Fiscal policy, government debt, and economic growth in the Kaleckian model of growth and distribution

Abstract

This article presents the Kaleckian model of growth and distribution that sets a budget deficit ratio as an indicator of fiscal policy and examines the short- and long-run effects of an increase in budget deficits and a rise in income tax rates on the economy. The key short-run outcomes are as follows. First, expanded budget deficits have a positive effect on the rate of capacity utilization. Second, the tax rate for wage income does not affect the rate of capacity utilization, whereas the tax rate for capital income has a favorable impact on it. This result implies that raising the tax rate for capital income can be an important policy instrument for stimulating the economy. Third, we find that the economy exhibits a wage-led aggregate demand in the short run. The main long-run results are as follows. First, the effect of expanded budget deficits on the growth rate is ambiguous, since a higher debt burden negatively influences the rate of capacity utilization and hence economic growth, despite the increase in demand caused by government borrowing. A higher budget deficit ratio thus raises the growth rate only if a certain condition is satisfied. Second, the tax rate for capital income has a positive impact on the growth rate. Third, the economy shows a wage-led growth in the long run.

Keywords:

• Budget deficit ratio
• government debt
• income tax rates
• Kaleckian model of growth and distribution

JEL classifications:

• E11
• E12
• E62

Appendix

The total differentiation of the dynamic system composed of Equations (17)(17) $$\dot{g}=\frac{\mathrm{\Lambda }}{bh-\delta }\left[(bh\hspace{0.17em}-\hspace{0.17em}\delta )\alpha +\beta \left(g\hspace{0.17em}-\hspace{0.17em}bi\lambda \right)-(bh\hspace{0.17em}-\delta )\gamma i-(bh\hspace{0.17em}-\hspace{0.17em}\delta )g\right],$$(17) and (20)(20) $$\dot{\lambda }=\frac{1}{bh-\delta }\left[\delta (g-bi\lambda )-(bh-\delta )g\lambda \right].$$(20) is given by (A) $$J\left(\begin{array}{c}\mathrm{d}g\\ \mathrm{d}\lambda \end{array}\right)=\left(\begin{array}{c}\frac{\mathrm{\Lambda }\beta b\left(g\hspace{0.17em}-\hspace{0.17em}bi\lambda \right)}{{\left(bh\hspace{0.17em}-\hspace{0.17em}\delta \right)}^2}\\ \frac{\delta b\left(g\hspace{0.17em}-\hspace{0.17em}bi\lambda \right)}{{\left(bh\hspace{0.17em}-\hspace{0.17em}\delta \right)}^2}\end{array}\right)\mathrm{d}h+\left(\begin{array}{c}-\frac{\mathrm{\Lambda }\beta \left(g\hspace{0.17em}-\hspace{0.17em}bi\lambda \right)}{{\left(bh\hspace{0.17em}-\hspace{0.17em}\delta \right)}^2}\\ -\frac{bh\left(g\hspace{0.17em}-\hspace{0.17em}bi\lambda \right)}{{\left(bh\hspace{0.17em}-\hspace{0.17em}\delta \right)}^2}\end{array}\right)\mathrm{d}\delta +\left(\begin{array}{c}\frac{\mathrm{\Lambda }\left[\beta b\lambda +\left(bh\hspace{0.17em}-\hspace{0.17em}\delta \right)\gamma \right]}{bh-\delta }\\ \frac{\delta b\lambda }{bh-\delta }\end{array}\right)\mathrm{d}i+\left(\begin{array}{c}-\mathrm{\Lambda }\\ 0\end{array}\right)\mathrm{d}\alpha +\mathrm{ }\left(\begin{array}{c}\frac{\mathrm{\Lambda }\beta h\left(1\hspace{0.17em}-\hspace{0.17em}{t}_c\right)\left(g\hspace{0.17em}-\hspace{0.17em}bi\lambda \right)+\mathrm{\Lambda }\beta \left(1\hspace{0.17em}-\hspace{0.17em}{t}_c\right)i\lambda (bh\hspace{0.17em}-\hspace{0.17em}\delta )}{{(bh-\delta )}^2}\\ \frac{\delta h\left(1\hspace{0.17em}-\hspace{0.17em}{t}_c\right)\left(g\hspace{0.17em}-\hspace{0.17em}bi\lambda \right)+\delta \left(1\hspace{0.17em}-\hspace{0.17em}{t}_c\right)i\lambda (bh\hspace{0.17em}-\hspace{0.17em}\delta )}{{(bh\hspace{0.17em}-\hspace{0.17em}\delta )}^2}\end{array}\right)\mathrm{d}s+\left(\begin{array}{c}-\frac{\mathrm{\Lambda }\beta hs\left(g\hspace{0.17em}-\hspace{0.17em}bi\lambda \right)+\mathrm{\Lambda }\beta si\lambda (bh\hspace{0.17em}-\hspace{0.17em}\delta )}{{(bh\hspace{0.17em}-\hspace{0.17em}\delta )}^2}\\ -\frac{\delta hs\left(g\hspace{0.17em}-\hspace{0.17em}bi\lambda \right)+\delta si\lambda (bh\hspace{0.17em}-\hspace{0.17em}\delta )}{{(bh\hspace{0.17em}-\hspace{0.17em}\delta )}^2}\end{array}\right)\mathrm{d}{t}_c.$$(A)

