Fiscal expansion, government debt and economic growth: a post-Keynesian perspective

Abstract

Constructing a post-Keynesian macro-model, we investigate the impact of fiscal expansion on aggregate demand and economic growth, explore public debt sustainability, and analyze whether fiscal policy plays any role in stabilizing the economy. We explore how the interaction between capital accumulation and government debt opens the possibility of multiple equilibria and instability in the economy. We investigate the impact of various parameters on short-run aggregate demand and long-run equilibrium growth rate, and public debt-capital ratio. We explore the relationship between a progressive tax system and a wage-led demand regime. In some cases, a sufficiently high government expenditure to GDP ratio is essential for achieving stability in the system. A sufficiently high government expenditure to GDP ratio ensures economic stability in other circumstances. The possibility of the limit cycle is also explored. Higher autonomous investment demand is desirable as it enhances the stable region of the economy.

Keywords:

• Government deficits and debt
• post-Keynesian
• instability
• limit cycle
• growth model

JEL CODES:

• C62
• E12
• E32
• E62
• O41

Notes

1 Note that by the degree of capacity utilization we mean the ratio of actual output to the potential output, i.e., $u=\frac{Y}{Y^F}=\frac{Y}{K}\frac{K}{Y^F}.$ Where Y^F represents the potential output level. However, as long as the potential output to capital ratio is fixed, the actual output to capital ratio can be used as a proxy for the degree of capacity utilization. Throughout this paper, without any loss of generality, we assume that $\frac{Y^F}{K}=1.$ Therefore, $u=\frac{Y}{K}.$

2 Note that the conclusions reached in the basic short-run model greatly depend on the restrictive assumption that capital accumulation rate, g, is assumed as strictly exogenous. Here the output level (and hence the capacity utilization rate) adjusts to changes in any parameters like tax rates t_W or t_P. Instead of considering an exogenous capital accumulation rate, if we assume g also adjusts in the short run (where $g={\gamma }_0+{\gamma }_{1}u+{\gamma }_2(1-t_P)r+{\gamma }_3\left(\frac{G}{K}\right)$), we may get slightly different results.

3 Note that our result is sensitive to the assumption that the tax rates are constant and government spending rises or falls to keep the budget balanced. For example, if we consider an alternative scenario like Blecker (2002) in which government expenditure is fixed, but the tax rates adjust to retain the balanced budget assumption, we may get the opposite results.

4 For example, see Aschauer (1989) and Barro (1990, 1991).

5 Devarajan, Swaroop, and Zou (1996), using data from 43 developing countries for 20 years, find that a rise in the share of government current-expenditure positively affects economic growth.

6 For example, see Dutt (2013).

7 In fact, even if we consider that (i) only the government investment expenditure through its complementary and other external effects ‘crowds in’ private investment and (ii) the government spends a fraction of its total expenditure as government investment expenditure, our results will not change qualitatively. More formally speaking, suppose $I_G=\alpha .G,$ where $\alpha \in (0,1).$ Equation (15)$$\frac{\partial u^{*}}{\partial \pi }=\frac{-g\left\{(1-t_P)s_P-(1-t_W)s_W\right\}}{{\left[\left\{(1-t_P)s_P-(1-t_W)s_W\right\}\pi +(1-t_W)s_W\right]}^2}$$ will be converted then to $g^d={\gamma }_0+{\gamma }_1{u}^{*}+{\gamma }_2(1-t_P)r^{*}+{\gamma }_3\left(\frac{I_G}{K}\right)={\gamma }_0+{\gamma }_1{u}^{*}+{\gamma }_2(1-t_P)r^{*}+{\gamma }_3\alpha \left(\frac{G}{K}\right).$ However, there would not be any qualitative change in the results.

8 Note that in equilibrium we get $\dot{g}=0.$ This in turn implies $g^{*}=\frac{{\gamma }_0\Psi }{\Psi -\Gamma }>0.$ Therefore, $\frac{\partial g^{*}}{\partial {\gamma }_0}=\frac{\partial }{\partial {\gamma }_0}\left(\frac{{\gamma }_0\Psi }{\Psi -\Gamma }\right)=\frac{{\gamma }_0}{\Psi -\Gamma }>0.$

9 $\frac{\partial g^{*}}{\partial \theta }=\frac{{\gamma }_0{\gamma }_3\Psi }{{(\Psi -\Gamma )}^2}>0.$

10 $\frac{\partial g^{*}}{\partial t_W}=\frac{{\gamma }_0\Gamma (1-\pi )s_W}{{(\Psi -\Gamma )}^2}>0.$

11 $\frac{\partial g^{*}}{\partial t_P}=\frac{{\gamma }_0\pi (\Gamma s_P-{\gamma }_2\Psi )}{{(\Psi -\Gamma )}^2}⋛\mathrm{\hspace{0.17em}0.}$

12 Following Dutt (2013), we introduce it. The purpose of introduction of it is to show that even if we consider the neo-classical argument of financial crowding-out of private investment for a rise in public debt, government debt-capital ratio does not necessarily rise without bound. The model also does not necessarily become unstable.

