Long-run Effective Demand in the US Economy: An Empirical Test of the Sraffian Supermultiplier Model

ABSTRACT

The Sraffian supermultiplier is a model of demand-led growth that stresses the importance of the autonomous components of aggregate demand (exports, public spending and autonomous consumption). This article tests empirically some major implications of the model employing macroeconomic data for the United States. In particular, we study the long-run relation between autonomous demand and output through cointegration analysis. The results suggest that autonomous demand and output are cointegrated and that autonomous demand exerts a long-run effect on output. There is also some evidence of simultaneous causality, especially in the short-run. Movements in autonomous demand and in the investment share are also found to be positively related, with Granger-causality going from Z to I/Y.

KEYWORDS:

• Effective demand
• growth
• supermultiplier
• US economy

JEL CODES:

• B51
• E11
• E12
• O41
• O47
• O51

Acknowledgments

We are grateful to Sergio Cesaratto, Óscar Dejuán, Massimo Di Matteo, Gary Mongiovi, Fabio Petri, Rafael Wildauer, three anonymous referees and the editor for useful comments and suggestions on earlier drafts of this article. We also thank participants in the INFER Workshop on Heterodox Economics at the University of Coimbra and the XIX Annual ESHET Conference at Roma Tre University. All remaining errors are, of course, our own.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 See Solow (1956) and Lucas (1988) for two different versions of neoclassical growth theory. See Kurz (1994), Cesaratto (1999) and Petri (2004) for a critical discussion of these contributions.

2 See Bortis (1997), Trezzini (1995, 1998), Barbosa-Filho (2000), Park (2000), Palumbo and Trezzini (2003), Dejuán (2005), Smith (2012), Lavoie (2016) and Allain (2015).

3 In a neo-Kaleckian theoretical framework, Lavoie (2016) and Allain (2015) present similar models in which, analogously to the supermultiplier model, growth is driven by autonomous demand.

4 This represents a significant difference with respect to other heterodox growth models, as for example the Marglin–Bhaduri contribution on growth and distribution (Marglin and Bhaduri 1990; Bhaduri and Marglin 1990), where investment is assumed to depend also on the profit share.

5 Equation 4 is, of course, an over-simplification. A more realistic formulation would relate current investment to past output levels and would model explicitly the expectations formation process. For the sake of simplicity, we abstract from these aspects. The hypotheses we derive from the theoretical model and submit to empirical scrutiny are not affected by the specific formulation of the investment function.

6 See, for example, Blanchard (1986), Ford and Poret (1990), Chirinko (1993), Sharpe and Suarez (2014), Kothari, Lewellen, and Warner (2014) and Lim (2014).

7 In order to have meaningful results, we assume 1 – c(1 – t) + m – h to be positive.

8 We adopt the convention of defining the actual degree of capacity utilization as the ratio of actual over normal output, with the latter being in general lower than full capacity output (see Steindl 1952; Kurz 1986). It follows that the normal degree of capacity utilization is equal to one (u_n= 1). Hence, our notation differs from the one used by part of the literature, in which full capacity output (instead of normal output) is at the denominator of u—reflecting a different notation for the same theoretical concept.

9 From Equations 4 and 7, it follows that investment dynamics depend on output growth and capacity utilization: .

10 In this article we neglect technical progress; hence the parameter v is taken as a given constant.

11 Freitas and Serrano (2015) provide the conditions for the dynamic stability of the model. See also Lavoie (2016) and Allain (2015) for an analysis of the stability of similar models.

12 The latter is a significant difference from the so-called Cambridge growth model (see Robinson 1962). That framework’s assumption of a degree of capacity utilization constantly equal to the normal one implies that capacity output determines actual output. Hence, in the long run a causal relation is postulated from the rate of accumulation to normal distribution that becomes endogenous to the process of accumulation. For a discussion of the theoretical problems raised by the Cambridge growth model, see Ciccone (1986) and Garegnani (1992). On the other hand, generally neo-Kaleckian models also share the exogeneity of income distribution (see, for example, Amadeo 1986, pp. 88–89). For a discussion of the differences and the similarities between these models and the supermultiplier, see below and Cesaratto (2015).

13 See Pivetti (1991) and Stirati (1994) for a comprehensive discussion of the classical approach to income distribution.

14 The warranted rate is defined by Harrod (1939, p. 16) as ‘that rate of growth which, if it occurs, will leave all parties satisfied that they have produced neither more nor less than the right amount’ and is given by g_W= s_i/v (p. 18).

15 s_i= 1 – c(1 – t) + m.

16 See Lavoie (2006, Chapter 5) for an exhaustive overview.

17 With this term we refer to real government consumption expenditures and gross investment (see Appendix A).

18 Unfortunately, there is no obvious way to quantify the share of consumption financed by accumulated wealth.

19 We employ net inflows, rather than gross, because in this way we take into account the fact that when households repay a share of previous incurred debts, these fixed amounts are subtracted from current consumption independently of the current level of income, so in this sense they represent ‘negative’ autonomous spending.

