# External debt sustainability and devaluations

Kohler (2017) follows a different approach. The objective of his model is to analyse external debt sustainability' and to evaluate how a devaluation may kick external debt out of that stable path, when that debt is denominated in a foreign currency. In the model firms can borrow both from domestic banks and from international lenders, so that strong negative balance sheet effects on firms may counteract the positive impact of a devaluation on the trade performance.

The goods market is depicted in a usual Kaleckian fashion. Prices are set with a mark-up over (labour) costs. The mark-up determines the profit share and the wage share. The real exchange rate may affect the mark-up in either direction, according to the bargaining power of capital and labour, as in Blecker (2011).

Firms may borrow from domestic banks (B) or from foreign lenders *(eB *^{f}), while banks accept deposits from foreign investors (D).While Kohler assumes that *B** is always positive, it can be the case that *В* becomes negative, and even that *eB ^{1} + В <* 0 , in which case domestic banks would actually have a

*creditor*position with the rest of the world, and a

*debtor*position with regards to firms. Let us call A the ratio of external indebtedness to the nominal capital stock

*eB ^{1}* . В

(-= *e _{t}A), X* the ratio of domestic debt to the capital stock (-) and

*r*

*pK pK*

the profit rate (-). Savings arise out of profits minus interest payments, as in

*pK*

Equation (7):

Investment depends, as in most Kaleckian models, on capacity utilisation and the profit share. But also the external-debt-to-capital ratio exercises a depressing influence on investment. Due to currency mismatch, devaluations may end up deteriorating the balance-sheet of firms:

The balance of trade, in turn, reacts to domestic and foreign capacity utilisation, and to the real exchange rate:

However, it is *not* assumed a priori that the influence of the real exchange rate will be positive, i.e. whether *b _{{}* is greater than zero. It may or may not, depending on whether the Marshall-Lerner Condition holds or not. The usual Keynesian stability' condition, in turn, requires that savings and the balance of trade react stronger to changes in capacity' utilisation than investment.

In this short-term model, external debt has detrimental impact on the equilibrium levels of capacity utilisation and growth, the intensity of the impact depending on the reaction of investment to external debt £_{3}. External debt can also counteract the eventually positive impacts of real devaluations on capacity utilisation, if the Marshall-Lerner Condition holds.

So far, this is a traditional short-run Kaleckian model. But in the medium- run, the external-debt-to-capital ratio becomes and endogenous variable. This rises up the question of how firms fund their investment plans. They have three alternatives: either through retained earnings, through domestic debt or through foreign debt. The latter is somewhat cheaper than the former, because of a liquidity premium usually charged on domestic borrowing p_{0}. Lenders are also concerned about booming debt, and increase their lending rates accordingly, though the sensitivity of domestic and external rates can be different:

There are a couple of issues to keep in mind. Debt dynamics is not only affected by retained earnings and investment funding, but also with the repayment of principal and interest. Second, in the model, there is a preferential order with regards to the sources to fund investment and interest payments: retained earnings and external debt borrowing take primacy with regards to domestic debt, which accommodates any difference between required funds, retained earnings and external debt:

The reason behind is that external debt is usually cheaper than domestic borrowing, as mentioned in Equations (10)—(11). Third, external currency amounts to a *proportion* of total investment, but that proportion is not constant. In fact, it changes with the difference in the relative costs of both types of borrowing. In linear terms, we have:

Where *ф _{0}* includes the liquidity premium

*p*and

_{n}*ф*the relative sensitivity of domestic and external rates to rising external indebtedness. The dynamics of the ratio is explained by Equation (14):

_{1}

The last part of equation (14) makes use of the fact thate) is equal to zero (because the exchange rate is fixed and inflation is assumed away), that *g *reached its short-run equilibrium value *g*,* and of Equation (13).

The other state variable is the domestic-debt-to-capital ratio T. As said in Equation (12), domestic debt accommodates the differences between financial needs (investment and interest payments), retained earnings and external debt. The equation describing the dynamics is:

Making use of Equation (12), Equations (10) and (11) for the interest rates, Equation (13) for the dynamics of external debt, and noting again that inflation is assumed away, we obtain (15’):

Now we have a two-dimensional dynamic system on *e,A* and f:

Calculations are easier once we realise J_{12} is zero. So we are interested in the signs of *J*и and /_{22}, both of which have to be negative in the surroundings of equilibrium for stability purposes.The sign of J_{n} is negative if:

So, as long as the equilibrium growth rate is positive, and domestic rates are not *too* sensitive to external indebtedness (low value of 0,), then external debt is stable. What is the reasoning behind this relation between *domestic* rates and *external* indebtedness? It may be the case that, concerned by high external indebtedness, foreign investors leave the country and the central bank is forced to increase interest rates, therefore increasing the financial needs of firms.This is the instability case. In normal times, as long as money flows in, *J _{u}* is negative.

In turn:

For stability, the equilibrium growth rate must be greater than domestic interest rate, the usual condition for public debt sustainability. In this model, however, things might be somewhat out of the control of central banks: a shock to the liquidity premium might send the system into unstable territory. Also a high

debt ratio j and high sensitivity of domestic rates to the steady state

external debt ratio (p,) may complicate the stability of domestic debt.

An interesting question Kohler (2017) addresses is the effect of currency devaluations on the sustainability of external debt. As long as a devaluation stimulates capital accumulation, the effect will reinforce the stability of the system. But if they depress investment (say, because they are strongly contractionary), the effect is the opposite, even if the balance of trade improves. In that sense, the wage-led or profit-led nature of the demand (and growth) regime has an important bearing on the results of the model. Debt crises out of devaluation episodes can also happen even when the balance of trade moves into surplus.