Are estimates of labour demand functions mere statistical artefacts?

Abstract

This paper considers the estimation of putative neoclassical aggregate labour demand functions using constant price value data. Regression results normally find that employment is negatively related to the real wage and that the constant‐output elasticity of employment with respect to the real wage is about −0.3. This is taken as evidence that unemployment is the result of the real wage being too high, ceteris paribus. This paper shows that these estimates are purely the result of an underlying identity and cannot be interpreted as implying any causal relationship and, as such, they have no policy implications.

Keywords:

• labour demand functions
• accounting identity

JEL classification:

• J23

Acknowledgement

We are grateful to two anonymous referees for their helpful comments. This paper represents the views of the authors and does not represent those of the Asian Development Bank, its Executive Directors or the countries that they represent.

Notes

1. The quotation is from T.S. Eliot’s poem, ‘Little Gidding’.

2. Some Keynesians, while accepting the marginal productivity theory of factor pricing, would dispute this line of reasoning. They argue that while there is an inverse relationship between the wage rate and the level of employment (because of diminishing returns), the causation is not that of the neoclassicals. It is the level of demand that determines the demand for labour, which in turn determines the real wage (see, for example, Davidson 1983; Thirlwall 1993). We shall not pursue this argument here.

3. This is because under the usual neoclassical assumptions, the rate of technical progress is given by the growth of the real factor prices weighted by their factor shares. This means the specifications become exact identities.

4. However, an increase in the money wage may increase the price of output relative to that of other goods and services. Assuming a demand equation for output as Q = cp^−π , where π ≥ 0 is the absolute value of the elasticity of product demand and c is a constant, the wage elasticity of the demand for labour becomes −(1 − a)σ − aπ. As precise estimates of the price elasticity of demand for output are difficult to obtain, the demand side is normally ignored in the literature, which is equivalent to assuming that the demand for the industry’s output is either completely price inelastic or supply constrained.

Another implicit assumption is that the elasticity of supply of capital goods and structures is infinite. If it is not, the expression for the wage elasticity becomes more complicated with the elasticity of supply of the capital stock being one of its arguments. Again, it is normally assumed that this is infinite, in which case the elasticity of demand for labour is again equal to −(1−a)σ or alternatively to −(1 − a)σ − aπ.

5. The argument holds equally if we use the identity for gross output, or sales, instead.

6. If there are measurement errors in the calculation of ρ, this will affect the value of r_nc , which is calculated residually.

7. A serious problem is that there is no way of testing whether ρ (which is calculated using a number of restrictive assumptions and suffers from serious aggregation problems) correctly measures the competitive rate of profit. It can be compared with the ex post rate of profit but it is impossible to determine whether any difference is due to the state of competition or to errors inherent in calculating ρ.

8. In a perceptive comment, Jorgenson and Griliches (1967, 257 fn 2, emphasis in the original) note:

 The answer to Mrs. Robinson’s … rhetorical question, ‘what units is capital measured in?’ is dual to the measurement of the price of capital services. Given either an appropriate measure of the flow of capital services or a measure of its price, the other measure may be obtained from the value of income from capital. Since this procedure is valid only if the necessary conditions for producer equilibrium are satisfied, the resulting of quantity may not be employed to test the marginal theory of distribution, as Mrs. Robinson and others have pointed out.

However, what they have overlooked is that this holds regardless of whether or not the conditions for producer equilibrium exist, as we show in the text.

9. It could also be argued that it is not clear that large oligopolistic firms necessarily base their investment and labour‐hiring decisions on the rental price of capital, which is derived from an untested optimizing microeconomic model. The rate of profit of a firm, which closely correlates with its internal funds from which most investment is financed, may actually be of greater importance (as, indeed, is the state of expectations about future demand). Thus, the labour demand function is correctly specified using r, the ex post rate of profit. However, it must be emphasized that the argument we are making in this paper does not rely on this assumption. Moreover, equations (2), (3) and (4) do not use the rental price of capital.

10. Note that all we require is for factor shares to be constant for a Cobb‐Douglas to give a perfect fit to the identity. This does not have to result from a constant mark‐up. The Kaldorian theory of distribution, for example, will give the same result. The seminal article is Kaldor (1956).

11. Recall the discussion above about the difference between the rate of profit and rental price of capital if markets are not competitive.

12. In fact, any underlying physical production functions will give rise to an aggregate Cobb‐Douglas production function if factor shares are constant.

13. Under the usual neoclassical assumptions the dual of total factor productivity growth, when factor shares are constant, is given by λ(t) ≡ aŵ + (1 − a)[rcirc] and also lnA(t) = lnB + alnw + (1−a)lnr.

14. As we are illustrating a theoretical point, the exact period of the data set used is not particularly important.

15. As we are not dealing with behavioural equations, the exact specifications in terms of lags etc. in the empirical results are determined by the goodness of fit.

16. We are grateful to a referee for posing this question.

17. Simply regressing lna on a constant gives a coefficient of −0.318 with a t‐ratio of −57.21. This gives a value of labour’s share of 0.728.

18. The long‐term estimates of Lewis and MacDonald (2002) using Australian quarterly data for the whole economy over the period 1961–1998 are:

19. There was a rejoinder by Nickell (1989), but it is difficult not to agree with Anyadike‐Danes and Godley (1989b) that, while it raised some interesting issues, it did not address their argument.

20. It is positive and statistically significant in their Model 1, which we have not discussed.

21. We are grateful to Anwar Shaikh for providing us with his capacity utilization estimates.