EE. 2021. Engel's treadmill: the perpetual pursuit of cornucopia Work. Pap. Northwest. Univ. Evanston, IL:
  13. Boppart T. 2014. Structural change and the Kaldor facts in a growth model with relative price effects and non-Gorman preferences. Econometrica 82:62167–96
    [Google Scholar]
  14. Buera FJ, Kaboski J. 2009. Can traditional theories of structural change fit the data?. J. Eur. Econ. Assoc. 7:2–3469–77
    [Google Scholar]
  15. Buera FJ, Kaboski J. 2012a. The rise of the service economy. Am. Econ. Rev. 102:62540–69
    [Google Scholar]
  16. Buera FJ, Kaboski J. 2012b. Scale and the origins of structural change. J. Econ. Theory 147:684–712
    [Google Scholar]
  17. Caliendo L, Parro F. 2015. Estimates of the trade and welfare effects of NAFTA. Rev. Econ. Stud. 82:1–44
    [Google Scholar]
  18. Caron J, Fally T, Markusen JR. 2014. International trade puzzles: a solution linking production and preferences. Q. J. Econ. 129:31501–52
    [Google Scholar]
  19. Caron J, Fally T, Markusen JR. 2020. Per capita income and the demand for skills. J. Int. Econ. 123:103306
    [Google Scholar]
  20. Caselli F. 2016. Technology Differences over Space and Time Princeton, NJ: Princeton Univ. Press
  21. Caselli F, Ventura J. 2000. A representative consumer theory of distribution. Am. Econ. Rev. 90:4909–26
    [Google Scholar]
  22. Chari VV, Kehoe PJ 1999. Optimal fiscal and monetary policy. Handbook of Macroeconomics, Vol. 1 JB Taylor, M Woodford 1671–745. Amsterdam: Elsevier
    [Google Scholar]
  23. Christensen LR, Jorgenson DW, Lau LJ. 1973. Transcendental logarithmic production frontiers. Rev. Econ. Stat. 55:128–45
    [Google Scholar]
  24. Christensen LR, Jorgenson DW, Lau LJ. 1975. Transcendental logarithmic utility functions. Am. Econ. Rev. 65:3367–83
    [Google Scholar]
  25. Comin D, Lashkari D, Mestieri M. 2021. Structural transformation with long-run income and price effects. Econometrica 89:1311–74
    [Google Scholar]
  26. Costinot A, Donaldson D, Komunjer I. 2012. What goods do countries trade? A quantitative exploration of Ricardo's ideas. Rev. Econ. Stud. 79:581–608
    [Google Scholar]
  27. Cravino J, Sotelo S. 2019. Trade-induced structural change and the skill premium. Am. Econ. J. Macroecon. 11:3289–326
    [Google Scholar]
  28. Deaton A. 1974. A reconsideration of the empirical implications of additive preferences. Econ. J. 84:338–48
    [Google Scholar]
  29. Deaton A, Muellbauer J. 1980a. An almost ideal demand system. Am. Econ. Rev. 70:3312–26
    [Google Scholar]
  30. Deaton A, Muellbauer J. 1980b. Economics and Consumer Behavior Cambridge, UK: Cambridge Univ. Press
  31. Dixit AK, Stiglitz JE. 1977. Monopolistic competition and optimum product diversity. Am. Econ. Rev. 67:3297–308
    [Google Scholar]
  32. Eaton J, Kortum S. 2002. Technology, geography, and trade. Econometrica 70:51741–79
    [Google Scholar]
  33. Fajgelbaum PD, Grossman GM, Helpman E. 2011. Income distribution, product quality, and international trade. J. Political Econ. 119:4721–65
    [Google Scholar]
  34. Fajgelbaum PD, Khandelwal AK. 2016. Measuring the unequal gains from trade. Q. J. Econ. 131:31113–80
    [Google Scholar]
  35. Fally T. 2022. Generalized separability and integrability: consumer demand with a price aggregator. J. Econ. Theory 203:105471
    [Google Scholar]
  36. Fieler AC. 2011. Nonhomotheticity and bilateral trade: evidence and a quantitative explanation. Econometrica 74:41069–101
    [Google Scholar]
  37. Flam H, Helpman E. 1987. Vertical product differentiation and North-South trade. Am. Econ. Rev. 77:5810–22
    [Google Scholar]
  38. Foellmi R, Zweimueller J. 2006. Income distribution and demand-induced innovations. Rev. Econ. Stud. 73:941–60
    [Google Scholar]
  39. Fujiwara I, Matsuyama K. 2022. A technology-gap model of premature deindustrialization CEPR Discuss. Pap. 15530 Cent. Econ. Policy Res. London:
  40. Goldman SM, Uzawa H. 1964. A note on separability in demand analysis. Econometrica 32:3387–98
    [Google Scholar]
  41. Hanoch G. 1971. CRESH production functions. Econometrica 39:5695–712
    [Google Scholar]
  42. Hanoch G. 1975. Production or demand models with direct or indirect implicit additivity. Econometrica 43:3395–419
    [Google Scholar]
  43. Houthakker HS. 1960. Additive preferences. Econometrica 28:2244–57
    [Google Scholar]
  44. Hurwicz L., Uzawa H. 1971. On the integrability of demand functions. Preferences, Utility, and Demand: A Minnesota Symposium JS Chipman 114–48. New York: Harcourt Brace Jovanovich
    [Google Scholar]
