A Short Period Sraffa-Keynes Model for the Evaluation of Monetary Policy

ABSTRACT

This paper develops a short period, one sector, Sraffa-Keynes model that can be used for the evaluation of various recommendations outlined in the Post Keynesian monetary policy literature. The model is characterised by the principle of effective demand, Sraffa or target-return pricing (which integrates the determination of key distributive variables and allows for short run cyclical variation in prices), conflict inflation, endogenous money and a basic approach to monetary policy in the Smithin–Wray tradition of fixing the policy rate to achieve low or specified rates of unemployment. The model is calibrated to the Australian economy and subjected to two standard macroeconomic shocks, a demand shock and a cost shock. After each shock, the economy returns to long period equilibrium characterised by the achievement of the target rate of return, desired capacity utilisation and Sraffian prices of production. Active monetary policy that targets employment, reduces the depth and duration of recessions in this model compared to a ‘park-it’ approach but at the cost of increased volatility in income distribution. Flexible prices (where firms respond to the additional costs of running the capital stock at other than full capacity) are shown to have similar effects to monetary policy.

KEYWORDS:

• Monetary policy
• demand shock
• cost shock
• income distribution

JEL CODES:

• E11, E12, E52

Acknowledgements

Thanks to Tony Aspromourgos, Graham White, Corrado DiGuilmi, Peter Skott, Prabhu Sivabalan and two anonymous referees for comments and suggestions.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

1 The assumption is made here that the Sraffian tradition falls within the classification of post-Keynesian economics. While the literature contains some support for this classification (see Lavoie 2006, pp. 89–91), it is recognised that others are less comfortable with it. King (2015, pp. 114–117) analyses potential reasons for such discomfort in terms of the long period focus of Sraffian analysis in contrast to the short period focus of Kaleckian and other models, and their tendency to downplay the possibility that the long run has any unique analytical character. The intention in the present paper is not to contribute to this debate but simply to accept the various theoretical perspectives that Sraffian models (especially those associated with the so-called Sraffa-Keynes synthesis) have in common with Kaleckian and other heterodox traditions, and to use the term ‘post-Keynesian’ to express those commonalities. Other models could of course be used for this purpose and it would be useful if this were done and results with the present analysis compared.

2 It should be noted that this is not the same thing as the Hicksian method of temporary equilibria in which there is no such thing as the long period but only a sequence of short period positions. We have been very careful to specify the conditions that constitute the long period, and when these conditions hold, the economy is indeed in a long period position. But the context considered here is one in which there are periods in which these conditions may fail to hold, and the question is how the economy finds its way back to a long period position. As a matter of definition, situations in which the long period conditions fail to hold will be regarded as short period positions.

3 Freitas and Serrano (2015), however, distinguish between long period positions and fully adjusted positions in which capacity utilisation is equal to its ‘desired’ level. It is thus possible for long period positions not to be characterised by equality between actual and desired capacity utilisation in their approach.

4 This may differ from the level of output necessary to employ all of the available workforce.

5 This ignores the issue of firms choosing a normal rate of capacity utilisation that is profit maximising (see White 1996, 1998). The normal rate of capacity utilisation is simply treated as a convention in this model set equal to one for the sake of simplicity. We assume that this does not rule out running the capital stock above its conventional capacity so that the capacity utilisation rate can exceed 1 for short periods of time. But this will have two effects in the present model: it will lead to additional investment according to equation 3 which will expand capacity over time; and it will increase costs and reduce profits according to a pricing equation developed below. It should also be emphasised that equation 3 does not suggest that firms are spending out of the circular flow of income, so that $\delta \cdot \nu$ could be understood as a marginal propensity to invest (as, for example, Freitas and Serrano 2015, p. 261 appear to do). Investment may thus require external finance although we abstract from this issue.

6 An alternative formulation of the investment function might make investment spending responsive to the actual rate of profit earned relative to the target rate of profit, for example: $I_t=\delta \cdot \nu \cdot Y_{t-1}\cdot [1+q\cdot (r_{n,t}^a-r_{n,t}^{\ast })]$ where $r_{n,t}^a$ is the actual rate of profit in a given period, $r_{n,t}^{\ast }$ is the desired or target rate of profit in any period, and q is an adjustment parameter. We tested this formulation and it made no fundamental difference to equilibrium, stability or the general shape of the time paths of any variable.

7 We rationalise the presence of additional costs when running the capital stock above the desired rate of capacity utilisation with the assumption of having to use older, less efficient equipment during such periods of increased production (see Bitros 1976, p. 920). In a recent paper by Lavoie and Nah (2020), unit costs fall as capacity utilisation increases due to the presence of significant overhead labour costs (in the form of large managerial salaries). It would be interesting in extensions to the present work to explore the impact of interactions between this important feature of income distribution, recently identified by Piketty (2014), with a more complex and perhaps asymmetric structure in the operating costs of the capital stock across the cycle. Thanks to an anonymous referee for identifying this possibility.