13 Note that some post-Keynesian economists like Dallery (2007), and Skott (2010, 2012), however, have shown their doubt on whether the Keynesian stability condition holds. However, a reply on this issue can be found in Lavoie (2010) and Hein, Lavoie, and van Treeck (2010). Lavoie (2014, 377–410) provides a summary of this controversy.

14 In this context, also note that while trying to reproduce Reinhart and Rogoff (2010), Herndon, Ash, and Pollin (2014) find simple spreadsheet errors and irregularities concerning country and time coverage in Reinhart and Rogoff (2010). Panizza and Presbitero (2014) find that the link between public debt and growth disappears once the endogeneity problem is corrected. Pescatori, Sandri, and Simon (2014) find no evidence of any particular debt threshold beyond which growth prospects are dramatically compromised. Instead, Pescatori, Sandri, and Simon (2014) find that countries with high but declining debt levels grow equally as fast as countries with lower debt. Furthermore, Jacobs et al. (2020) find no causation from public debt to growth, irrespective of the levels of the public debt ratio.

In this regard, it is important to note that the idea that a high level of public debt is a drag on economic growth is much disputed, as well as the contribution of Reinhart and Rogoff (2010). However, the focus of this paper is not to investigate whether the contribution of Reinhart and Rogoff (2010) is worthy. Instead, one of the prime objectives of this paper is to show that even if we consider that a high level of public debt to GDP ratio is a drag on economic growth, instability does not necessarily arise in the economy.

A vast literature that includes Reinhart and Rogoff (2010), Herndon. (2014), Cecchetti, Mohanty, and Zampolli (2011), Checherita-Westphal and Rother (2012), Afonso and Jalles (2013), and Kumar and Woo (2015) find an inverted U-shaped relationship between public debt and economic growth where for a high level of debt ratio, debt has a negative impact on the economic growth. Although we have not included this possibility that δ can non-linearly influence the desired investment to capital ratio, it can easily be shown in our model once we assume

$g^d={\gamma }_0+{\gamma }_1{u}^{*}+{\gamma }_2(1-t_P)r^{*}+{\gamma }_3\left(\frac{G}{K}\right)-{\gamma }_4{\delta }^2.$

Then we get,

$J_{12}\equiv \frac{\partial \dot{g}}{\partial \delta }=\rho [-2{\gamma }_4\delta +\frac{\Gamma \zeta i}{\Lambda }]\gtrless 0 \text{iff }\delta \lessgtr \frac{\Gamma \zeta i}{2{\gamma }_4\Lambda }.$

Consequently we get an inverted U-shaped relationship between public debt and economic growth (i.e., an inverted U-shaped $\dot{g}=0$ isocline in $(\delta ,g)$ space). However, the qualitative result, under that circumstances, would not differ from what we get in our simpler model.

15 Note that $\Omega >0$ implies $\theta >\left\{t_P\pi +t_W(1-\pi )\right\}.$

16 Here as $J_{12}<0$ and $J_{21}<0, tr{\left(J\right)}^2-4Det\left(J\right)={(J_{11}-J_{22})}^2+4J_{12}{J}_{21}>0.$ Hence the steady state is a stable node.

17 See Isaac and Kim (2013, 264–265) for more on the concept of stable region.

18 Note that for a rise in i, the slope of the $\dot{g}=0$ isocline increases, i.e., $\frac{d}{di}\left(\frac{dg}{d\delta }{|}_{\dot{g}=0}\right)=\frac{\Gamma \zeta }{\Lambda -\Gamma }>0.$ However, the vertical intercept of the $\dot{g}=0$ isocline does not change, i.e., $\frac{d}{di}(g{|}_{\dot{g}=0}^{\delta =0})=\frac{d}{di}\left(\frac{{\gamma }_0\Lambda }{\Lambda -\Gamma }\right)=0.$

19 Note that for a rise in $\theta ,$ the slope of the $\dot{g}=0$ isocline increases, i.e., $\frac{d}{d\theta }\left(\frac{dg}{d\delta }{|}_{\dot{g}=0}\right)>0.$ The vertical intercept of the $\dot{g}=0$ isocline also rises, i.e., $\frac{d}{d\theta }(g{|}_{\dot{g}=0}^{\delta =0})>0.$

Additional information

Notes on contributors

Pintu Parui

Pintu Parui is at the School of Economics, XIM University, Bhubaneswar, India. The author is indebted to C. Saratchand, Gogol Mitra Thakur, participants in the Economics Research Discussion Group (India, October 2022), and in particular to Shubhro Sarkar, the CIETP conference (at St. Xavier’s University, Kolkata, India, March 2023) and in particular to Saikat Sinha Roy, and two anonymous referees of this journal for their valuable comments and suggestions. However, the author is solely responsible for the remaining errors.