Household debt, knowledge capital accumulation, and macrodynamic performance

Motivated to some extent by the empirical significance of student loans in the U.S., this paper incorporates knowledge capital formation by working households financed through debt to a demand-led dynamic model of physical and knowledge capital utilization and output growth. Average labor productivity varies positively with the average knowledge capital across the labor force. A rise in labor productivity resulting from knowledge capital accumulation is fully passed on to the real wage so that the wage share remains constant. In the unique long-run equilibrium, which is stable, an exogenous rise in the wage share raises the rates of physical capital utilization and output growth but has an ambiguous effect on the rate of employment (which also measures the rate of knowledge capital utilization). The long-run equilibrium also features the following interrelated results: the output growth rate is greater than the exogenous interest rate; the debt ratio (working households' debt as a ratio of either the physical or the knowledge capital, or the output) is independent of the interest rate; and the allocation of a higher (lower) proportion of wage income to debt repayment (consumption) raises instead of lowers the debt ratio, which we dub the paradox of debt repayment.