Unit 7 Macroeconomic policy in the global economy

7.3 A flexible exchange rate regime with no stable inflation target (FlexNIT)

In two of the three policy regimes set out in the previous section, the government deliberately ‘ties its hands’: in a FlexIT economy by giving independence to an inflation-targeting central bank; in a Fix economy by giving up domestic monetary policy entirely.

To understand why governments choose to tie their hands, we first consider the case of a FlexNIT economy—in which the government does not tie its hands: a country with a flexible exchange rate, but without the discipline of an inflation target. As a result, it conducts its own monetary policy—but is susceptible to problems controlling inflation. We also show in this section that exchange rate flexibility may then exacerbate inflationary pressures.

The real exchange rate with a flexible nominal exchange rate

Consider the definition of the real exchange rate (competitiveness) between two countries:

\[c = \frac{e \times P^*}{P}\]

Taking the foreign price level, \(P^*\), as given, the formula tells us that there are two ways in which the real exchange rate can change in a flexible exchange rate regime: either through domestic inflation, or through changes in the nominal exchange rate.

Starting with a FlexIT regime in both the domestic and foreign countries, if they had similar inflation targets and get close to those targets, then \(P\) would change at approximately the same rate as \(P^*\), so the price ratio, \(P^*/P\), would be reasonably stable.

As a result, in a FlexIT economy, a change in the nominal exchange rate, \(e\), typically translates into a similar proportional change in the real exchange rate, \(c\). As illustrated in Figure 7.5, this is the mechanism in a FlexIT regime through which exchange rate adjustment reinforces the central bank’s interest rate decision.

However, in the FlexNIT regime, the central bank does not have an inflation target. So things work differently. We begin by rearranging the expression for the real exchange rate. Dividing both top and bottom of the fraction by the foreign price level, \(P^*\), we can write the real exchange rate as:

\[c = \frac{e \times P^*}{P} = \frac{e}{P/P^*}\]

In words:

\[\text{Real exchange rate} = c = \frac{\text{Nominal exchange rate}}{\text{Price ratio}}\]

This tells us that, other things being equal, a rise in \(e\) (a depreciation) will translate to a rise in \(c\) (a real depreciation or improvement in home competitiveness), but that will be offset by any increase in the price ratio, \(P/P^*\) (home prices relative to those elsewhere). The price ratio will increase if domestic inflation is higher than foreign inflation.

If one country has systematically higher inflation than another, it would lose competitiveness continuously unless its nominal exchange rate depreciated continuously to offset this. But if both the nominal exchange rate, \(e\), and the price ratio, \(P/P^*\), rose in proportion (for example, if both doubled) then the real exchange rate and home’s competitiveness would not change at all.

To understand the implications of this relationship, we again analyse the impact of a positive aggregate demand shock, as in Figure 7.5, but this time without the discipline of a stable inflation target.

FlexNIT regime: The impact of a positive domestic demand shock

To clarify the contrast with the FlexIT case, we start from the same initial position as in Figure 7.5. A country is hit by a demand shock that is specific to the domestic economy. Follow the steps in Figure 7.7 to analyse what happens next.

The impact of a positive demand shock on a country with a flexible exchange rate regime and no inflation target, FlexNIT. (Contains Question 7.6.)
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https://www.core-econ.org/macroeconomics/07-macroeconomic-policy-global-economy-03-flexible-exchange-rate-regime.html#figure-7-7

Figure 7.7 The impact of a positive demand shock on a country with a flexible exchange rate regime and no inflation target, FlexNIT. (Contains Question 7.6.)

The initial effects of a positive demand shock:
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The initial effects of a positive demand shock

We start by assuming the domestic economy is initially in supply-side equilibrium, with actual inflation and expected inflation both at 2%.
There is then a positive demand curve shock that shifts the curve upwards to \(AD_1\).
The initial impact will be the same as in Figure 7.5.

Inflation rises:
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Inflation rises

The initial impact on inflation is the same too: it increases to 4%.
Here is where the difference between the regimes comes in.
With independent monetary policy and an inflation target, the central bank responds to the rise in inflation by increasing the policy interest rate to offset the impact of the demand shock.
However, in an economy with a flexible exchange rate, but without an inflation target, this mechanism does not come into play, which means that the economy can, for now, at least stay at \(Y_1\). But not without consequences.