20 Often the developer starts building the home before it is sold.

21 Note that, in any case, even when paid for in cash, dwellings are not financed out of current income. So in this sense they fit our definition of autonomous spending. (The median price of a new home is worth several times the median yearly income in all countries.)

22 In principle, if housing expenditure was included in C (real personal consumption expenditure) of national accounts, induced consumption would be (C – CC – RES). However, in national accounts, housing expenditure is already excluded from C, given that it is classified as investment. So we do not need to subtract it.

23 This indicator (private non-residential investment as a share of GDP) is provided directly by the US national accounts.

24 Of course an equation like M_t = m_tY_t, with m_t, calculated as the ex-post ratio of M to GDP, is a tautology.

25 Inclusion of a constant trend is suggested by visual inspection of the data. In order to select the lag order, we estimated a VAR in levels including Z and GDP and computed several standard information criteria. Schwarz’s Bayesian information criterion (BIC), Akaike’s information criterion (AIC) and the Hannan–Quinn information criterion (HQIC) all point to the inclusion of two lags. As shown by Nielsen (2001), these tests are valid even in the presence of I(1) variables. As a test of robustness, we ran the Johansen test with any possible number of lags between 1 and 16. In all cases the test rejects the null of no cointegration at the 0.05 significance level (in most cases, also at the 0.01 level).

26 The trace statistic for the null of no cointegration is 18.7, which is significant at the 0.05 significance level.

27 We exclude the 1947–1959 period in which our proxy for the supermultiplier displays wide fluctuations and the cointegration relation appears unstable (Figure 4). Note that the equilibrium results of the model presented in Section One (see, in particular, Equation 11) require that the supermultiplier is stable. Otherwise, the equation for the rate of growth of output would look like g^Y= g^Z+ g^SM + g^Zg^SM. The model is thus unfit to analyze periods of sharp changes in the supermultiplier, driven by fluctuations in the propensity to save and/or to import. Besides being strongly indicated by Figure 4, our hypothesis of a break in the cointegrating relation in 1960 is supported by a simple formal test: we estimate equation GDP_t = c₁ + θ₁Z_t + c₂D + θ₂DZ_t + ε_t, where D is a dummy equal to 1 if t > 1960:Q1 and 0 otherwise. Both c₂ and θ₂ are significant at the 0.0001 significance level. Since 1960, the overall constant term passes from around 3 to 0, while the coefficient on Z increases from 0.6 to around 1.

28 One obtains Equation 14a by normalizing the cointegrating vector w.r.t. GDP_t.

29 In order to obtain the OIRF we have to impose an identification restriction to the underlying structural model. We choose to employ a Cholesky decomposition, assuming that Z is ‘causally prior’ to GDP. That means that GDP growth can be affected by contemporaneous and lagged autonomous changes in Z, while Z can be affected by lagged autonomous changes in GDP, but not by contemporaneous ones. This restriction appears the most sensible one: changes in Z are bound to have a contemporaneous effect on output growth, since Z shares some components with GDP. To the contrary, Z is composed by autonomous variables that are discretionally determined by individuals and institutions. When choices influencing Z are made (government budget choices, house purchases, foreign citizens’ spending, etc.), the individuals and institutions involved can possibly observe estimates of growth in the preceding quarters, but they cannot observe unexpected changes in GDP that take place in the same quarter.

30 See, for example, Baxter and Kouparitsas (2005) and Cerqueira (2013).

31 Note that the result of a long-run relationship between autonomous demand and output runs counter to standard mainstream macroeconomics, according to which increases in autonomous demand should cause a crowding out of the other components of aggregate demand.

32 Our OIRFs can be interpreted as elasticities (given that we take variables in natural logarithms), so the multiplier at a given time horizon is simply the IR divided by the ratio Z/Y.

33 See Spilimbergo, Symansky, and Schindler (2009) for precise definitions of multipliers and cumulative multipliers.

34 See, for example, the review in Delong and Summers (2012, pp. 244–246).

35 For this analysis, it is not our intent to provide a comprehensive account of the determinants of the long-run investment share of an economy, which would require a detailed analysis of technical progress and its impact on the desired capital–output ratio. Our test has the more limited scope of investigating the relation between variations in autonomous demand and the investment share itself.

36 It is apparent from Equation 12 that, theoretically, the positive effects of Z on I/Y could be partially counteracted by independent variations in the behavioral and structural parameters that make up the supermultiplier.

37 A Granger-causality test is useful in identifying lead-and-lag relationships between time-series. The variable X causes the variable Y, in the sense of Granger, if past values of X contain useful information to predict the present value of Y. Formally, X Granger-causes Y if E(yt|yt − 1, yt−2, … , xt − 1, xt − 2, … )≠ E(yt|yt − 1, yt − 2, … ).

38 Note that we are imposing the constraint that the simultaneous effect of g^Z is zero, by definition of Granger-causality. Hence, our estimate of the long-run effect can be considered prudential.