Refining the inclusion of debt in a simple growth model

In a September 8th post, I proposed a growth model for a country

growth in output = a*growth in (1+d) + growth in F

where a is a constant, d is the share of debt in the national economy, and F is all other factors like capital and labour. The derivation is in the earlier post. The logic is that increased production will occur in response to demand increases, and production will fall in response to demand decreases.

The argument can be refined to make allowance for the dual role of debt in funding consumers and companies. As debt rises or falls it may have an impact on business' ability to fund itself, so that realisable output can fluctuate. We assume firstly that banks can create money through loans during times of credit expansion, and secondly that some borrowers will find it difficult to repay at times of credit contraction so that banks will see their loanable funds fall. Thus companies will be more credit constrained during times of credit contraction than expansion. Thus, the effect of debt repayment will not be neutral as in the first model - repaying debt does not undo the earlier debt-funded economic expansion near perfectly. Rather, the effect of the repayment is to undo the expansion and additionally contract the productive capacity of companies. So the net effect of the increased borrowing, if it cannot be repaid, should be to contract the economy.

The model does not imply that debt is a hindrance for the economy. In the model it is essential for funding companies. But unrepayable debt may be a hindrance.

An empirical specification following from the theory would be something like

change in output =
a * change in (1+d) * a zero-one indicator that d is increasing
+ b*change in (1+d) * a zero-one indicator that d is reducing
+ c * growth in F
+ error term

since growth in debt and contraction in debt may have different effects.

One could also split d into different ranges to see what size of debt is non-contractionary for an economy.