*This unpublished paper contains figures in its full version. Unfortunately I can’t work out how to include them. I’ll send the figures if requested.*

**Summary**

This paper derives a locus between the real exchange rate and net national savings (gross savings less gross investment). Its essence is that a rise in net savings reduces the real exchange rate. Conversely a rise in dis-savings increases the real exchange rate.

The derivation is based on the assumptions of standard trade theory and uses a standard model in which is introduced a third (non-tradeable) commodity of production and consumption. The standard assumption of full employment may be crucial.

The paper is in three main sections. The first gives a verbal intuition of the result; the second derives the formal result using a standard graphical model (an appendix derives the same result using simple algebra); the third explores the assumptions of the model and some possible extensions.

Interpretation of the relationship tends to be in terms of the net savings (and dis-savings) setting the real exchange rate. However what is derived here is a locus, so that in principle it might suggest that a real exchange rate determines net national savings, although it is harder to envisage circumstances in which the real exchange rate is exogenous (a government may fix the nominal exchange rate, but the domestic prices may alter to thwart any fixing of the real exchange rate).

**1. Intuition**

<>*This intuition is an edited version of a column ‘Boom time Rats’ published in “The New Zealand Listener”, 24 October, 2009.*(http://www.eastonbh.ac.nz/?p=1033)

Suppose a large highly productive foreign exchange earning sector evolved. It would squeeze the existing tradeable sector, which was not able to supply or conserve foreign exchange so efficiently including competing successfully for inputs from it. Ultimately the squeeze would operate by a lifting of the exchange rate, making the existing businesses earning or conserving foreign exchange earning less profitable.

That’s what happened in New Zealand about a century ago. Refrigeration unleashed the pastoral sector, enabling it to export meat and dairy products. Manufacturing was squeezed, falling from about 25% to 15% of the labour force. (Excluding the freezing and dairy processing industries, the fall was even more dramatic.) The new growth industry was more productive than those it displaced, so the economy was better off. The grumbles came from those in the displaced industries.

The scenario also applies when the emerging industry is mining. The exploitation of the North Sea gas fields reduced Holland’s manufacturing industry or during the mineral boom in Australia. The phenomenon is sometimes called the “Dutch disease” (after what happened to Dutch manufacturing when their offshore gas fields started producing)or the “Gregory effect” (after Australian economist Bob Gregory). It’s called a disease because when the gas or minerals run out, the country needs to expand its manufacturing industry to replace the lost earnings. But that is difficult, because of the enfeebled state of the industry.

We can simplify the analysis by imagining the mine is a vault containing bars of gold, which are exchanged for US dollars to buy imports. Same conclusion: up goes the exchange rate at the expense of tradeable production; exporting and import-substituting production diminishes.

Or suppose the vault contained IOUs that could be converted into US dollars. It is another source of foreign exchange, so the analysis is much the same. The exchange rate would rise and the tradeable sector would suffer because borrowing is an easier way to get foreign exchange.

But when this vault runs out, the situation is worse. Not only has the sustainable tradeable sector been damaged, as in the Dutch disease case, but the borrowings have to be serviced (and perhaps repaid), so there is an even greater need for foreign exchange in the long run.

In summary capital inflows lift the exchange rate at the expense of the ability of the economy to earn and conserve foreign exchange by production and sales.

That is exactly what has happened to the New Zealand economy since 2002, when it embarked on a splurge of foreign borrowing. Not surprisingly, the tradeable sector stagnated while the non-tradeable sector expanded rapidly, fuelled by the borrowing.

It is absurd to expect a central bank to hold down the currency while the country continues to borrow heavily offshore. Admittedly, some short-term measures can influence the exchange rate, but in the medium term the bank cannot keep the dollar low when there is heavy offshore net borrowing.

**2. A Graphical Representation**

Figure 1 has non-tradeable production on the vertical axis and tradeable production on the horizontal axis. PP’ is a conventional production possibility frontier (shown as a quarter circle).

It is assumed that the community consumption preferences are lexicographic – that is, the proportion of consumed non-tradeables and tradeables is fixed. This assumption is entirely for presentational convenience; the standard analysis of indifference curves which allow substation in consumption preferences could be included but it only adds to the complexity without adding to insights. (The algebraic formulation in the appendix has substitution at a cost of an extra parameter.)

More subtly the horizontal tradeable axis is measuring two different tradeable commodities. For the production frontier it measures the exportable commodity, but for consumption it measures the importable commodity. The analysis assumes there is a fixed terms of trade between the two (that is this is a small economy). The implications of a change in the terms of trade are discussed in the third section.

The lexicographic community consumption preference is represented by a diagonal OC from the origin which cuts the Production Possibility Frontier at E. This is the point where the economy consumes exactly what it produces (after exchanging its exportables for importables).

At E the real exchange rate (the price of tradeables divided by the price of importables) is tangential to the Production Possibility Frontier. It is represented by the line R_{1}R_{1′}.

Now suppose (for some reason) the real exchange rate is actually the line R_{2}R_{2}‘, which is a higher real exchange rate (that is, tradeables are cheaper relative to non tradeables.). The economy now produces at AB on the production possibility frontier (assuming full employment). At this point production of the non-tradeable amounts to AO and the production of the tradeable amounts to OB.

