INDUSTRIAS QUÍMICAS

One final point needs to be made with respect to the concept of an index. Our definition refers to an average price, whereas all our numerical examples referred to price changes. The reason is that no unambiguous meaning can be attached to an average of prices for different goods. What meaning can we attach to the statement that the average of the price of salt and the price of petrol was £10 in February 1986? Apart from anything else, the figure will be unit dependent, in other words, if you use the price of a litre of petrol instead of a gallon, you will substantially change your price average.

If, instead, we look at percentage rates of price increase, we will be dealing with common units (per cent) and the weighted average will have an obvious interpreta- tion, which is the rise in the price of the typical good or service during the period in question.

We then face another problem: it is a rise in price, but since when? A price that has fallen by 2% in the past year may have fallen by 60% in the last two years but risen by 400% over the last 10. The only solution to this particular problem is to bear in mind that the choice of the period to be used for comparison, called the base period, is always arbitrary. Depending on the use to which the index is put, you may get a completely different impression if you change the base period.10_{(Note that, by con-}

vention, the value of the price index for the base month or year is usually set equal to 100.)

Subject to all these caveats, there is no reason in principle why an index cannot be compiled to keep track of movements in the price of any commodity or set of com- modities. For our purposes, we shall confine ourselves to considering the general level of prices. This means, in practice, the Retail (or consumer) Price Index (RPI), which is based on a sample of prices in shops and other retail outlets, and the Wholesale (or producer) Price Index (WPI), which measures prices ‘at the factory gate’. The former measures prices from the point of view of the household sector, including indirect taxes and distributors’ margins and so on and covers all goods and services in the typical consumption basket, whether imported or domestically pro- duced. The WPI, by way of contrast, is intended to be a guide to the underlying price level of inputs coming into and output leaving the firms in the corporate sector of the economy.

2.4

Purchasing power parity

Now, at long last, we are in a position to be able to understand the notion of pur- chasing power parity (PPP). The basic proposition will be seen to be very simple, although its ramifications are potentially much more complex. We shall build the theory by putting together the components we have assembled in Sections 2.2 and 2.3. To start with, suppose that we are dealing with two countries, the UK and USA. Assume transaction costs such as transport, tariffs and so on are negligible, so that the law of one price applies to all goods and services consumed. Under these circumstances, let us rewrite Equation 2.2. Instead of the superscripts L and NY for London and New York, we shall nominate one country, the UK, as the ‘home’ country, and leave its variables unsuperscripted, with asterisks as superscripts for the other, ‘foreign’, country.

60 Chapter 2 · Prices in the open economy: purchasing power parity

Now, remembering that C is zero, because we are assuming away transaction costs, we have:

Pi= SP*i i= 1 . . . N (2.3)

Notice the Ps have acquired subscripts, to show that they relate to the good or ser- vice number i. We had no need of a subscript in Sections 2.1 and 2.2 because we were always referring to a particular case of a specific good. Now that we have introduced the notion of a price index, we have to distinguish carefully between individual and general price levels. Equation 2.3 states that the law of one price holds with respect to the relationship between the domestic and foreign prices of good number i. We happen also to be assuming that Equation 2.3 holds with respect to all the goods (and services) consumed in the two countries. So, if there are N such goods, Equation 2.3 could be repeated N times over, with a different subscript each time, which explains the term i= 1 . . . N.

Now ask yourself the question: what can be said about the price index for the domestic country (UK) compared to that of the foreign country, for example the USA?

In general, not much – unless we make an additional assumption. One possibility would be to assume the weights used in compiling the respective price indices are iden- tical. In other words, suppose that, for each one of the N goods, we can say that its share in total US expenditure (and hence its weight in the US price index), is exactly the same as its share of UK expenditure. Under these circumstances, we can be confident that Equation 2.3 will apply equally to the general level of prices, so that we can write:

P= SP* (2.4)

where P and P* (without a subscript) refer to the home and foreign country’s price index respectively.

This is the simplest possible version of the PPP hypothesis and we shall return to it a number of times in one form or another throughout the rest of this book. To be more precise, Equation 2.4 is a statement of what is sometimes called the absolute purchasing power parity doctrine, which amounts to the following proposition:

Proposition 2.1. The general level of prices, when converted to a common cur- rency, will be the same in every country.

The remainder of this chapter will be spent exploring its implications, its short- comings and its ability to explain the facts.

Notice that we are dealing with a theory that predicts equality between national price levels translated, via the exchange rate, into a common unit of account. Nothing has so far been said about the mechanism that brings about this result. Now the drift of this chapter so far might seem to offer an obvious answer to this ques- tion. After all, if the prices of individual goods are aligned according to the law of one price, either as a result of arbitrage or the normal competitive trading processes, then it is to these forces one should look for an explanation of how PPP asserts itself. According to this microeconomic view, then, the PPP hypothesis is a natural con- sequence or a by-product of the law of one price, reflected at aggregate level.

