Conflict, growth, distribution, and employment: a long-run Kaleckian model

Abstract

This paper presents a Kaleckian growth model in which (i) the rate of capacity utilization, the profit share, and the rate of employment are adjusted in the medium run, and (ii) the normal rate of capacity utilization and the expected rate of capital accumulation are adjusted in the long run. The long-run equilibrium is a continuum of equilibria and is characterized by hysteresis in that the long-run position of the economy depends on where it starts. An increase in the bargaining power of workers lowers the rate of unemployment in both the medium-run and the long-run equilibrium.

Keywords:

• Kaleckian model
• long-run equilibrium
• unemployment
• path-dependency

JEL Classifications:

• E12
• E24
• O41

Acknowledgements

The author would like to thank seminar participants at Kyoto University and Hitotsubashi University, and two anonymous referees for their helpful comments and suggestions, which have substantially improved the paper. Any remaining errors are the author’s responsibility.

Notes

1. See Kalecki (1971) for his economic theory. For the framework of the Kaleckian model, see Rowthorn (1981), Lavoie (1992), Foley and Michl (1999, ch. 10), Blecker (2002), and Taylor (2004, ch. 5).

2. The theory of conflicting-claims inflation is developed by Rowthorn (1977). For Kaleckian models with the conflicting-claims inflation, see Dutt (1987) and Cassetti (2002, 2003, 2006).

3. Ohno (2009) presents a long-run Kaleckian model which considers capital-labour substitution and increasing returns to scale in the production function. In the long-run equilibrium, the desired capital-labour ratio and the actual capital-labour ratio are equalized.

4. Cassetti (2002, 205–6) also points out that the long-run rate of employment in the conventional Kaleckian models is not constant.

5. Rowthorn (1981), Lavoie (1992, 322), You (1994), Cassetti (2003), and Stockhammer and Onaran (2004) also endogenize technical progress in the Kaleckian model through use of Kaldorian technical progress functions. Lima (2004) develops a Kaleckian model with endogenous technical progress in which the growth rate of labour productivity depends non-linearly on the wage share.

6. The view that increases in wages induce labour-saving technical change is consistent with an empirical study by Marquetti (2004), who investigates the co-integration between real wages and labour productivity by using US data.

7. Given the fixed coefficients production function, a cost minimizing firm operates at a point on isoquant curves such that aE = (u/k)K, from which we obtain a = Y/E.

8. Cassetti (2006) uses the investment function that contains the rate of profit as an endogenous variable in addition to the rate of capacity utilization. To simplify the analysis, our model uses the investment function that contains only the rate of capacity utilization. Introducing the rate of profit as a second variable does not change the main results in this paper. For the specification of the investment function, see also Marglin and Bhaduri (1990). They assert that the profit share, not the rate of profit, should be a variable in the investment function. In this case, according to the shape of the investment function, we obtain various equilibrium regimes. For this issue, see also Bhaduri and Marglin (1990) and Blecker (2002). Agliardi (1988) and Mott and Slattery (1994) disagree with the logic of Bhaduri and Marglin (1990). Using Marglin and Bhaduri’s (1990) investment function, Sasaki (2010) presents a Kaleckian growth model in which the rate of employment is endogenously determined as in the present paper. He shows that whether or not an increase in the relative bargaining power of workers raises the equilibrium employment rate depends on which regime is realized in the equilibrium.

9. Cassetti (2002, 2003, 2006) derives an equation of motion for the profit share by specifying a price-setting equation of firms and differentiating it with respect to time. However, this procedure is unnecessary for deriving the equation of motion for the profit share; plus, our procedure is easier than his procedure. With the conflicting-claims inflation theory, the price-setting equation in Cassetti’s model plays the role of determining the mark-up rate rather than the price level.

10. If we introduce both the real-wage Phillips curve and equation (8(8) $g_a(e)=\lambda e^{\psi },\hspace{0.17em}\hspace{0.17em}\lambda >0,\hspace{0.17em}\psi >0,$(8) ) below into our model, the medium-run equilibrium can be stable or unstable depending on which effect dominates, the effect of the real-wage Phillips curve or the effect of equation (8(8) $g_a(e)=\lambda e^{\psi },\hspace{0.17em}\hspace{0.17em}\lambda >0,\hspace{0.17em}\psi >0,$(8) ). However, as long as the medium-run equilibrium is stable, results of comparative statics analysis are the same as those of our model. Moreover, we can assume that the target profit share of workers depends negatively on the growth rate of labour productivity while the target profit share of firms depends positively on the growth rate of labour productivity. Because the growth rate of labour productivity is an increasing function of the employment rate, it amounts to saying that the workers’ target is a decreasing function of the employment rate while the firms’ target is an increasing function of the employment rate. In this case also, as long as the medium-run equilibrium is stable, similar arguments hold. For details, see section A of the Appendix, available on request.

11. The constraint 0 < θ _w , θ _f < 1 is also adopted by Dutt and Amadeo (1993), who, however, do not assume θ _f + θ _w = 1. Even if we impose only 0 < θ _w , θ _f < 1 and not θ _f + θ _w = 1, we obtain similar results.

12. For details, see section B of the Appendix, available on request.

13. For details of comparative statics analysis, see section D of the Appendix, available on request.

14. Recall that we assume that m _f > m _w . With this assumption, an increase in A corresponds to an increase in θ.

15. Stockhammer (2004) uses a Marglin and Bhaduri (1990) type of investment function, thereby leading to both wage-led growth and profit-led growth in the equilibrium.

16. Our classification of regimes is based on Blecker (2002). The stagnationist regime contrasts with the exhilarationist regime and the wage-led growth regime contrasts with the profit-led growth regime.

17. Cassetti (2006) develops a model in which, in addition to the normal rate of capacity utilization and the expected rate of capital accumulation, the normal rate of profit and the drop-out ratio of capital equipment are also adjusted in the long run.

18. Lavoie, Rodríguez and Seccareccia (2004) apply the Hodrick-Prescott filter to the actual series of capacity utilization to obtain the series of normal rates of capacity utilization. Skott (2008) uses the Koyck transformation to delete the normal rate of capacity utilization from the estimated equation, and accordingly, he dispenses with unobservable variables.

19. The other eigenvalue is the trace of the Jacobian matrix.

20. For the derivation of equation (22(22) $\gamma =\frac{s(A-n)u_n}{1-s{u}_n}.$(22) ), see section E of the Appendix, available on request.

21. For the solution method below, see Giavazzi and Wyplosz (1985) and van de Klundert and van Schaik (1990).

22. Indeed, in addition to these two constraints, there are two additional constraints: one is given by γ < n + λ, which represents that the long-run equilibrium rate of employment is less than unity; the other is given by γ < 1 − (A − n), which represents that the long-run equilibrium profit share is less than unity. For ease of presentation, we omit the two additional constraints.

23. For numerical computation, we use Mathematica 7. The Mathematica code used is available on request.

24. For the time paths for Cases 1 and 2, see sections F and G of the Appendix, available on request.