A simple monetary Keynesian portfolio model

Keynes (1936, chapter 17) argues that every asset, such as wheat, copper, real estate as well as money has a rate of return which depends potentially on three elements: (a) the assets pecuniary rate of return, (b) carrying costs expressed in a rate, and (c) a non-pecuniary liquidity premium. The pecuniary rate is an interest rate or a profit rate. Carrying costs are for example costs to store an asset. We will assume carrying costs to be zero.The liquidity premium covers several dimensions. First, it expresses the subjective judgement how quickly an asset can be used for any purpose its owner wants to use it. It is also convenient and saves transaction costs to hold a liquid asset. Second, it expresses the subjective expectation how the value of the asset develops. If the asset is a credit claim it also can include the risk of default.Third, it includes the general trust in an asset including all subjective factors which makes it attractive to keep an asset or not. For example, wealth owners may have a preference to hold real estate as they believe this is an especially safe asset.

The liquidity' premium for money is of special importance. ‘The amount (measured in terms of itself) which they' are willing to pay for the potential convenience or security given by this power of disposal ... we shall call its liquidity premium.’ (Keynes 1936, p. 226, see also Keynes 1937, p. 316) Riese (1986) speaks in this context from the asset safeguarding quality⁰ which can be expressed in the liquidity premium of money. We can assume that money has usually the highest liquidity premium. However, in certain historical constellations ‘the possession of land has been characterised by a high liquidity-premium in the minds of owners of wealth’ (Keynes 1936, p. 241).This shows that the liquidity premium covers much more than liquidity' in the narrow sense. In our simple portfolio model, we assume two types of monetary wealth — liquidity' or shortterm monetary wealth and long-term financial wealth. Money' is here understood as liquidity including demand deposits, short-term time deposits and other liquid assets.The definition of liquidity depends on the concrete situation of a financial system. However, it should be clear that the character of assets as liquid can quickly' change. Short-term liquidity' earns a liquidity premium and a short-term interest rate. The latter is completely determined by' the central bank via its refinancing rate. Long-term financial wealth earns a long-term interest rate plus also a liquidity premium. For simplification we also assume that firms for investment purposes can only take long-term credits.

The portfolio equilibrium for monetary wealth is then

120 Hansjorg Hen and Zeynep Nettekoven or in gross returns

with i, as long-term interest rate, l_B as marginal liquidity premium of long-term interest-bearing wealth, l_M marginal liquidity premium of money, respectively short-term liquidity, and i, short-term interest rate determined by the central bank. We assume falling marginal liquidity premiums with increasing stocks of wealth held in an asset. For short-term liquidity' the fall of the liquidity premium with increasing liquidity holding may be small. In an extreme case of a so-called liquidity' trap, the marginal liquidity premium may not fall at all with an increasing stock of liquidity'.

The long-term interest rate increases when the central bank increases its refinancing rate, when the level of the marginal liquidity premium of short-term liquidity increases or the level of the marginal liquidity premium of long-term wealth decreases, for example because of the expectation of higher default rates.

The portfolio model also allows us to explain functional distribution of income in the monetary Keynesian approach. According to Keynes (1936, chapter 17) money earns a marginal liquidity premium which in an uncertain world does not go down to zero. Interest rates cannot fall, so Keynes, below the marginal liquidity premium. ‘If, however, the interest rate exceeds zero, a new element of cost is introduced which increases with the length of the process.’ This leads to a situation that ‘the prospective price has increased sufficiently to cover the increasing costs’ (Key'nes 1936, p. 216). In an economy of pure competition only' the existence of a positive interest rate allows profits; otherwise, competition would bring prices down to levels without profit. Of course, this model can be made much more complicated with the central bank fixing a minimum interest rate or with a certain spread between the interest rate and the rate of return of productive capital. A second explanation of profit is the existence of monopolistic, oligopolistic or monopsonistic markets, but this goes beyond this analysis (Herr 2019).

We transfer now this approach to the international level to analyse the hierarchy of currencies (see also Fritz et al. 2018; Kaltenbrunner 2015 as well as Bonizzi/Kaltenbrunner and Ramo/Prates in this book).The currency in which monetary wealth is denominated becomes an important and in many cases a dominant element to determine the level of the liquidity premium or the respective monetary wealth. Different currencies deliver for holder different convenience and a different asset safeguarding quality. It makes for an economic agent a difference, for example, to keep monetary wealth in United States (US) dollar or in Ugandan shilling. A representative Ugandan wealth owner may have a desire to hold US dollars whereas this desire is not very much distinct of US wealth owners.

