Household Debt, Dynamic Stability, and Change in Demand Creation Patterns

Abstract

This paper examines dynamic stability and demand creation patterns of an economy in the context of the augmentation of household debt. First, we investigate the dynamic characteristics specific to an economy with household borrowing. Second, we reveal how demand creation and economic growth pattern change with the introduction of households' active borrowing. Our results shows that it is more favorable for the stability of an economy to politically control the interest rate on lending rather than to leave it to be determined by private financial institutions. Our results also indicate that even if the demand regime is wage-led, paradoxically, a rise in wage share may not necessarily stimulate economic growth. On the other hand, profit-led growth is more likely.

Acknowledgment

I would like to thank Akinori Isogai, Robert Boyer, Takashi Ohno, the participants at the 2009 meetings of the Japanese Society for Post Keynesian Economics at Nishogakusha University, and an anonymous referee for their helpful comments.

Notes

¹Setterfield (2004), examining a business cycle with financial fragility, introduced autonomous spending via debt finance of households and firms. But he aggregates the borrowing of households and firms. Other studies that incorporate household debt are: Dutt & Amadeo (1993) and Taylor (2004), who consider a model in which the liquidity constraint of household workers is relaxed through interest income from their deposits or wealth, and show that a rise in interest rate might stimulate their consumption demand via increased interest income. In contrast, the present study considers a case where the liquidity constraint on households is relaxed by borrowing.

²The debt/capital ratio represents the debt dependence of economy. Since we assume the potential output/capital ratio to be constant, it follows that, . We can rewrite , and thus, obtain the result: . By substituting the equations and , we can show that the second term of the equation above, , is always zero. Therefore, the term reflects the variation fo households' debt/potential output ratio, . Thus, we can regard as a proxy for the economy's debt dependence.

³In each time period t, the production of output X is determined by where both capital K and labor E are not zero. u and b represent the output/capital ratio and labor/output ratio, respectively. This formalization means that capital and labor are not substitutes for one another but instead complementary. We assume that there is a sufficient labor force in the economy and that capital is always effective on the short side. That is, output is determined by X=uK, and since represents the potential output at the current capital level K, the terms ‘output/capital ratio’, ‘capacity utilization rate’ and ‘effective demand’ can be used interchangeably to refer to u=X/K. In a steady state where capacity utilization becomes constant over time, the growth rate of capital K determines the growth rate of output X. Finally, the growth rate of labor demand E is determined by the growth rate of output X.

⁴See Palley (1991) and Fontana (2004) for surveys of the horizontalist and the structuralist views.

⁵Since an increase in wage income facilitates interest payment, it is also possible to suppose that the target rate of financial institutions is determined according to the income of households. Taking this into consideration, the target rate can be formalized as , and the derivative is negative. However, although such formalization does not change the result of the stability analysis, the analysis of the change in distribution and of the demand creation pattern becomes extremely complicated. Therefore, we ignore the effect of income on interest rate determination.

⁶This line is derived as follows. We denote equation (11) by the following function F:

For this function, the following condition ensures the unique existence of an equilibrium for the interest rate:

This assumption ensures that the target interest rate of the financial institutions is always positive and finite regardless of the actual interest rate. That is, this assumption means that the realized nominal interest rate cannot be negative.

⁷Since the numerator of equation (12) is assumed always to be positive, the domain of the abovementioned functions is

For this domain, we set the following function:

on which we get the following properties from the above discussion: , , and . These properties ensure the unique solution of in this domain of function. By substituting the steady state value of , which gives , into equations (12), (13), and (14), we can obtain the steady state value of the output-capital ratio and the interest rate on lending , respectively.

⁸Since the proof is rather complicated, we relegate it to the Appendix, which is available from the author upon request.

⁹When we refer to wage- or profit-led ‘demand’ we are concerned with the relationship between capacity utilization u and income distribution. When we refer to wage- or profit-led ‘growth’ we are concerned with the relationship between growth rate g and income distribution.

¹⁰Dutt (2006, p. 356) does recognize that profit-led growth is possible in his model if one sets the desired accumulation to depend positively on the profit share. Such an extension is important, because profit-led growth is an empirical fact. This is particularly true in the US, where household borrowing played a significant role, at least, until the subprime problem emerged. In this respect, our paper is a generalization of Dutt's model in terms of growth and distribution.

¹¹Taking US housing loans as an indicator, we can see that they increased significantly starting in the mid-1980s. While home mortgage debt was worth only $12.8 million in the first quarter of 1955, it reached $1009.6 million in the fourth quarter of 2004, according to the Flow of Funds Debt Tables published the Federal Reserve Board of Governors.

¹²The annual average wage share in the US was 66.0% in the 1980s, 65.1% in the 1990s and 64.8% from 2000 to 2008, according to calculations based upon Flow of Funds data compiled by Board of Governors of the Federal Reserve.