2.4 Purchasing power parity 61

This however, is by no means the only way to arrive at a PPP equilibrium. It is equally possible to argue in favour of what we might call a macroeconomic approach, one that was hinted at indirectly in Sections 2.1 and 2.2. Suppose, instead of the prices of individual goods and services being equated internationally, it is the general price levels themselves that are brought directly into the relationship predicted by PPP. Those readers who have done some macroeconomics before now may well be familiar with simple models of how the price level is determined in a closed economy; in any case, the subject will be covered in Chapter 4. For present purposes, let us simply assume each national price level is determined by that country’s macro- economic policy in the same way it would be if the economy were completely closed. Then, given these independently determined national price levels, the exchange rate could move to satisfy PPP.

There are three points to note about this macroeconomic view of PPP. First, notice that it amounts to treating Equation 2.4 as one that determines the exchange rate. In fact, it is a simple version of what we shall later call the monetary model of

the exchange rate (see Chapter 5).

Second, it follows that this scenario presupposes a floating exchange rate. In periods when the exchange rate is fixed, PPP either fails to work or it is assumed to function in a different way, which is precisely the subject of the so-called monetary model of the balance of payments, also covered in Chapter 5.

Third, note that, in principle at least, this approach does not rely on the law of one price. However, it might still apply, even if there were wide divergences between countries in the price of individual goods and services. As was suggested in Sec- tion 2.2, even if there is no mechanism to equate the price of, say, haircuts inter- nationally, there may well be forces generating a broad equality between the cost of living in different countries.

In a sense, then, we would not require the law of one price to hold in each and every case – it might never hold for any good or service and, as we saw, the existing evidence is far from reassuring. It would be sufficient that upward deviations from the law of one price in the case of one good were offset by downward deviations in another case. For example, as between the UK and USA, it might be that relatively high prices for some UK services (hotels, restaurant meals and so on) are compens- ated for by relatively low prices for clothing, healthcare and so forth.

Notice also that, on this interpretation, we do not require equally weighted price indices. What we do require is no less restrictive, however: that if one good with a weight of 1% is overpriced by 50%, contributing (0.01 × 50%) = 0.5% to the general price level, there has to be another good contributing exactly −0.5%, for example, one carrying a 5% weighting underpriced by precisely 10%. This may seem unlikely, but, as with the law of one price, its plausibility or otherwise is ultimately an empir- ical question. In other words, the proof of the pudding is in the eating!

One final point about the interpretation of PPP. We have chosen to approach the subject by way of the real-world concept of a price index, for the essentially peda- gogic reason that it is one with which the reader should be familiar and one that is going to crop up in Chapters 5 and 7. But this is not the only way PPP can be viewed. At the very least, most economists would agree that none of the published price indices is anything like a perfect measure of the appropriate price level for PPP pur- poses. In part, the shortcomings may be the same ones that make the Retail Price

62 Chapter 2 · Prices in the open economy: purchasing power parity

Index, for example, an imperfect measure of the cost of living: problems of account- ing for differences of quality between products, problems of sampling prices actually paid, rather than listed prices, and so on. In other cases, the shortcomings may be of the kind that are really only significant in an open economy context, like the fact that different tax regimes and differing degrees of provision of public goods make inter- national cost of living comparisons highly questionable.

Since it is virtually impossible to remedy these deficiencies, you may have con- cluded by now that PPP is a dead duck, in advance of looking at the evidence. Apart from being premature, the judgement is also misguided, for the following reason. Even if there does turn out to be little empirical support for PPP, it is at least poss- ible that, because we are dealing with price level measures that are so imperfect, PPP is in fact alive and kicking in the real world. In other words, Equation 2.4 may be completely valid, but only with the ‘true’ price level variables which are unobservable and only very distantly related to what we actually observe, that is, the published UK and US price statistics.

In that case, you may think PPP is untestable, because it relates to unobservable variables and not of much practical use for the same reason. As we shall see in Chapter 5, that conclusion does not necessarily follow either. If the true price levels (in other words those relevant to PPP) are in fact related to other observable vari- ables, then the PPP hypothesis becomes fully operational. Of course, that does not make it any more likely to be true.

Whether true or not, PPP is an important benchmark for the analysis of exchange rate movements, particularly insofar as they impinge on international competit- iveness. If the general level of prices is a reasonably accurate index of the cost of production in a country (and this is almost certain to be the case) then the ratio of price levels for any two countries will serve as a measure of relative competitiveness. Notice that if PPP could be relied on to obtain at all times, competitiveness meas- ured in this way would not only be constant, it would in some sense be equalized across different countries. No country would have a price advantage over another, at least in terms of the broad spread of goods and services represented by the general price level. In practice, as we shall see, international competitiveness has been far from constant in the post-war world. For this reason, economists often wish to measure deviations from PPP and the concept most often used for this purpose is the so-called real exchange rate:

The real exchange rate is the price of foreign relative to domestic goods and services.