To keep the analysis simple, we assume one domestic and one foreign country' and look only' at interest bearing long-term monetary wealth. The well-known interest rate parity formula 1 + i = (1 + i*)(//e) with i* as foreign interest rate, e as spot exchange rate (number of domestic currencies for one unit of foreign currency) and / as exchange rate in the future exchange market or the expected exchange rate, gives the condition for the same rate of return in both countries. Adding non-pecuniary rates with /_B as the marginal liquidity premium for long-term monetary wealth in domestic currency and /_B* as marginal liquidity premium for long-term monetary wealth in foreign currency, the condition becomes:

For example, if the United States is the domestic country and Uganda is the foreign country and Uganda wants to keep the exchange rate stable, an increase of US long-term interest rates or a higher marginal liquidity premium for longterm US monetary wealth would lead to an increasing interest rate in Uganda — enforced by a higher refinancing rate of the central bank in Uganda. A fall in ef/e (expected appreciation of the US dollar) leads to an increase of the interest rate in Uganda, otherwise the Ugandan shilling immediately depreciates.

Permanent and/or strong depreciations are hardly possible for developing countries. Depreciations may trigger expectation of further depreciation. Also depreciations most likely reduce the level of the domestic liquidity premium further. In addition, depreciations trigger inflationary pressures and a depreciation-inflation spiral may develop. A real depreciation reduces the living standard in a country which can be problematic in a developing country. Last but not least, in case of debt denominated in foreign currency, real depreciations increase the real debt burden with the effect of financial crisis.

If we assume that developing countries must keep the exchange rate stable (or have to avoid strong depreciations) this allows us to set the value of d/c as one. As the liquidity' premiums in each country' decrease with the stock of monetary wealth denominated in the country-specific currency, it follows /jj = /_B(MW) and I/* = l_B‘(MW*) with MW domestic and MW* foreign longterm monetary wealth in country-specific currencies. When we insert the two functions in equation 3 and set ef/e = 1 we derive:

The level of the marginal liquidity premium functions /_B = /_B(MW) and /_в* = //(MW*) depend to a large extent on the currency in which the monetary wealth is denominated.The marginal liquidity premium function of monetary wealth in US dollar has a much higher level than the marginal liquidity premium function of the Ugandan shilling. The convenience and security delivered for an economic agent keeping monetary wealth in US dollar must be judged much higher than for keeping monetary wealth in Ugandan shilling. Even if the interest rates in both countries are the same and the exchange rate stable, in a world of uncertainty a wealth owner would have a preference to keep US dollars. The different levels of the marginal liquidity premiums

122 Hansjorg Hen and Zeynep Nettekoven

Figure 9.1 Interest bearing monetary wealth held by a representative wealth owner in US dollar and Ugandan shilling assuming a stable exchange rate and the same interest rates in both countries.

of currencies signal the hierarchy of currencies. The different levels signal the different qualities of currencies. A currency with a relatively low level of the marginal liquidity premium is of relatively low quality.

To make the argument clear and its consequences, we assume that the marginal liquidity premium function of the Ugandan shilling is positioned below the marginal liquidity premium function of the US dollar. Let us in addition not only assume a stable exchange rate, but also the same interest rates in Uganda and the United States. Then it follows: (1 + (,) = (1 + /,*) = z with z being the value of this equation. From equation 4, it follows that in equilibrium: z + /_f( (MW) = z + l₈*(MW*). In Figure 9.1, the marginal liquidity premium functions for Ugandan shilling and US dollar of a representative wealth owner are shown. Monetary wealth held in both countries is measured in US dollar. As the level of the marginal liquidity premium function of the US dollar is on the top, in equilibrium monetary wealth held in Ugandan shilling (MW*) is much smaller than in the US dollar (MW).

What we see here is of fundamental importance to understand the relationship between the quality of a currency and underdevelopment. As behind the creation of monetary wealth stands the creation of credit, it shows that Uganda is seriously constrained to expand credits in domestic currency. The Schumpeterian-Keynesian credit-income-creation process mentioned above, which is the backbone of any prosperous development, is fundamentally constrained in countries with low quality currencies.

If we relax the assumption of the same interest rate a country like Uganda can increase the interest rate above the level of the United States. In this case, wealth owners keep more Ugandan shilling and Uganda can expand its domestic credit expansion without triggering depreciation. However, higher interest rates have negative effects for investment. In addition, higher interest rates change income distribution towards the rich and reduce in this way the growth chances of developing countries (Ostry 2015; Herr 2018).

The typical developing country will end up with a combination of higher interest rates than the United States and at the same time a lower stock of monetary wealth or credits in percent of gross domestic product (GDP) .This constellation very much fits to the empirical reality. In Table 9.1 it can be shown that private credit to GDP in 2018 was highest in high-income countries and lowest in low-income countries. If we take the United States as a comparison the table clearly shows that in a typical developing country domestic credit to the private sector as share of GDP is relatively low and/or the real interest rate is relatively high. Because of the highly regulated financial system, China is an exception.

A country with a low-quality currency can increase credit via credit denominated in foreign currency. In this case credit expansion can continue without increasing wealth in domestic currency. This sounds tempting. But the sweet poison of foreign debt is extremely dangerous. It creates currency mismatch and fragility of the financial system. As soon as credits are not rolled over

Table 9.1 Domestic credit to private sector in percent of GDP and real interest rates, selected countries, 2018

Source: WDI (2019) and credit expansion in foreign currency stops, a strong depreciation cannot be avoided, which triggers a foreign exchange and domestic financial system crisis without possibilities of the domestic central bank to stabilise the situation.