Question 7.6 Choose the correct answer(s)

Read the following statements about potential consequences and choose the correct option(s). Assume the demand shock is one-off and lasts a few periods.

  • The Phillips curve will shift upwards in the next period.
  • Output will eventually return to \(Y_0\).
  • Inflation will eventually return to 2%.
  • Inflation will eventually stabilize but at a rate higher than 2%.
  • The Phillips curve will shift upwards because inflation expectations change from 2% to 4%. (There is no inflation target to anchor expectations.)
  • The demand shock is one-off (the AD curve shifts upwards once) so output will eventually return to its initial level.
  • Inflation will not return to 2%; it will keep rising because inflation expectations are not anchored.
  • When output eventually returns to \(Y_0\), inflation will be stable but higher than 2% since there is no inflation target to anchor expectations at 2%.
Inflation expectations change:
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Inflation expectations change

One very likely consequence is that, without the ‘anchoring’ of inflationary expectations, the new higher inflation rate will become embedded in inflation expectations, meaning that the Phillips curve will shift upwards, such that last year’s inflation becomes the new expected inflation.
So if output remains at \(Y_1\), with employment above the supply-side equilibrium, inflation will rise further.

Inflation becomes permanently higher:
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Inflation becomes permanently higher

By the time the temporary demand shock has ended and output has fallen back to its initial level, actual and expected inflation have both risen further. (Here we assume 10%.)
As a result, higher inflation becomes embedded into the system.

Figure 7.7 shows that without the discipline imposed by an inflation target, there is nothing to stop inflation drifting upwards, as inflationary expectations adjust at each round of wage and price setting. As a result, by the time the demand shock unwinds, higher inflation will have become embedded in the system.

In the example in Figure 7.7, inflation in the domestic economy ends up stabilizing at 10% while it is 2% elsewhere. What does this imply for the nominal exchange rate?

Different long-run inflation rates and nominal depreciation with a flexible exchange rate

At supply-side equilibrium, the real exchange rate (competitiveness) must be constant—otherwise, net exports and therefore output and employment will change and it will not be an equilibrium.

The formula for the real exchange rate shows that it changes if the nominal exchange rate changes, or if the home and foreign inflation rates are different. But with a flexible exchange rate, it is possible in principle for the exchange rate to adjust to keep competitiveness constant when inflation rates differ. If home’s inflation is higher than abroad’s, then home’s competitiveness can stay unchanged as long as its nominal exchange rate depreciates enough.

To formulate this more precisely, we introduce a new Greek letter, \(\delta\) (lower case ‘delta’, the Greek letter ‘d’), to represent the rate of depreciation of the nominal exchange rate. If \(e\) changes from \(e_0\) to \(e_1\) over one year, the depreciation rate is:

\[\delta = \frac{e_1 - e_0}{e_0}\]

and \(\delta > 0\) implies that the nominal exchange rate is depreciating: that is, an increase in the price of foreign currency in home currency.

When we carefully examine the expression for competitiveness:

\[c = \frac{e \times P^*}{P}\]

we can work out how c changes in response to inflation and depreciation:

  • Depreciation, \(\delta\), increases \(e\), raising \(c\).
  • Foreign inflation, \(π^*\), increases \(P^*\), raising \(c\).
  • Domestic inflation, \(π\), increases \(P\), reducing \(c\).

The overall effect can be summarized by:

\[\text{Rate of change of competitiveness} \approx \delta + \pi^* - \pi\]

Remember: a real depreciation implies that the relative price of foreign goods increases, so home competitiveness improves. In Extension 7.3, we show how to derive the approximation mathematically.

In words, this says that the rate at which the real exchange rate depreciates is approximately equal to the rate at which its nominal exchange rate depreciates plus the extent to which foreign inflation abroad exceeds home inflation.

We argued at the start of this section that supply-side equilibrium requires that competitiveness (the real exchange rate) must be constant—otherwise, output and employment will be changing. The expression above for the rate of change of competitiveness implies that competitiveness will remain constant (its rate of change will be zero) only if the right-hand side of the expression is precisely zero. Rearranging this expression, we have:

\[\text{Constant competitiveness} \Rightarrow \delta = \pi - \pi^*\]

That is, for the real exchange rate to be stable, the rate of depreciation of the nominal exchange rate must exactly offset the difference between inflation at home and abroad. If home has higher inflation, the nominal exchange rate must depreciate to maintain competitiveness.