The Jacobian matrix of the dynamic system composed of Equations (26)(26) $$\dot{g}=\frac{\mathrm{\Lambda }}{bh}\left\{bh\alpha +\beta \left[g+(1-b)i\lambda \right]-bh\gamma i-bhg\right\}$$(26) and (27)(27) $$\dot{\lambda }=(i-g)\lambda .$$(27) is given by (B) $$J=\left(\begin{array}{cc}-\frac{\mathrm{\Lambda }(bh\hspace{0.17em}-\hspace{0.17em}\beta )}{bh}& \frac{\mathrm{\Lambda }\beta (1\hspace{0.17em}-\hspace{0.17em}b)i}{bh}\\ -\lambda & i-g\end{array}\right).$$(B)

With the equilibrium values $g=\frac{bh(\alpha -\gamma i)}{bh-\beta }$ and $\lambda =0$ are the signs of the components of the Jacobian matrix $J=\left(\begin{array}{cc}-& +\\ 0& ?\end{array}\right)$. This dynamic system is stable if the condition $J_{22}<0$ is fulfilled. Therefore, $g>i$ is a sufficient condition for the stability of the dynamic system that consists of Equations (26)(26) $$\dot{g}=\frac{\mathrm{\Lambda }}{bh}\left\{bh\alpha +\beta \left[g+(1-b)i\lambda \right]-bh\gamma i-bhg\right\}$$(26) and (27)(27) $$\dot{\lambda }=(i-g)\lambda .$$(27) . The total differentiation of the dynamic system is represented by $$J\left(\begin{array}{c}\mathrm{d}g\\ \mathrm{d}\lambda \end{array}\right)=\left(\begin{array}{c}\frac{\mathrm{\Lambda }\beta b\left[g+\left(1-b\right)i\lambda \right]}{{\left(bh\right)}^2}\\ 0\end{array}\right)\mathrm{d}h+\left(\begin{array}{c}\frac{\mathrm{\Lambda }\left[bh\gamma \hspace{0.17em}-\hspace{0.17em}\beta \left(1\hspace{0.17em}-\hspace{0.17em}b\right)\lambda \right]}{bh}\\ -\lambda \end{array}\right)\mathrm{d}i+\left(\begin{array}{c}-\mathrm{\Lambda }\\ 0\end{array}\right)\mathrm{d}\alpha +$$ (C) $$\left(\begin{array}{c}\frac{\mathrm{\Lambda }\beta h\left(1-t_c\right)\left(g+i\lambda \right)}{{\left(bh\right)}^2}\\ 0\end{array}\right)\mathrm{d}s+\left(\begin{array}{c}-\frac{\mathrm{\Lambda }\beta sh\left(g+i\lambda \right)}{{\left(bh\right)}^2}\\ 0\end{array}\right)\mathrm{d}{t}_c.$$(C)

Notes

1 Herndon et al. (2014) criticized Reinhart and Rogoff’s (2010) empirical analysis as follows: “Selective exclusion of available data, coding errors and inappropriate weighting of summary statistics lead to serious miscalculations that inaccurately represent the relationship between public debt and GDP growth. … Contrary to Reinhart and Rogoff’s broader contentions, both mean and median GDP growth when public debt levels exceed 90% of GDP are not dramatically different from when the public debt/GDP ratios are lower. The relationship between public debt and GDP growth varies significantly by period and country.”

