# Monetary policy and the exchange rate *.

1. IntroductionDuring the first decade of the reformed Reserve Bank of New Zealand Act 1989, there were often repeated concerns that monetary policy was responsible for large swings in the value of the New Zealand exchange rate; see, for example, Whitwell (1990), Grimes and Wong (1994), Grimes (1996), Easton (1997, pp. 238-240) and Dalziel (1997, 1998). Criticism along these lines by some business and political leaders peaked as the nominal exchange rate rose 14 percent in 1995 and 1996, to the extent that the Reserve Bank (1996a, 1996b) felt it prudent to publish two booklets explaining its policies to farmers and exporters. Partly in response to a widespread belief that monetary policy had created an over-valued New Zealand dollar in the mid-1990s, the ceiling of the Bank's inflation target was raised in' December 1996. The Reserve Bank itself did not accept this argument (see especially Brash 1999) and this paper presents a theoretical note supporting the alternative hypothesis that monetary policy per se has a relatively small influence on the exchange rate compared to movements induced by other factors.

The analysis begins in Section 2 by setting out the standard transmission mechanism whereby tighter monetary conditions lead to an appreciation of the currency in foreign exchange markets. There are feedback mechanisms limiting this influence, however, which can be set out by analysing the implications of the uncovered interest parity condition for any departure of the exchange rate from its purchasing power parity value as a result of a temporary policy-induced change in the domestic interest rate. Section 3 therefore sets out the fundamental condition for uncovered interest parity (UIP) under the assumption of purchasing power parity (PPP). This defines the PPP-compatible domestic interest rate in any given period, but also reveals that it may imply inflation that departs from the Reserve Bank's policy target. Section 4 analyses the impact on the exchange rate if the Bank moves the domestic interest rate away from its PPP-compatible value for one period in order to achieve the inflation target. As in section 2, the exchange rate and interest rate move in the same direction, but section 4 also provides a precise formula for this relationship assuming UIP is maintained (equation 8), which is the main contribution of the paper. Sections 5 and 6 generalise this result by analysing the impacts if the monetary response must be maintained for more than one period or if the market anticipates the policy change before implementation. The main point to emerge from this analysis is that changes in the exchange rate caused by changes in monetary policy are small relative to the size of the swings in the value of the New Zealand dollar during the 1990s. As section 7 discusses, this means it is both wrong to hold the Reserve Bank responsible for these swings in the past and unrealistic to expect monetary policy to eliminate such swings in the future.

2. The Monetary Policy Exchange Rate Transmission Mechanism

Suppose the Reserve Bank forecasts that inflation will rise above target in the absence of any policy response, and therefore decides to tighten domestic monetary conditions. In the past, this would have been done by reducing the value of settlement cash (a key component of the monetary base) or by issuing a warning to markets that the Bank was ready to do so if interest rates did not rise (so-called `open mouth operations'; see Guthrie and Wright, 2000). Since March 1999, the Bank implements monetary policy by adjusting its official cash rate, which acts as the base interest rate for the New Zealand financial sector. In all three cases, the result is a higher domestic nominal interest rate.

The transmission mechanism to the exchange rate then proceeds as follows (see, for example, Monetary Policy Committee, 1999, p. 4, or Taylor and Dalziel, 2002, pp. 155-157). The tightening of monetary conditions raises the domestic nominal interest rate and lowers expected inflation. Hence the real interest rate rises or, equivalently, the price of domestic assets falls relative to the price of assets in the rest of the world. International and domestic investors readjust their portfolios to purchase more of the relatively cheap New Zealand assets. Net capital inflows increase, which raises the demand for New Zealand dollars in the foreign exchange market. Ceteris paribus, the New Zealand currency appreciates in real terms.

This is the basis for concerns that changes in monetary policy can have a profound impact on the real exchange rate. There is, however, an important limiting mechanism. As Dalziel (1991, p. 335) observed, ceteris paribus the real exchange rate appreciation will be reversed once the output gap is closed and monetary conditions return to a neutral stance. This future depreciation must be taken into account when calculating the expected return on holding New Zealand financial assets, limiting the extent to which exchange rate overshooting is possible (Dornbusch, 1976). The purpose of this paper is to analyse the limits created by this mechanism.

There are two ways to approach this problem. The first is to build an econometric model of the exchange rate in an attempt to identify all factors, including monetary policy, influencing its value. Two referees suggest that this approach (known as `empirical realism') would be preferable, although difficult. It is not the method adopted here. Instead the paper adopts a 'critical realist' approach, which isolates the particular mechanism under study in much the same way as an experimental scientist seeks to hold all other influences constant when researching an individual phenomenon in the laboratory (see Dalziel, 2001, chapter 4, for further discussion). In this case, the isolated phenomenon is the transmission mechanism from temporary changes in monetary policy to the exchange rate, holding all other influences constant. The analysis begins by using arbitrage principles to set out some basic relationships between the domestic interest rate, the exchange rate and the expected rate of inflation. Sections 4 to 6 then use these relationships to quantify the size of this transmission mechanism.