For example, assume that inflation abroad is 2%, and domestic inflation has stabilized at 10%. Then constant competitiveness implies that the nominal exchange rate must be depreciating at a rate of 8%. Note that we have not said that the nominal exchange rate will end up depreciating by this amount—just that, unless it does, the real exchange rate will be appreciating or depreciating. This would have an impact on the real economy (output and employment), taking the economy away from its supply-side equilibrium.

Question 7.7 Choose the correct answer(s)

Read the following statements and choose the correct option(s).

  • The real exchange rate can be expressed as the nominal exchange rate divided by the price ratio, where the price ratio is prices in the home country relative to prices abroad.
  • If there was an appreciation in the nominal exchange rate, and the price level at home rose faster than the price level abroad, it is possible that competitiveness would remain unchanged.
  • If the foreign inflation rate is equal to 2%, the domestic inflation rate is equal to 8% and the rate of depreciation is equal to 3%, then we would expect the rate of change of competitiveness to be approximately equal to 7%.
  • An appreciation of the real exchange rate would make imports cheaper, but could lead to a decline in demand for the country’s exports, and hence a decline in output and employment.
  • \(c = eP^*/P = e / (P/P^*)\), or in other words, the nominal exchange rate divided by the price ratio. \(P\) refers to prices in the home economy and \(P^*\) refers to prices abroad.
  • If there was an appreciation in the nominal exchange rate (a decrease in \(e\)) and domestic inflation was higher than inflation abroad, then \(c\) would definitely decrease (a real appreciation and a decline in competitiveness).
  • The rate of change of competitiveness would be approximately equal to \(3\% + 2\% \text{ } – \text{} 8\% = \text{ } –3\%\). In this case, the real exchange rate would be appreciating at a rate of approximately 3%.
  • There may be a decline in employment in exporting sectors, as well as a decline in employment in sectors where domestic production competes with imports.

Without a stable inflation target, changes in the real exchange rate may reinforce shocks, rather than stabilizing them

Figure 7.5 shows that in our benchmark FlexIT economy, changes in the real exchange rate play an important role in stabilization. When a positive demand shock hits the economy, the central bank tightens monetary policy, and the resulting appreciation of the nominal and real exchange rate depresses aggregate demand, thereby reinforcing the impact of the monetary contraction.

What would we expect to happen in a FlexNIT economy with its own monetary policy, but without a stable inflation target? Without a clear objective of stabilizing inflation, there is a real possibility that exchange rate movements may actually amplify shocks. This will be the case where the government attempts to maintain aggregate demand higher than the level consistent with equilibrium unemployment. This has indeed been quite a common feature of such economies.

Figure 7.8 describes the interaction between changes in the exchange rate and inflation in a FlexNIT economy during the period when inflation is increasing. This illustrates the possibility that, in order to maintain a given level of output, the policymaker may seek to maintain a competitive real exchange rate when inflation picks up, by allowing the nominal exchange rate to depreciate to offset the impact of inflation on competitiveness.

The depreciation will initially accentuate the impact of the demand shock by increasing net exports; but the depreciation will in turn boost inflation through its impact on import prices. Wage inflation will respond to the higher cost of living. As inflation picks up, nominal depreciations will need to become progressively larger to offset the impact of inflation on the real exchange rate. For as long as the policymaker attempts to keep a competitive real exchange rate, the outcome is likely to be a mutually reinforcing spiral of depreciation followed by higher inflation followed by ever-larger depreciations.

Positive demand shock in a FlexNIT economy: an inflation–depreciation spiral.
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Figure 7.8 Positive demand shock in a FlexNIT economy: an inflation–depreciation spiral.

Effect on inflation:
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Effect on inflation

Figure 7.8a

Effect on the price ratio:
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Effect on the price ratio

Figure 7.8b

Impact of inflation on the real exchange rate if the nominal exchange rate stayed unchanged:
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Impact of inflation on the real exchange rate if the nominal exchange rate stayed unchanged

Figure 7.8c

Monetary policy relaxes:
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Monetary policy relaxes

If the policymaker wants to prevent a real exchange rate appreciation, they will loosen monetary policy by choosing to not raise, or to even cut, nominal interest rates when inflation increased, thus lowering real interest rates.

