A structure of the consumption function

Abstract

It is claimed in the structural realism in philosophy of science that scientists aim to preserve the true structure, represented by the equations in their models. We reinterpret structural realism as a doctrine involving representation. Proving the existence of a representation theorem secures the problem of lacking independent criteria for identification between structure and non‐structure. This paper argues that a similar realist view of structure can be found in the theory of consumption in which the Fisherian framework of intertemporal choices is regarded as the true structure of the consumption function. Unlike the passive strategy of inducing the structure contained in structural realism, economists define structure in terms of invariance under intervention. Such a definition serves as a crucial device to examine and develop models for the adequacy of representing the structure of the consumption functions.

JEL Classification: B22, B41, C50, E21

Keywords:

• consumption function
• Euler‐equation approach
• invariance
• representation
• structure
• structural realism

ACKNOWLEDGEMENTS

An early version of this paper was titled ‘A structural realist interpretation of the euler‐equation approach in macroeconomics’, published as a research memorandum of the Amsterdam Research Group in the History and Methodology of Economics, Faculty of Economics and Econometrics, University of Amsterdam (No. 01‐9). I thank Marcel Boumans and Mary Morgan for their advice and encouragement. I am also most grateful to Kevin Hoover and an anonymous referee for their constructive comments and suggestions.

Notes

1. Modigliani (1947, 1949) has shown a Keynesian consumption function, which consists of the ‘highest previous income peak’, that is similar to Duesenberry's relative income hypothesis.

2. See, inter alia, Psillos (1999, esp. Ch. 8), Votsis (2004), and papers that appear in the special issue of Synthese in 1999 on structural realist interpretations of quantum field theory.

3. Note that some philosophers of science, for example, French and Saatsi (2004), use the terms ‘structural realism’ and ‘realism about structure’ interchangeably.

4. See Grower (2000) and Votsis (2004) for the history of structural realism.

5. The contrast between Keynes's consumption function and Fisher's account can be seen as early as Holden (1938). Note that in the General Theory, before he proposes the formal definition of the fundamental psychological law, Keynes discusses the ‘objective factors’ that he thinks would affect the marginal propensity to consume. These objective factors include ‘changes in the rate of time‐discounting’ and ‘changes in expectations of the relation between the present and the future level of income’ (Keynes 1936: 93–6). But he goes on to state that ‘ [f]or whilst the other factors are capable of varying (and this must not be forgotten), the aggregate income measured in terms of the wage‐unit is, as a rule, the principal variable upon which the consumption‐constituent of the aggregate demand function will depend.’ (Keynes 1936: 96). I thank a referee for pointing out this to me. Also see Keynes' (1938) reply to Holden (1938).

6. See Deaton (2005).

7. See Sheffrin (1983: 105–6).

8. The term ‘solved‐out approach’ appears in Muellbauer (1994). In this way, the consumption function is solved, for example, by substituting the Euler equation (equation (1)) into the intertemporal budget constraint , where A_t is the asset in period t, c_t is the consumption in period t, E_t is the mathematical expectation conditional on all information available in period t; r is the constant real interest rate, and w_t is income in period t. .

9. Hall (1988) measures the elasticity of intertemporal substitution.

10. Discussions on the hypotheses of precautionary saving and liquidity constraints can be seen in Carroll (2001) and the references therein.

11. Laibson (1998) further shows that the standard exponential Euler equation is a special case of his hyperbolic Euler equation.

12. One major difference between invariance under intervention and invariance under transformation is that the former account explicitly addresses the existence of an outside force affecting the structure and hence associates itself to the structural account of causality firmly. In modern terminology, a causal structure consists of superexogenous relations that are invariant to interventions. In this way, the requirement for invariance and the Lucas critique can be understood as a type of statement on using models to represent a causal structure satisfactorily. The structural account of causality in macroeconomics has been extensively explored in Hoover (2001). Also note that causal relations and invariant relations cannot be treated as equal. See Hoover (2001) and Chen (2002).

13. Also see van Fraassen (1989, 2006) and Nozick (2001) for discussion of the ontological issue of invariance in science.

14. The introduction to Hendry and Morgan (1995) provides an excellent review on the development of the notion of structure in econometrics before the 1950s. Sims's acceptance of the Cowles Commission's definition of structure, especially in Hurwicz (1962), can be seen in Sims (1980, 1982).

15. Hendry (1995: 34) argues that invariance is only a necessary – but not sufficient – condition for structure because he requires the structural parameters to be non‐reducible: structural parameters are those which are invariant and not derived from more fundamental parameters.