Paperback buyer (Sorry, Sir Paul)

Does the exchange rate matter?

In the past week or two, an intriguing argument has been making the rounds in Almaty. The word is that the depreciation of the tenge, which traded at the rate of 180 per United States dollar a year ago and now trades at 330, nearly hitting 400 a few weeks ago, is not too important, since it doesn’t affect our ability to buy foreign goods.  It’s just a change in the local price of a dollar, a mere technical correction.

Strictly speaking, the argument is right, at least in the long run.  Our capacity to produce, and consequently to trade our goods for foreigners’, ultimately depend on how many workers and machines we have and on how much we know about producing.  It doesn’t depend directly on prices.  In principle, these will adjust in a way ensuring that we eventually employ all our inputs.  For example, if some people are out of work but want jobs, then they will offer to work at a pay cut.  The wage – the price of labor – will fall until firms find it profitable to hire them.

Similarly, the exchange rate, which we can express as the dollar price of a tenge, will fluctuate over time until it clears the currency market, just as the wage clears the labor market. If we have more tenge than we want to hold – that is, if we’d rather have more dollars – then the dollar price of a tenge will fall until we’re satisfied with the number of tenge that we have.  That’s why the dollar price of a tenge since August has dropped from 1/190 of a dollar to as low as 1/390. It’s rising now.

Trump priced

In short, like any other price, the exchange rate does not affect our ability to produce and thus consume in the long run.  Strictly speaking.

But strict speech is not always much help. In the short run, which is where we happen to live, the exchange rate does matter, and it does affect our purchasing power over foreign goods.

Consider American paperbacks selling for $10 each. To keep things simple, suppose that the exchange rate rises from 100 tenge per dollar to 200.  Then the tenge price of a US paperback will double, from 1,000 tenge to 2,000.  Suppose that you have 10,000 tenge. No matter how you slice it, you now can buy only five US paperbacks, not 10. Your foreign purchasing power has halved.

One way to express this purchasing power is in terms of Kazakhstani goods that we could have bought instead. Suppose that a paperback published in Kazakhstan costs 500 tenge.  Then the “price” of a US paperback is four Kazakhstani paperbacks, since we could have purchased these instead of spending 2,000 tenge on, say, Donald J. Trump and other natural disasters. Thanks to the new exchange rate, the price of this bestseller has doubled in real terms, from two to four Kazakhstani books. Once again, your foreign purchasing power has dropped 50%.

Here’s a handy formula for these ideas.  The price of the American book, relative to the price of the Kazakhstani book, is $10 / 500 tenge. This ratio isn’t very enlightening, since the numerator and denominator are expressed in different units (dollars on top, tenge on bottom).  If we could convert the dollar price to a tenge price, then the ratio would express the relative price of the Yank book clearly. The exchange rate provides that conversion.  The US paperback costs $10, and each dollar trades for 100 tenge, so the tenge price of the book is 10 * 100 tenge, or 1,000 tenge.  The relative price of the American paperback is 1,000 tenge / 500 tenge, or two (Kazakhstani books).

Currency chaos

In general, the price of a US good, relative to that of a Kazakhstani good, is e*P_us / P_kz, where P_us is the dollar price of the US book, P_kz is the tenge price of a Kazakhstani book, and e is the rate of exchange of tenge for a dollar.  Economists call this a real exchange rate, since it is expressed in terms of goods -- books, in our example -- rather than currencies.  (The number of tenge trading for a buck or euro is called the nominal or market exchange rate.)

In other words, the real exchange rate indirectly expresses our purchasing power over foreign goods.  If you have two Kazakh books, or enough tenge to buy them, then you can trade them for the Trump book.  If the real exchange rate rises to four, then you will need four Kazakhstani paperbacks to buy one American book.  In other words, with the formula I’m using here – it’s not the only way to express the real exchange rate – a rise connotes a greater expense of foreign goods (in terms of the domestic goods that you must give up) and thus a loss of purchasing power. Given your wealth, you can’t buy as many American books as you could before.

The formula matters less than the intuition: Purchasing power over foreign goods may change because of a modification in either the market exchange rate or the price ratio.  The rate of change in this purchasing power is roughly the rate of change in the market exchange rate plus the rate of change in relative foreign prices (that is, American prices divided by Kazakhstani prices).  Since last year, the rate of exchange of tenge for a dollar has risen 93%, and relative foreign prices have fallen 14%.  So the real exchange rate has risen considerably, roughly by more than two-thirds (see the Notes). The exact change matters less than the fact that it has been dominated by fluctuations in the market exchange rate.

Also notice that the exchange rate has risen while relative foreign prices have fallen.  That’s typical. A dollar can buy more tenge than it could last May, so foreigners want to buy more goods from Kazakhstan than before.  This pushes up Kazakhstani prices.  So US prices, relative to Kazakhstani prices, fall. In principle, they will keep tumbling until they fully offset the depreciation of the tenge. In the long run, the real exchange rate tends toward a value of 1; that is, the tenge price of the Trump book will be the same in the US as in Kazakhstan (never mind transport costs). That’s the law of one price. Whether it holds throughout the real world is controversial, but it has done pretty well in Kazakhstan.

The point to mark is that the market exchange rate changes more quickly than product prices do, so it dominates short-run changes in the amount of foreign goods that we can buy with our given tenge wealth.  Paperback buyers should keep their eyes on the currency market. As for paperback writers, well, you’ll have to consult Paul McCartney.  --Leon Taylor tayloralmaty@gmail.com

Notes

Here’s a way to decompose the change in the real exchange rate.  For simplicity, denote the real exchange rate as r, the nominal exchange rate as e, and the relative foreign price as p.  Then r = ep.  Taking natural logs yields ln r = ln e + ln p.  Take differentials by using derivatives: (d ln r/dr)*dr = (d ln e/ de)* de + (dp/dp )*dp. Finally, evaluate the derivatives and simplify: dr/r = de/e + dp/p.  Translation: The rate of change in the real exchange rate roughly equals the sum of the rates of change in the nominal exchange rate and the relative foreign price.  The approximation is most exact when the changes in r, e and p are small.

To calculate the change in the nominal exchange rate, I compared the average rate of exchange of tenge for a dollar for the first quarter of 2015 (185) to its counterpart for 2016 (357).  The data are from the National Bank of Kazakhstan.                                 

To calculate the change in relative foreign prices, I computed the change in the US Consumer Price Index (seasonally unadjusted) for each month in the first quarter of 2016, compared to that month in 2015.  I then took the arithmetic average of these three numbers and compared it to the average for the first quarter of 2015.  Finally, I did the same for Kazakhstan’s CPI.  The change in prices was 1.1% for the US and 15.1% for Kazakhstan.  The overall change in relative foreign prices was -14%.  The data are from the US Bureau of Labor Statistics (bls.gov) and the National Bank of Kazakhstan (nationalbank.kz).

Again, these figures are approximations.  A more precise approach may be to calculate log differentials directly, in order to decompose the change in the real exchange rate: d ln r = d ln e + d ln p, where d denotes a differential.  By my calculations, d ln e = .66 and d ln p = -.14.  Using these numbers, the change in the market exchange rate is more than four times larger than the change in the relative foreign price level.  The implied change in the log of the real exchange rate, as I have defined it here, is about .52.  Taking antilogs yields a value of 1.68:  The real exchange rate depreciated by about two thirds from the first quarter of 2015 to the first quarter of 2016.