2 Commendatore, Panico, and Pinto (2011) classified government expenditure into productive and unproductive and dealt with how these different types affect the economy. Through an interpretation of the Kaleckian model, they argued that productive government expenditure can have a positive or a negative impact on the economy depending on the relative size of the ratio of government expenditure to income, while unproductive government expenditure always has a positive effect on the economy. However, we have no choice but to question the meaning of “productive” in their analysis.

3 The rate of capacity utilization is defined as the ratio of real output (Y) to potential output (Y). Because $u=\frac{Y}{\overline{Y}}=\frac{1}{\nu }\frac{Y}{K}$ holds, u=Y/K is established if we assume the capital coefficient (ν) to be 1 for the sake of simplicity.

4 We can rewrite Equation (1)(1) $$C=\left(1-t_w\right)wL+(1-s)(1-t_c)\left(hY+iD/p\right),$$(1) as follows: $C=\left[(t_w\hspace{0.17em}-\hspace{0.17em}{t}_c)\hspace{0.17em}-\hspace{0.17em}s(1\hspace{0.17em}-\hspace{0.17em}{t}_c)\right]hY+\left(1\hspace{0.17em}-\hspace{0.17em}{t}_w\right)Y+\left(1\hspace{0.17em}-\hspace{0.17em}s\right)\left(1\hspace{0.17em}-\hspace{0.17em}{t}_c\right)iD/p$. $\left[(t_w\hspace{0.17em}-\hspace{0.17em}{t}_c)\hspace{0.17em}-\hspace{0.17em}s(1\hspace{0.17em}-\hspace{0.17em}{t}_c)\right]$ represents changes in consumption expenditure to a unit change in profit (hY).

5 Bräuninger (2005) set the ratio of budget deficits to income as an indicator of fiscal policy in an overlapping generations model. He derived a different result to ours, finding that a rise in the budget deficit ratio hinders the growth rate.

6 In this article, although the government debt ratio (λ) is considered to be a long-run target variable of the government, this does not mean that the government can control the government debt ratio arbitrarily. The policy instrument that the government can set arbitrarily is the budget deficit ratio (δ). With this policy instrument, the realized value of the government debt ratio may differ from the target value.

7 The results that the tax rate for wage income does not affect the rate of capacity utilization, but the tax rate for capital income has a positive effect on the rate of capacity utilization are similar to those of Kalecki (1971) that an increase in tax on wage goods does not change total profit or national income, whereas a rise in the tax rate for capital income increases total profit and national income. However, this article derives the above results under the assumption of a budget deficit financed by debt, whereas Kalecki derives his results under the assumption of a balanced budget. For Kalecki’s theory of taxation, see Laramie (1991).

8 The total differentiation of the dynamic system composed of Equations (17) and (20) is given by (A) in the appendix.

9 This condition is similar to that found in Dutt (2006). He argued that the sign of the effect of an increase in workers’ borrowing on the growth rate depends on whether g>si or g<si. The only difference between the condition in the present study and that in Dutt (2006) is that the former additionally includes the tax rate for capital income.

10 Meanwhile, mainstream economists have argued that the long-run effect of expanded budget deficits on economic growth can be constrained by the possibility of the crowding-out effect (Elmendorf & Mankiw, 1999). However, the presence of the crowding-out effect is a contentious issue. Taylor et al. (2012) made use of an empirical study with U.S. data from 1961 to 2011 to argue for a positive effect on the growth of a higher primary deficit, even when possible increases in the interest rate are taken into account. Traum and Yang (2015) examined when government debt crowds out investment for the U.S. economy using an estimated New Keynesian model. They argued that higher debt can crowd in investment despite a higher real interest rate for a reduction in capital tax rates or an increase in productive government investment. Overall, they concluded that contrary to the conventional view of crowding out, no systematic relationship among debt, real interest rates, and investment exists.

11 The fact that a wage-led growth regime appears in the long run has to be modified if we consider the investment function with the profit share to be an additional determinant. By using an investment function of the Bhaduri–Marglin type, the long-run effect of the profit share on the growth rate is ambiguous and depends on the relative size of the parameters.

12 The Jacobian matrix and total differentiation of the dynamic system composed of Equations (26) and (27) are represented by (B) and (C) in the appendix, respectively.

Additional information

Funding

This study was financially supported by Wonkwang University in 2017. The basic idea of this article arose from the ongoing discussion with Dr. Sangheon Lee.