The real exchange rate depreciation is only temporary:
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The real exchange rate depreciation is only temporary

Figure 7.8e

Inflation rises:
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Inflation rises

Figure 7.8f

Effect on the price ratio and competitiveness:
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Effect on the price ratio and competitiveness

Figure 7.8g

The impact of further nominal depreciation:
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The impact of further nominal depreciation

Figure 7.8h

The spiral continues:
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The spiral continues

For as long as the policymaker continues to attempt to offset the impact of inflation on the real exchange rate, the process will continue, with the risk of a destabilizing spiral of depreciation and inflation, both responding to each other. This spiral results in increasingly large shifts in both the exchange rate and inflation.

For how long this process goes on will depend on the extent to which the general public is prepared to tolerate ever-rising inflation, and whether the policymaker takes this into account. Below, we will discuss evidence of this process in Spain, before it adopted the euro. But first we consider the objectives of the policymaker.

Why might a policymaker allow an inflation–depreciation spiral to take hold?

We know that both high unemployment and high and rising inflation are unpopular because they cause real suffering for households (as discussed in Unit 4). But unless the government is willing and able to make improvements on the supply side of the economy to reduce equilibrium unemployment, it faces an unpleasant trade-off between unemployment and inflation.

The attempt to keep unemployment below equilibrium implies a positive bargaining gap. Combining this with the updating of inflation expectations produces ever-increasing inflation, as shown in Section 4.6. In the model in Unit 4, the economy had no interactions with the rest of the world. We now extend that analysis to an economy integrated in global markets.

In a flexible exchange rate economy without an inflation target (FlexNIT), if the policymaker tries to keep unemployment below equilibrium, it will result in inflation at home rising above inflation abroad. To prevent competitiveness from worsening, with the associated decline in exports and rise in unemployment, the government must keep monetary policy loose and allow the exchange rate to depreciate. But this will raise inflation further. The only way to keep unemployment below equilibrium is to have a process of rising inflation and an ever more rapidly depreciating nominal exchange rate.

This flowchart shows the effects of loose monetary policy in a FlexNIT economy. Last period’s inflation becomes the expected inflation. When combined with the bargaining gap, this leads to high domestic inflation and a decline in export competitiveness. Policymakers respond by maintaining loose monetary policy, which causes the nominal exchange rate to depreciate. The depreciation has two effects: it increases the price of imports, raising overall prices, and restores competitiveness. Inflation rises as a result of the increased prices.
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Figure 7.9 The effects of loose monetary policy in a FlexNIT economy.

An example: Spain before the euro—Floating exchange rates and inflation

For almost 30 years before Spain joined the eurozone in 1999, it had a FlexNIT regime, with its own currency, the peseta. Figure 7.10 shows what happened to inflation and the exchange rate during this period, and helps to provide background on why Spain chose to join the eurozone.

Spanish vs German inflation during the period of flexible exchange rates.
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Figure 7.10 Spanish vs German inflation during the period of flexible exchange rates.

Inflation rates in 1970:
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Inflation rates in 1970

Figure 7.10a

Spain and Germany’s response to the 1970s oil shocks:
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Spain and Germany’s response to the 1970s oil shocks

Spain and Germany were both hit by the inflationary oil price shocks of the 1970s, but their central banks responded differently. The Spanish government (which directly controlled the central bank, the Bank of Spain) allowed inflation to rise significantly. With operational independence and a strong focus on keeping inflation low, the Bundesbank was effectively a pioneer of inflation targeting. The Bundesbank tightened policy, with the result that inflation remained in single figures.

Inflation rises in Spain:
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Inflation rises in Spain

The rise in Spanish inflation led to a significant rise in the ratio \(P/P^*\), the ratio of CPIs in the two countries.
The figure shows this ratio relative to its value at the start of 1970. The vertical axis uses a ‘ratio’ (or ‘log’) scale, where each value is double the one before it. The steeper the slope, the more rapid the growth rate.

