Thursday, 26 November 2015

International Balances and the Exchange Rate

I've read a few things recently on the complex relationships between interest rates, exchange rates and trade balances.

I like to approach this by starting with the stock variables.  We can imagine a simple global balance sheet matrix like that set out below.  This looks at the position of Country X, which uses Currency X (and we'll assume for simplicity that only Country X uses Currency X).  The assets in other currencies are converted into Currency X at prevailing spot rates, so that we can do some adding up.

So at a particular point in time, investors of Country X hold total assets of 100, which they need to allocate.  Being based in Country X, there will be some preference for investing in currency X assets.  However, those investors will probably also wish to hold some level of other assets to diversify their portfolio.  The balance will depend to some extent on potential returns in different currencies, with the return being a function of nominal interest rates in the respective currencies and potential exchange rate movements.

Currency X Assets

Other Currency Assets

Country X Investors
Rest of World Investors

Likewise, investors in the rest of the world will also want to diversify their investments, so they will want to include some Currency X assets in their portfolio.  Again they will take potential returns into account.  There will be many other factors, of course, effecting what assets investors choose to hold.  But, all other things being equal, the better the prospects for returns in a currency, the more of it investors will want to hold.

Just as Country X investors have a preference for investing in their own currency, so will investors in the rest of the world.  So, the greater the share of total investments held by Country X investors, the greater the overall demand for Currency X assets.

This is what determines exchange rates in the very short term.  At any point in time, the amount of assets in each currency is given, as is the assets of each investor class.  Taking interest rates as given, the exchange rate must find a level where investors want to hold the assets that are available in each currency.

Generally, if there are more Currency X assets than investors wish to hold, then Currency X needs to become cheaper and it will depreciate until it finds the right level.  However, since the right level depends on potential future movements of the currency, which in turn depends on what the exchange rate will be in the future, this can be hard to pin down.  I will come back to this.

So far we have said nothing about trade flows.  In fact, current account items do not matter in themselves.  There is no need for the current account to balance in either the short or the long term.  The relevance of trade flows and investment income is that, over time, they change the balance of assets.

So, if country X is running a persistent current account deficit, then there will be corresponding changes in our matrix.  This could be reflected in a growth of Currency X assets, as Country X finances its spending with borrowing[1], or it might be reflected in a reduction in the total assets of Country X investors (or some combination of the two).

The impact depends on what is going on with investors and assets in the rest of the world.  In combination, these changes may result in the ratios of values within the matrix remaining relatively stable.  However, they could lead to significant changes.  For example, Country X's persistent deficits might lead to Currency X assets becoming a greater and greater proportion of the whole.  In that event we might expect to see some consequences for interest rates and/or exchange rates.

We can see what is happening with interest rates, but we are left with the question of what drives expectations of exchange rate movements.  If today's exchange rate falls, we might hazard a guess that it is more likely to return gains in the future, but it all depends on where the exchange rate needs to be going into the distant future.  We seem to need some kind of target exchange rate to which the actual exchange rate will move over time.

In some models, this target exchange rate role is filled by a measure of purchasing power parity.  The framework I'm using here suggests a slightly different approach.  What it requires is that the exchange rate moves towards a level that allows the values in the matrix to remain in balance.  In a growth scenario, this would mean all the values ultimately growing at the same rate.  Any exchange rate that fails to meet this criterion will lead to an unsustainable position of ever diverging values.

We can write down models that reflect this.  By making certain assumptions about behaviours, we can trace out exchange rate paths that tend towards these steady state positions, while fulfilling relative return requirements along the way.  But it should be noted that there are many factors coming into play in these models, not least how fiscal and monetary policy are expected to develop into the future.  However clearly the equilibrium exchange rate might be defined under perfect foresight, the reality of exchange rate determination is probably closer to blind guesswork.

[1] I have assumed here that Country X borrowers only borrow in Currency X, but in reality they might borrow in different currencies.  The same issues apply, but this explanation is much simpler if we ignore that.  On the whole, it is much less common for an entity to borrow (other than on a matched basis) outside its functional currency than it is to invest.


  1. Nick,

    " towards a level that allows the values in the matrix to remain in balance."

    What do you mean by that?