However given that all the production of the non-tradeables is consumed, it follows that the consumption point will be where the A to AB line intersects with the consumption line at AC, giving a total consumption of the tradeables as OC. Since production is only OB, the economy has to borrow CB measured in tradeables.

So we get the fundamental result. As the real exchange rate rises the amount of borrowing rises (or perhaps causally in the opposite direction).

Figure 2 shows the result which is derived from directly for Figure 1. Its exact shape depends on the various parameters but basically it is monotonically rising (as a consequence of the convexity of the production possibility frontier). Net borrowing is zero (in this example) where the real exchange rate is unity.

## 2. **Questions and Extensions**

*How important is the lexicographic consumption assumption?*

Not at all. Suppose substitution were allowed. As The real exchange rate rose, importables became cheaper and would increase relative to non-tradeable consumption. Thus C shifts out, the borrowing increases and the locus in Figure 2 is steeper.

*What about the terms of trade?*

The effect of an increase the terms of trade is to increase the amount of importables for a given amount of exportables. This will rotate the consumption preference line (and E) in an anti-clockwise direction. For a given real exchange rate the quantity of borrowing is reduced.

The reason is that the real exchange rate sets the production and consumption of non-tradeables, and now fewer exportables are necessary to pay for the matching importables. So there is less borrowing. Of course the real exchange rate may change when there is a change in the terms of trade, but that lies outside the scope of this model.

*If a country is borrowing offshore, then doesn’t it have to service the debt?*

Yes, Figure 1 describes an economy which has no offshore debt and it has just begun borrowing. Figure 3 generalises to when the economy has been borrowing and has to service OO’ debt (measured in tradeable prices). The lexicographic consumption function shifts left but remains parallel to the old one,now intersecting the horizontal axis at O’ rather than the origin. The line of non-tradeable production and consumption determined by the real exchange rate (A-AB-AC) intersects the new consumption line at AC’ (where AC’- AC equals O’-O).

The debt servicing appears as additional borrowing. Note that as the debt servicing rises E’ rotates in a clockwise direction, implying a need to reduce the real exchange rate if exportables and importables are to balance.

*Stein’s Law says this if it cannot go on forever, it wont. Doesn’t the model contradict Stein’s Law because it involves unlimited borrowing?*

Not really. The model assumes that lenders will continue to provide the funds to pay for the borrowing. They wont.

At some time the funding will be restricted. What that means is that net dis-savings (offshore borrowing) has to be reduced (sounds familiar?) and the real exchange rate has to fall (if full employment is to be maintained) and so will production in the non-tradeable economy as resources shift to the exportable sector.

*That sounds like a tricky transition.* Absolutely. These international trade models are not very rigorous when the economy shifts off the production frontier, while the shift along it is typically a long term process so they sd not rigorously describe the transition.

*Where do Interest Rates fit In?*

Presumably lenders require higher interest rates as the amount of borrowing increases. The exact behavioural function is a bit tricky, because it will depend on many things (including expectations and the state of the international economy). Whatever, it will be upward sloping.

Both the offshore debt and the current borrowing requirements will be important;the higher either is the higher will be the interest rate. What this means is the higher the real exchange rate the higher will be the interest rate that lenders require. The more prolonged the high interest rate – and hence the higher offshore debt – the higher will be the required interest rate too.

Stein’s law implies that sometimes the interest rate function will go inelastic, that is, no increase in interest rates will induce more funds to be borrowed. That’s when the phase comes to an end.

*Does that mean that interest rates are externally determined and the central bank has little influence on them?*

Apparently. It may be that there is some jiggle room, say fine tuning on the production frontier, or perhaps changing net dis-saving by encouraging savings and discouraging investment. That could lead to a fall in the real exchange rate. Contrary to the conventional wisdom this requires a higher exchange rate (to reduce the dis-saving) in order to reduce the real exchange rate. This needs to be explored.

**Appendix: A Simple Mathematical Formulation**

Suppose the economy consists of Non Tradeables (N) and produced/exported Tradeables (T).

Suppose the Production Possibility Frontier is given by

N^{2} + T^{2} = 1.

Suppose the real exchange rate (the price of non-tradeables relative to the price of tradeables) is r. (The economy will operate where the tangent touches the production possibility curve, in which case dT/dN = -r.)

The economy will produce at

N = r/ (1+r^{2})^(½)

T = 1/ (1+r^{2})^(½)

(The results can be derived a number of ways; perhaps the most elegant is to use trigonometrywith r = tan(θ). Substitution will show both conditions are met.)

Since the consumption of tradeables equals N, total borrowing is given by N-T or

(r-1)/ (1+r^{2})^(½)

which is the shape of Figure 2.

If the demand for consumption goods is not lexicographic, the demand for tradeables for consumption might be represented by r^{α}N, where α>1 (because one consumes more tradeables as the relative price of non-tradeables rise.

From which it follows that the offshore borrowing is

(r^{(1+α)}-1)/ (1+r^{2})^(½)

which is greater than (r-1)/ (1+r^{2})^(½).