A two-sector model with target-return pricing in a stock-flow consistent framework

ABSTRACT

In this paper, we build a generalized two-sector Kaleckian growth model and explore the dynamics towards long-run positions. The model incorporates conflicting claims of labour and firms over income distribution and endogenous labour-saving technical progress. Adopting a stock-flow consistent framework, our simulation experiments yield the following results. First, the ‘paradox of thrift’ and the ‘paradox of costs’ hold, meaning that lower saving rates generate higher growth rates while higher real wages generate higher profit rates, but the magnitude of the impact depends on the initial status of income distribution and monetary policy. Second, changes in autonomous labour-saving innovations might explain the phenomenon of the ‘New Economy’ of the second half of the 1990s within an alternative framework. Our simulations with a two-sector model retrieve the analytical results achieved with a one-sector Kaleckian model, with the addition of path dependence.

KEYWORDS:

• Two-sector model
• paradox of thrift
• paradox of costs
• technical progress
• New Economy
• New Consensus

Acknowledgements

We wish to thank the editor Bart Los for his patience and advice as well as the two anonymous referees for their suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 A number of scholars are currently developing empirical stock-flow consistent models (Caverzasi and Godin, 2015), which would constitute a move towards the integration suggested by Klein.

2 Note that capital gains do not appear in the transaction matrix while they are embodied as a change in the net worth of each sector (i.e. the net worth of households and firms in this model) in the balance-sheet matrix.

3 In addition to its realistic appeal, as recalled by Lee (1998), target-return pricing allows to take explicit account of the intersectoral dependence of cost margins among sectors, as shown in Lavoie and Ramírez-Gastón (1997, p. 150).

4 One would think that trade unions target a real wage or a wage share. But recall from Equations 9a and 9b that a profit share is m = θ/(1 + θ), while a costing margin is θ = (1/α − ω)/ω, where ω is the real wage rate. Thus, by using Equations A6.1 and A6.2 in Appendix 1 the target real wage rate can be described in terms of the target rate of return.

5 Constant adjustment-speed coefficients, of course, might be a strong assumption because those would be determined by the wage negotiation of trade unions and capitalists and be influenced by business cycles. Here, we assume that those coefficients are determined only by non-economic factors such as institutional conditions which are exogenously given.

6 In the present model, it is assumed that a change in labour productivity does not have a direct effect on the determination of the nominal wage rate, but indirectly affects the real wage rate via a change in prices due to changing unit costs.

7 We can also write ${\gamma }_{i0}={\overline{\gamma }}_{i0}-{\gamma }_{i4}{u}_{i(-1)}^s$.

8 Note that in our model the q ratio does not necessarily converge towards unity, neither in the short run nor in the long run, because a firm's market value does not exactly reflect its replacement value and investment is also determined by other factors. In fact, historical data show that the q ratio has no tendency towards unity.

9 Park (2001–2002, p. 319) insists that in the long-run equilibrium the rate of return on equities should be equal to the profit rate as a result of the free mobility of financial capital. Following his argument, Equations 24a and 24b could be replaced with g_e,i = g_e,i(−1) + δ_i (r_e,i – r_i(−1)). However, in the present model, there is no mechanism bringing about a uniform rate of profit, so that incorporating this alternative equation will not do the trick and will result instead in differentiated rates of return on equities.

10 Consumption function (27) is similar to the famous consumption equation proposed by Modigliani with his life-cycle hypothesis. However, our consumption function is different from Modigliani's since ours depends on ‘current’ income whereas his depends on ‘lifetime’ income. Also, we could interpret the last term of Equation 27 as autonomous consumption, independent of current income, because the level of wealth is relatively stable in the short period. In this sense, Equation 27 can also be interpreted as consumption behaviour in terms of norms.

11 Equation 31a implies that the amount of money balances held by households is a residual, meaning that it bridges the gap between the expected and the actual values of wealth at the end of the period. In other words, the money deposits held in banking accounts absorb unexpected changes in monetary transactions.

12 This adjustment of equity prices allows the targeted portfolio choice to be obtained in the steady state (because $V^e=V$ and $Y_{hr}^e=Y_{hr}$).

13 In fact, it is beyond the scope of this paper to estimate parameter values of equations.

14 We also need to point out that there is not enough empirical literature corresponding to our equations because time-series data are not stationary so that most empirical models are examined in difference form, so that parameter estimates do not correspond to the variables used in our model.

15 As a consequence, in our simulations, we only deal with the case where investment decisions are more sensitive to the rate of capacity utilization than to the q ratio, thus avoiding the ‘puzzling’ case identified by Lavoie and Godley (2001–2002) which does not fit with the most recent empirical evidence that shows that the q ratio has little or no impact on the investment decisions of firms (Arestis et al., 2012).

16 An exceptional case appears when examining the impact of a change in interest rates. With some parameters related to interest rates, the negative impact on investment of a rise in interest rates can be overcome by the positive impact that it has on the disposable income of households and on their consumption. When this is the case, an increase in the interest rate could lead to a higher growth rate and a higher inflation rate. This is a possible surprising effect that has been noted in the literature.

17 A list of the values taken by the various variables and parameters is given in Appendix 2 in the supplementary file.

18 Also, an increase in the propensity to consume out of financial income or out of household wealth leads essentially to an identical outcome.

19 Storm and Naastepad (2012) show that this ambiguity also arises in empirical studies.

20 If accumulation reacts strongly to technical progress (the reaction coefficient γ_i5 in Equation 18 is large), a faster long-run growth rate of employment could be achieved.

21 As shown in Equation A4 of Appendix 1.

22 Note that equity prices can rise in the short run as shown in Figure 4(c). In our model, this appears because the effect of an increase in households’ wealth due to the rise in the interest income overwhelms the substitution effect in the portfolio decision of households, even though the equity ratio declines in the short run.

23 For the post-Keynesian critique of the New Consensus, see in particular the chapters found in the book edited by Fontana and Setterfield (2009).

24 To show more clearly this negative effect, for this experiment, we modified the values of the γ_i2 parameters relative to the impact of the debt burden on investment, moving these parameters from 0.1 and 0.11 to 0.4, thus obtaining the results shown in Figure 4(b).

25 In fact, this result has much similarity with that obtained in a neo-Marxian model developed by Duménil and Lévy (1999), where a lower saving rate ends up diminishing the long-run growth rate, a result which is also similar to the results obtained in the mainstream New Consensus model (Lavoie and Kriesler, 2007).

26 The former is the targeted total profits induced by the price Equations 9a and 9b and the latter is the targeted total profits derived from the target rate of return on capital. The two equations should be equal by the definition, which means that the costing margin is adjusted along with the changing target rate of return in our model.