    1. Hi Ramanan,

      I'm trying to invoke a kind of steady state growth path, where all the values in the matrix grow at the same rate. This requires the real exchange rate to be at a level where the trade balance is consistent with growth of the overseas balances (both inbound and outbound). The nominal exchange rate then depends on how prices respond to exchange rate movements and visa-versa. Does that make sense?

      I have some models that do this, so maybe I'll write something up for a post to illustrate it.

    2. Nick,

      So do you mean that there's an equilibrium reached in which stock/flow ratios converge to some value?

      I am reminded of the last line in Godley and Lavoie's book in which they claim that such a thing is not likely to work.

    3. All I'm really saying here is that we can write down models that wil produce this type of solution. But these models do require assumptions to be made about things like how prices adjust and how policy is constructed. I think these models are useful in helping understand the forces at work and how they interact.

      But I think it is very difficult to use this as a way of predicting real world exchange rate movements. For a start, I don't think you can meaningfully make statements about long term policy. We can ask the question what would happen if monetary policy took the form of inflation targetting for evermore, but one thing we know for sure is that will not happen. At some point, it will be done differently, exactly how being anyone's guess.

      So, basically, I'm saying we can produce models where the long run exchange rate is determined. But we have to make many assumptions to get there, so all we have is a model that helps us understand the dynamics, rather than know the answers. I would not disagree with G&L that it is not feasible to determine equilibrium exchange rates in practice.

  2. Interesting. Thanks.

    I think unsustainable is one of the key words. I think we can see currency moves or inflation as balancing factors, not totally unlike say defaults. Given all balancing mechanics the asset and liability balances of different currency areas march forward like a cointegrated process. I think that is a useful idealization. As you said it is probably not very effective way to determine expectations driven current valuations.

    The "matrix" idea can be applied to take into account different types of growth models. (Emerging) Country X might import a lot of capital for utilizing its growth prospects. Then in good case the external liabilities (maybe in its own X currency) can be matched with internal assets (in currency X). All the currency X assets rise on both side of the balance sheet and that is not unsustainable - rational investors are then favoring X currency assets more. If the country relies on Y currency (eg. USD) in its funding then it is more complicated.

    I think the real bill doctrine type of currency valuation given robust taxing ability of the government fits in the picture nicely.

    1. I think I'd agree with what you're saying. I haven't really explored variations of this with different growth rates, but my sense is the framework should still be applicable.

      The use by borrowers of debt in currencies other than their functional currency can easily be handled within this analysis, but it does make the explanation somewhat more complicated and, if you're trying to build a model, it adds many more equations.

  3. wow a lot of effort in this article , thanks

  4. Andrew Jackson9 June 2016 at 11:22

    Regarding the idea that we seem to need a target exchange rate which the current exchange rate moves over time, there is a parallel with Keynes’s theory of how speculators allocate their portfolios between assets. Basically the idea is that each speculator forms a view of the “normal” interest rate, which is the interest rate that they expect the current interest rate to eventually return to. Hence market rates above their “normal” rate lead to expectations of lower interest rates in future, and so speculators move from money into risky assets to take advantage of expected capital gains. Other things equal this will increase asset prices and lower the interest rate, as expected. Of course not every speculator will have the same view on what the normal interest rate is, and it is this divergence in views which allows interest rates (alternatively assets prices) to display some stability. This is because without divergent views all speculators would all switch from money to bonds whenever the current rate of interest was above the normal rate of interest (and vice versa), leading to large swings in asset prices.

    Anyway the point of all this is that it seems to me that it would be possible to port this theory over to exchange rates, so that each speculator forms a view of the normal exchange rate to which they expect the current rate to return. Then, just as with Keynes theory of interest rate determination, expectations of changes in exchange rates would push exchange rates in their expected direction, with divergences in views amongst speculators creating a degree of stability. Of course this is all pretty elementary stuff, I just thought it was an interesting parallel. The real trick is to understand how speculators form expectations of the normal exchange/interest rate. And there doesn’t seem to be much on this.

    1. I think you can see the portfolio allocation here either way. Imagine you have n investors each with the same v to invest. We could have each of them allocating their v between the different assets in exactly the same proportions, based on a certain level of expected future exchange rates and a given risk aversion. The aggregate allocation would then just be n times that for the individual. Or we could have each investor with a different expectation of future exchange rates and investing theire entire v in one or the other based on whether they thought the current rate was too high or too low. The aggregate would then reflect the ratio of bulls to bears. Or, of course, we could have some mix of the two.