Models as measuring instruments: measurement of duration dependence of unemployment

Abstract

Nancy Cartwright views models as blueprints for nomological machines – machines that, if properly shielded, generate law‐like behaviour or regularities. Marcel Boumans has argued that we can look for devices inside models, which enable us to measure aspects of these regularities. Therefore, if models do produce regular behaviour (Cartwright), they might perhaps generate numbers about phenomena in the world, provided we can locate a good measuring device in the model (Boumans). How do they do this? Models are often understood to consist of internal principles and bridge principles. Both of these play a role in the measuring process. This paper suggests that we can understand the internal principles to be responsible for generating the regularities displayed by the model – and for many users of the model, this is sufficient use. The bridge principles (following Cartwright – ‘the real bridge principles’) are a matter of picking the right mathematical representation to make the model work with respect to some real world case at hand. These ‘real’ bridge principles may enable the model to generate numbers and so serve to make the model into a measuring device. This paper explores this construction of a measuring device of duration dependence of unemployment. Since search theory cannot be made operational for this purpose duration models, which model of the outflow process of unemployment with a Weibull function, are taken as a representation of reservation wage setting in search models. As I show, this Weibull function serves as a bridge principle to make a measure of the elasticity of response between unemployment benefit and duration of unemployment. It enables measurement to take place by modelling behaviour according to some assumptions, which operate as constraints. While this Weibull function serves this purpose, its assumptions are arbitrary rather than connected to theory, and measurements generated with this bridge principle turn out to be highly sensitive to its specification. The Weibull function does enable the model to function as a measuring device, but the lack of ability to make newly invoked unobservable variables operational makes it of dubious worth.

Keywords:

• measurement
• economic models
• transition data
• search theory
• theory of unemployment
• duration dependence of unemployment

Notes

1. A more detailed description of the functions models serve can be found in Morgan (1999).

2. The current state of representational measurement theory is well summarized in Finkelstein (1975, 1982) or Suppes (1998).

3. Several, partly overlapping accounts of models can be found in methodological literature, like the semantic account, the syntactic account, Mary Hesse's analogy account and Nancy Cartwright's simulacrum account. Daniel Hausman, Ronald Giere and Margaret Morrison and Mary Morgan provide other accounts. For an overview of these accounts, see, for example, Morgan (1998).

4. A point also stressed by Mary Morgan (2001).

5. See, for example, Carl Hempel (1966: 72–5)

6. The representational theory of measurement became accepted by Logical Positivism, as Hempel (1952: 50–78) shows, and under influence of Logical Positivism the representational theory of measurement became generally accepted in the philosophy of science.

7. One interpretation of calibration is that as method of estimation or ‘tuning’. Another interpretation is that as ‘testing’ of a model. See also Boumans (2001), and Hansen and Heckman (1996).

8. Simulacrum means ‘something having merely the form or appearance of a certain thing, without possessing its substance or proper qualities’ (Oxford English Dictionary).

9. Mostly taken as longer than 6 or 12 months.

10. The summed and discounted value of expected future income.

11. Or prices. Search theory has its counterpart in the analysis of consumer behaviour in the goods market.

12. Since Flinn and Heckman (1983), labour economists also try to infer the reservation wage from wage data where the lowest accepted wage is taken as the reservation wage. As do contemporary researchers make use of surveys in order to study the reservation wage. Both methods however are very sensitive to the exact specification.

13. In full: ‘reemployment probability function hazard of failure rate’ (Lancaster 1979: 940). Other names under which the function appears in scientific literature are, among others, age specific death rate, force of mortality, failure rate, hazard, etc.

14. Unfortunately, since this kind of duration analysis originates from mechanical engineering, which studied the breakdown or failure of physical objects in time, it follows that the (joyful) event of finding a job is interpreted as a ‘failure’.

15. Again, the terminology is unfortunately counterintuitive here.

16. A overview of this method can be found in Layard et al. (1991) and Machin and Manning (1999).

17. This implies that the re‐employment probabilities of unemployed follow the same time path, what in the literature is referred to as ‘proportional hazards’.

18. W. Weibull originally established the function in 1937 in Sweden for the analysis of fatigue in ball bearings.

19. The observable characteristics of ψ₁ are in Lancaster's model written as: logψ₁ = β₀+β₁logAGE+β₂logUNEMPLOYMENT+β₃logREPLACEMENT

20. See, for example, Diamond (1982).

21. Her account seems more akin with the semantic account of models, which considerers models representations.

22. An overview of the existing literature that deals with this problem can be found in Machin and Manning (1986: 3107–111).