Formally, it is measured by:

Q= SP*/P (2.5)

Notice that an alternative interpretation would be to say that it amounts to the exchange rate as we have so far understood it (that is the nominal exchange rate, S), corrected for relative prices, P*/P.

If PPP holds, then the value of Q ought, in principle, to be one, as you can see from Equation 2.4. In practice, however, no meaning can be attached to the absolute

2.4 Purchasing power parity 63

size of Q, for the same reason that the absolute level of a price index is meaningless, as we saw in Section 2.3.

To see that this is the case, suppose that at some point in time the UK price index is 200, while the US index stands at 250 and the exchange rate is £0.80 = $1.00. (Check that PPP holds and Q= 1 for these figures.) Now recall that the choice of base year for an index is completely arbitrary. Choose a different base period for an index and you will always end up with a different figure, unless by chance the index in the new base period is the same as in the old. So rebasing either or both of the price indices in our example will disturb the apparent equilibrium. Moreover, it will not help to base both UK and US price indices on the same period, as all that does is to arbitrarily set both price levels to equality (at 100).

For this reason, it makes more sense to think in terms, not of price levels, but of rates of change. In this form, the relative purchasing power parity hypothesis states that:

One country’s inflation rate can only be higher (lower) than another’s to the extent that its exchange rate depreciates (appreciates).

To reformulate our PPP Equation 2.4 in terms of rates of growth requires a little elementary calculus. First, take logs of Equation 2.4. Using lower case letters to denote logs, this gives us:

p= s + p* (2.6)

Now if we take the derivative of a natural logarithm, we arrive at the proportional rate of change, that is d(log P) = dp = dP/P and so on. In the present case, differenti- ating in Equation 2.6, we have:

dp = ds + dp* (2.7)

This equation only says that the home country’s inflation rate, dp, will be equal to the sum of the foreign inflation rate, dp*, and the rate of currency depreciation, ds.

It might be more illuminating, perhaps, to rewrite Equation 2.7 as:

dp − dp* = ds (2.8)

which says that the domestic country can only run a higher rate of inflation than the foreign country if its exchange rate falls pro rata. One way of interpreting this rela- tionship is simply as an extension of the familiar idea that when prices rise, the value of money falls. The more rapidly prices rise, the faster the value of money falls. In a two-country context, the more rapidly prices rise in the home economy relative to the foreign country, the more rapidly domestic money loses its value relative to foreign money – or the more its exchange rate depreciates.

Notice that the reformulation in terms of rates of change avoids all the difficulties of choosing a base for the price index. There is no problem in defining unambigu- ously the rate of inflation or the rate of exchange rate depreciation – at least, no problem of the kind involved in making the absolute PPP hypothesis operational. That is why, although absolute PPP often figures in theoretical models, it is only relative PPP that can actually be tested by an examination of the evidence.

Before going on to do just that, there is one important loose end to be tidied up. When discussing the law of one price, it was freely admitted that allowance would need to be made for transaction costs such as transportation, tariffs, non-tariff bar- riers and so on. Surely these costs ought to figure somewhere in our PPP equations, if PPP follows from the open economy version of the law of one price?

Rather than deny this obvious fact, the economics literature copes with the prob- lem in one of the following ways:

(1) For some purposes, where nothing very important hinges on the way it is specified, economists have tended to use the unadorned versions of absolute or relative PPP, as in Equation 2.4 or Equation 2.7 on the grounds that transaction costs are small enough to be negligible.

(2) If not negligible, it could be argued that most of the main elements in the total cost of trading vary in proportion to the value of the goods in question. For example, as already noted, tariffs are often charged ad valorem, transportation charges may frequently be related to the value of goods shipped and items such as insurance premiums will almost invariably bear some more or less fixed rela- tion to price per unit.

This being the case, if we make the assumption that all these costs are pro- portional to price, it is easy to see that they will not figure at all in our relative PPP Equation 2.7. Look back at the steps on the way from Equation 2.4 to Equation 2.7. Retrace them, starting with an absolute PPP equation modified to take account of transaction costs:

P = K(SP*) (2.4′′)

where K is a constant, greater or less than unity, covering the total cost of con- ducting international trade. As before, take logarithms:

p = k + s + p* (2.5′′)

From here, it is easy to see that we end up with the same result for relative PPP as before, simply because when we differentiate Equation 2.5, the cost term will disappear. (Remember that the derivative of a constant like k is zero.)