The nominal and real exchange rate:
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The nominal and real exchange rate

In this ratio-scale figure, when the price ratio and the nominal exchange rate have a similar slope, it means the rate of depreciation (\(\delta\)) is very close to the gap between Spanish and German inflation rates.
In terms of overall changes over this period, the model matches the data quite well. In theory, the real exchange rate does not change over the long run. The average rate of depreciation, \(\delta\) (part of the equation \(\delta = \pi - \pi^*\)), was 5.5% in this case. The average gap between inflation rates (\(\pi - \pi^*\)) over this period was 6.2%, so the implied rate of change in the real exchange rate was approximately –0.7% (an appreciation).

An inflation–depreciation spiral?:
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An inflation–depreciation spiral?

In order to prevent the real exchange rate appreciating, monetary policy was very loose, causing the nominal exchange rate to depreciate rapidly. This in turn reinforced the increase in inflation.

The nominal and real exchange rate in 1977:
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The nominal and real exchange rate in 1977

Figure 7.10f

High inflation and Spain’s policy response:
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High inflation and Spain’s policy response

Figure 7.10g

The real appreciation dampened aggregate demand:
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The real appreciation dampened aggregate demand

Figure 7.10h

The nominal exchange rate and inflation in Spain and Germany in the 1990s:
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The nominal exchange rate and inflation in Spain and Germany in the 1990s

In the last five years shown in the figure, while the nominal peseta–DM rate could still adjust, Spain was ‘shadowing’ the DM: effectively a dry run for adopting a fixed exchange rate.

Question 7.8 Choose the correct answer(s)

Read the following statements about Figure 7.10 and choose the correct option(s).

  • Central bank independence can partly explain the different paths of inflation in Spain and Germany during the 1970s oil shocks.
  • From 1970 to 1988, the real exchange rate between Spain and Germany changed by a larger amount than the nominal exchange rate did.
  • From 1970 to 1988, the average rate of depreciation was close to the average gap between the Spanish and German inflation rates.
  • After tightening monetary policy in the late 1970s, Spanish inflation quickly converged towards German inflation.
  • Spain’s central bank was controlled by the government, and let inflation rise. Germany’s central bank was independent from the government and was committed to an inflation target, so it took measures to keep inflation low.
  • The nominal exchange rate depreciated by a similar amount to the rise in the price ratio. These offsetting effects meant that the real exchange rate changed by a smaller amount than the nominal exchange rate did.
  • The average rate of depreciation, \(\delta\) was 5.5%, and the average gap between inflation rates over this period was 6.2%.
  • Spanish inflation converged towards German inflation only in the 1990s, as Spain was preparing to adopt a fixed exchange rate regime.

Extension 7.3 The rate of change of competitiveness

In the main part of this section, we used an approximation for the rate of change of the real exchange rate (or, equivalently, competitiveness), and to maintain unchanged competitiveness would require a rate of depreciation of 7.84%, not 8%. This extension explains where it comes from. We demonstrate a general method for determining the proportional rate of change of a product of two variables, and a fraction of two variables (without using calculus), and then apply it to competitiveness.

Before reading it, you should be familiar with Extension 6.9, which uses the same approach to find the real rate of return on investment in terms of the nominal rate and inflation.

Remember from Extension 6.9, if an amount \(X\) increases from \(X_0\) to \(X_1\) over a period of time, its proportional rate of increase (the increase as a proportion of the initial value), \(g_X\), satisfies:

\[1+g_X = \frac{X_1}{X_0}\]

We also refer to \(g_X\) as the growth rate of \(X\). This formula arises frequently in economics.

We used it to determine the real rate of return when \(X_0\) was the value of an initial investment in nominal terms, so what matters to an investor is the rate of increase of \(X/P\), the real value of their wealth, where the price level, \(P\), also changes over the period as a result of inflation. If inflation is positive, the real rate of return, \(\text{ROR}_r\), satisfies:

\[1+\text{ROR}_r = \frac{\frac{X_1}{P_1}}{\frac{X_0}{P_0}}\]

By rearranging the fraction on the right, we expressed it in terms of the rate of increase of \(X\), and the rate of increase of \(P\).

Working out growth rates

We can use this method to find the rate of increase of any fraction, \(A/B\), or any product, \(AB\). Suppose the growth rates of the quantities \(A\) and \(B\) are \(g_A\) and \(g_B\).