  45. Jehle GA, Reny P. 2010. Advanced Microeconomic Theory Chennai, India: Pearson. , 3rd ed..
  46. Jensen BS, de Boer P, van Daal J, Jensen PS. 2011. Global restrictions on the parameters of the CDES indirect utility function. J. Econ. 102:217–35
    [Google Scholar]
  47. Kongsamut P, Rebelo R, Xie D. 2001. Beyond balanced growth. Rev. Econ. Stud. 68:4869–82
    [Google Scholar]
  48. Krusell P, Ohanian LE, Rios-Rull JV, Violante GL. 2000. Capital-skill complementarity and inequality: a macroeconomic analysis. Econometrica 68:51029–53
    [Google Scholar]
  49. Lewis L, Monarch R, Sposi M, Zhang J. 2022. Structural change and global trade. J. Eur. Econ. Assoc. 20:1476–512
    [Google Scholar]
  50. Luttmer EGJ. 2017. Non-homothetic preferences: comments on some recent papers Work. Pap. Univ. Minn. Minneapolis:
  51. Markusen JR. 1986. Explaining the volume of trade: an eclectic approach. Am. Econ. Rev. 76:51002–11
    [Google Scholar]
  52. Markusen JR. 2013. Putting per-capita income back into trade theory. J. Int. Econ. 90:255–65
    [Google Scholar]
  53. Mas-Colell A, Whinston MD, Green JR. 1995. Microeconomic Theory New York: Oxford Univ. Press
  54. Matsuyama K. 1992. Agricultural productivity, comparative advantage, and economic growth. J. Econ. Theory. 58:317–34
    [Google Scholar]
  55. Matsuyama K. 2000. A Ricardian model with a continuum of goods under nonhomothetic preferences: demand complementarities, income distribution and North-South trade. J. Political Econ. 108:61093–120
    [Google Scholar]
  56. Matsuyama K. 2002. The rise of mass consumption societies. J. Political Econ. 110:51035–70
    [Google Scholar]
  57. Matsuyama K. 2009. Structural change in an interdependent world: a global view of manufacturing decline. J. Eur. Econ. Assoc. 7:2–3478–86
    [Google Scholar]
  58. Matsuyama K. 2019. Engel's law in the global economy: demand-induced patterns of structural change, innovation, and trade. Econometrica 87:2497–528
    [Google Scholar]
  59. Matsuyama K, Ushchev P. 2017. Beyond CES: three alternative classes of flexible homothetic demand systems CEPR Discuss. Pap. 12210 Cent. Econ. Policy Res. London:
  60. McFadden D. 1963. Constant elasticity of substitution production functions. Rev. Econ. Stud. 30:273–83
    [Google Scholar]
  61. Melitz MJ. 2003. The impact of trade on intra-industry reallocations, and aggregate industry productivity. Econometrica 71:61695–725
    [Google Scholar]
  62. Morishima M 1967. Danryokusei riron ni kansuru nisan no teian [A few suggestions on the theory of elasticity]. Keizai Hyoron 16:144–50
    [Google Scholar]
  63. Muellbauer J. 1975. Aggregation, income distribution, and consumer demand. Rev. Econ. Stud. 42:4524–43
    [Google Scholar]
  64. Muellbauer J. 1976. Community preferences and the representative consumer. Econometrica 44:5979–99
    [Google Scholar]
  65. Mukerji V. 1963. A generalized S.M.A.C. function with constant ratios of elasticity of substitution. Rev. Econ. Stud. 30:3233–36
    [Google Scholar]
  66. Ossa R. 2015. Why trade matters after all. J. Int. Econ. 97:266–77
    [Google Scholar]
  67. Pollak RA. 1971. Additive utility functions and linear Engel curves. Rev. Econ. Stud. 38:4401–14
    [Google Scholar]
  68. Pollak RA. 1972. Generalized separability. Econometrica 40:3431–53
    [Google Scholar]
  69. Redding SJ, Weinstein DE. 2020. Measuring aggregate price indices with taste shocks: theory and evidence for CES preferences. Q. J. Econ. 135:1503–60
    [Google Scholar]
  70. Samuelson PA. 1965. Using full duality to show that simultaneously additive direct and indirect utilities implies unitary price elasticity of demand. Econometrica 33:4781–96
    [Google Scholar]
  71. Sato R. 1967. A two-level constant-elasticity-of-substitution production function. Rev. Econ. Stud. 34:2201–18
    [Google Scholar]
  72. Sato R. 1975. The most general class of CES functions. Econometrica 43:5–6999–1003
    [Google Scholar]
  73. Sato R. 1977. Homothetic and non-homothetic CES production functions. Am. Econ. Rev. 67:4559–69
    [Google Scholar]
  74. Sposi M, Yi KM, Zhang J. 2021. Deindustrialization and industry polarization NBER Work. Pap. 29483
  75. Święcki T. 2017. Determinants of structural change. Rev. Econ. Dyn. 24:95–131
    [Google Scholar]
  76. Uzawa H. 1962. Production functions with constant elasticities of substitution. Rev. Econ. Stud. 29:4291–99
    [Google Scholar]
/content/journals/10.1146/annurev-economics-082322-013910
Loading
/content/journals/10.1146/annurev-economics-082322-013910
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error