8 To see this, replace $p_t$ in equation 8 with $p_{t-1}$ and rearrange to obtain:

$r_{n,t}\cdot p_{t-1}\cdot K_t=p_t\cdot Y_t-M{W}_t\cdot N_t-p_t\cdot \delta \cdot \nu \cdot Y_t$

Then divide by $p_t{Y}_t$ to obtain:

$r_{n,t}\cdot \nu \cdot p_{t-1}/p_t=1-w_t\cdot {\ell }_t-\delta \cdot \nu$

where everything has the same meaning as above but we retain the term $p_{t-1}/p_t$ on the left hand side of the expression. Since, by definition, $p_t=p_{t-1}(1+{\pi }_t)$, we may express the ratio $p_{t-1}/p_t$ as $1/(1+{\pi }_t)$. In this case, the expression becomes:

$\nu \cdot [r_{n,t}/(1+{\pi }_t)]=1-w_t\cdot {\ell }_t-\delta \cdot \nu$

If we define $r_{n,t}/(1+{\pi }_t)$ as a kind of real rate of profit, and designate this as $r_{r,t}$, our wage-profit relation becomes:

$w_t={\displaystyle \frac{1}{{\ell }_t}\cdot [1-\nu \cdot (r_{r,t}+\delta )]}$

Using $r_{n,t}/(1+{\pi }_t)$ or $r_{r,t}$ in this equation is likely to generate non-linearities in the reduced form and it will be convenient to approximate this term. The standard approximation is to let $r_{r,t}=r_{n,t}-{\pi }_t$. This is, however, a poor approximation. For the case where $r_{n,t}$ is in the neighbourhood, for example, of 0.08 and ${\pi }_t$ is of the order of 0.03, $r_{n,t}/(1+{\pi }_t)$ would be 0.0777. Approximating this with $r_{n,t}-{\pi }_t$ would yield 0.05 and would generate an approximation error of 0.0277. Simply using the nominal rate itself as an approximation would involve an approximation error of only 0.0023. Similar results obtain for a wide range of plausible values for $r_{n,t}$ and ${\pi }_t$. The nominal rate is thus the best approximation in the present context for the relevant rate of profit.

9 That $Y_t/K_t=u_t/\nu$ follows from the fact that we may express $Y_t/K_t$ as $(Y_t/K_t)\cdot (Y^P/Y^P)$. This product may be rearranged to give: $(Y_t/Y^P)\cdot (Y^P/K_t)$ This first bracketed term was shown above to equal the rate of capacity utilisation, $u_t$ and the second is simply the inverse of the technical capital-output ratio, $\nu$. Thus: $Y_t/K_t=u_t/\nu$. That $N_t/K_t=(\ell /\nu )\cdot u_t$ follows from the fact that we can express $N_t/K_t$ as $(N_t/K_t)\cdot (Y_t/Y_t)$. This can be rearranged to give: $(N_t/Y_t)\cdot (Y_t/K_t)$. The first of these bracketed term is simply the unit labour requirement for production, $\ell$ while we have just shown that the second term is $u_t/\nu$. It thus follows that $N_t/K_t=(\ell /\nu )\cdot u_t$.

10 Note that if we exclude the additional costs of running the capital stock at anything other than normal capacity, it can be shown that $r_{n,t}^a=u_t\cdot r_{n,t}^{\ast }$. The rate of profit adjusted by the rate of capacity utilisation in equation 21 would then simply be equal to the target rate of profit. It thus constitutes a reasonable pricing strategy for firms to replace $r_{n,t}^a/u_t$ in equation 21 with $r_{n,t}^{\ast }$ and to rely on the $z_t\cdot (1-1/u_t)$ term to account for additional costs associated with the business cycle. This is precisely what equation 22 above does.

11 This structure raises the question as to why workers would attempt to increase money wages if such increases have no effect on income distribution. We may offer two related answers to this question. The first is that workers have no other direct means of attemtping to influence income distribition apart from their wage claims. Such claims, therefore, provide workers with a sense of agency in attempting to influence the economic conditions which they face. Secondly, the economic system is sufficiently complex that workers may not understand that attempts to affect income distribution via changes to money wages have no effect. It seems plausible that an increase in money wages should lead to an increase in real wages, and it is only after some time that workers notice this has not happened. There may be an inherent optimism that any new increase in the money wage may lead to a change in income distribution.

12 This counter-cyclical behaviour of the real wage in our model appears to conflict with empirical evidence on real wage cyclicality according to which real wages (at least in the United States) appear to be mildly pro-cyclical (see Abraham and Haltiwanger 1994). This overall characterisation, however, masks considerable variability in findings and explanations for the effect. In surveying this evidence, Abraham and Haltiwanger (1994, pp. 1259–1252) argue that real wage behaviour across the cycle is sensitive to the period over which it is measured (pre- and post-1970 is especially important), to the price deflator used in calculating the real wage, and to the industrial composition of effects from particular cycle-generating shocks. It would thus be useful to explore the cyclical behaviour of real wages in our Sraffa-Keynes model for a range of shock-types and for a range of variations to the pricing behaviour represented by equation 22. One referee helpfully suggested making price responses to the cycle asymmetric with more limited downward flexibility than upwards flexibility, and separating money wage determination from price determination. In this case, higher unemployment during a downturn in demand, could slow money wage growth (for which Blanchflower and Oswald (1994) provide evidence in the United Kingdom) relative to inflation, leading to a fall in the real wage. We leave, however, a dedicated study of real wage cyclicality in the model to further work, noting the desirabilily of considering variations to the simple flexible pricing approach represented by equation 22.