If \(C = A/B\), the growth rate of \(C\) satisfies:

\[1+g_c = \frac{\frac{A_1}{B_1}}{\frac{A_0}{B_0}} = \frac{\frac{A_1}{A_0}}{\frac{B_1}{B_0}}\]

and since \(1+g_A = \frac{A_1}{A_0}\),

\[\Rightarrow 1+g_c = \frac{1+g_A}{1+g_B}\]

If \(D = AB\), the growth rate of \(D\) satisfies:

\[\begin{align*} 1+g_D &= \frac{A_1B_1}{A_0B_0} = \frac{A_1}{A_0} \times \frac{B_1}{B_0} \\ \Rightarrow 1+g_D &= (1+g_A)(1+g_B) \end{align*}\]

Approximations

We often use approximations for these growth rate relationships, obtained by arguing that if the rates of growth are not too big, then the product of two growth rates will be very small. (For example, 5.0% × 4.0% = 0.05 × 0.04 = 0.002 = 0.2%.)

From the equation for \(g_C\), if we multiply both sides by (\(1 + g_B\)), then multiply out the brackets, and rearrange we get:

\[\begin{align*} g_C &= g_A – g_B – g_C g_B \\ \Rightarrow g_C &\approx g_A – g_B \end{align*}\]

In words, we have shown that (approximately):

The growth rate of A divided by B is the growth rate of A minus the growth rate of B.

Similarly, from the equation for \(g_D\), if we multiply out the brackets and rearrange we get:

\[\begin{align*} g_D &= g_A + g_B + g_A g_B \\ \Rightarrow g_D &\approx g_A + g_B \end{align*}\]

In words, we have shown that (approximately):

The growth rate of \(A\) times \(B\) is the growth rate of \(A\) plus the growth rate of \(B\).

The rate of change of the real exchange rate

The real exchange rate (competitiveness) is defined as:

\[c = \frac{e \times P^*}{P}\]

We can now apply the two approximations obtained above to determine the rate of change of \(c\) in terms of the rates of change of \(e\), \(P\), and \(P^*\). We will use the notation \(g_c\) for the rate of increase of competitiveness. As in the main section, the rate of increase of the nominal exchange rate, \(e\), is the depreciation rate, \(\delta\), and the foreign and domestic price levels, \(P^*\) and \(P\), grow at inflation rates, \(\pi^*\) and \(\pi\).

Applying the result for a product, the proportional rate of increase of the numerator, \(e \times P^*\), is approximately \(\delta + \pi^*\). Then, applying the result for a fraction, the proportion rate of change of \(c\) is given by:

\[g_C \approx \delta + \pi^* - \pi\]

This is the approximation stated in the main part of the section. It is just as straightforward to write down the exact equation for \(g_c\). Applying the exact formulae derived above for \(AB\) and \(A/B\) together gives:

\[1+ g_C = \frac{(1+\delta)(1+\pi^*)}{(1+\pi)}\]

An example

Suppose that inflation abroad is at a rate of 2%, domestic inflation has stabilized at 10%, and the nominal exchange rate is currently depreciating at a rate of 5%. Then the rate of change of competitiveness is approximately 5% + 2% − 10% = −3%. Competitiveness is falling at a rate of 3%, because inflation is higher than the rate of depreciation. To maintain constant competitiveness at this level of inflation, the depreciation rate would have to increase to 8%.

In this example, the approximation is quite close. Using the exact equation instead, you can check that when the depreciation rate is 5%, the true rate of change of competitiveness is −2.64% rather than −3%. And if the depreciation rate were 8%, competitiveness would not be exactly constant; it would be increasing slowly, at a rate of 0.15%.

However when growth rates get large—as for example in the case of Argentina’s inflation rate and rate of depreciation—the approximations become much less accurate.

Exercise E7.1 The accuracy of approximations

Suppose the inflation rate abroad is 2% and the nominal exchange rate is depreciating at a rate of 5%. Using Excel or another statistical software:

  1. Calculate the rate of change of competitiveness using the approximate formula, for domestic inflation rates of 5, 10, 15, …, 100%. For each of these inflation rates, what would the depreciation rate have to be to maintain constant competitiveness?
  2. Use the exact equation to calculate the true rate of change of competitiveness for each inflation rate in Question 1. For the depreciation rates you calculated in Question 1, how close is competitiveness from staying constant?
  3. Comment on how your answers to Question 2 change as the inflation rate increases.