3. Uncovered Interest Parity and Purchasing Power Parity

Suppose US$1 invested in the United States earns a nominal rate of return denoted by R, so that at the end of the period US$1 becomes US$(1+R). Instead, the original US$1 could have been converted into New Zealand dollars at the current USD/NZD exchange rate denoted e, and invested in a New Zealand asset earning a nominal rate of return, i. The expected value of this alternative in United States dollars at the end of the period would be US$(1/e) * (1+i) * E, where E denotes the value of the USD/NZD exchange rate expected to prevail at the end of the period: Arbitrage between the two alternatives means that the following uncovered interest parity (UIP) condition must hold:

(1) (1+R) = (1+i) * E/e

Denote the purchasing power parity exchange rate as e. If Q is the price level in the United States and P is the price level in New Zealand, then e is defined by:

(2) e = Q/P

Given the nominal interest rate in the United States, R, equation (1) can be used to define the domestic interest rate, i, that maintains a PPP exchange rate at the end of the period, [e.sub.1], given e at the beginning of the period. The PPP-compatible i is defined by the implicit equation:

(3) (1+R) = (1+i) * [e.sub.1]/e

The ratio [e.sub.1]/e depends on the expected inflation rates in the two countries. Let the United States inflation rate, denoted [PI], also be a parameter. Assume the expected rate of inflation in New Zealand depends negatively on the domestic interest rate, i, given the prevailing values for certain parameters represented by the vector z. (1) This vector could include concepts such as the neoclassical `output gap' or the post-Keynesian `income distribution conflict' affecting a country's inflationary bias. The following analysis does not require precise details for its results, but z is included to emphasise that expectations about domestic inflation change over time. Hence, the New Zealand expected inflation rate is denoted by [pi](; z).

(4) [e.sub.1]/e = ([Q.sub.1]/[P.sub.1]) * (P/Q) = (1+[PI])/[1+[pi][i;z)]

Substitute (4) into (3) and rearrange:

(5) = 1+R/1+[PI] [1+i]/1+[pi](i; z)

The left-hand-side is the real interest rate in the United States, assumed to be fixed by the value of the two parameters R and [PI]. The right-hand-side is the real rate of interest in New Zealand. It is a strictly positive function of the nominal interest rate (since [delta][pi]/[delta]i < 0); hence i exists and is unique. There is no reason, however, to assume [pi](i; z) will equal the Reserve Bank's inflation target. Suppose without loss of generality that [pi](i; z) is greater than its target, so that the Bank must increase the domestic interest rate to meet its statutory obligations. From equation (5) this produces a higher domestic real interest rate than investors can obtain in the United States, and so net capital inflows into the country will increase. This pushes the exchange rate above its PPP value, as the remainder of this paper analyses in more detail.

4. A One-Period Tightening of Monetary Policy

Start with the simplest case, in which purchasing power parity is satisfied and the inflation rate [pi](i; z) satisfies the Reserve Bank's target. Let there be an unanticipated change to some component of z that increases inflationary pressures. Suppose that to choke off these pressures requires a one-period increase in the domestic interest rate from i to i. The UIP condition in equation (1) then requires the following to hold:

(6) (1+R) = (1+i) * E/e

Because the domestic rate of interest is expected to return to i at the end of the period, ceteris paribus E = [e.sub.1]. Thus equation (6) can be rewritten as:

(7) (1+R) = (1+i).([e.sub.1]/e) * (e/e)

which implies using equation (3) that:

(8) e/e = (1+i) * ([e.sub.1]/e)/(1+R) = (1+i)/(1+i)

This confirms the standard result that a tightening in domestic monetary conditions leads to the exchange rate being over-valued compared to the PPP standard, since i > i. Equation (8) provides a precise formula for the over-valuation, which can be further simplified using the approximation that ln(1+x) [congruent to] x for small values of x. Taking logs of both sides of equation (8), and recognising that the lefthand-side is just the change in ln(e) evaluated at e, this produces the following relationship:

(9) [DELTA]e/e [congruent to] i - i

That is, the percentage increase in the exchange rate equals the percentage points by which the interest rate is increased by the Reserve Bank in order to maintain its inflation target. This result will be discussed further in section 7 below, after the following two sections generalise the result in two important dimensions.

5. A Multi-Period Tightening of Monetary Policy

Suppose the example of section 4 is altered so that the period of tighter monetary policy is expected to last m periods rather than 1. The Reserve Bank, for example, might choose to impose a smaller increase in the domestic interest rate, accepting that this will involve a longer period of adjustment back to its inflation target. At the end of the m-th period, the domestic rate of interest is expected to return to i and the prevailing exchange rate will be [e.sub.m]. The UIP condition, therefore, becomes:

(10) [(1+R).sup.m] = [(1+i).sup.m] * ([e.sub.m]/e) * (e/e)

The m-period generalisation of equation (3) implies that:

(11) ([e.sub.m]/e) = [(1+R)/[(1+i)].sup.m]

Substituting equation (11) into (10) and rearranging produces the following:

(12) e/e = [(1+i).sup.m] * ([e.sub.m]/e)/[(1+R).sup.m] = [(1+i)/[(1+i)].sup.m]

Using the same approximation that produced equation (9) in the previous section, this result implies that:

(13) [DELTA]e/e [congruent to] m * (i-i)

Equation (13) suggests that a decision by the Reserve Bank to lower the interest rate by a smaller amount but for a longer period of restraint may have little effect on the current exchange rate. If, for example, the interest rate increase is half the one-period amount but remains in place for twice as long, this will not make any difference to the extent to which the exchange rate rises in the current period.

6. An Expected Tightening of Monetary Policy

Suppose participants in financial markets anticipate that the Reserve Bank will be forced to increase the domestic interest rate in the next period for one period. From equation (8), the exchange rate in the next period will be overvalued by:

(14) [e.sub.1]/[e.sub.1] = (1+i)/(1+i)

For the current period, the UIP condition is given by equation (1) with E = [e.sub.1]:

(15) (1+R) = (1+i) * [e.sub.1]/e

Recall from equation (3) that:

(16) (1+R) = (1+i) * [e.sub.1]/e

Equations (15) and (16) require that (e/e) = ([e.sub.1]/[e.sub.1]), and so from equation (14):

(17) e/e = (1+i)/(1+i)

Equation (17) reveals that the exchange rate appreciates by the exact required amount as soon as the market anticipates the monetary policy tightening. Thus a rising value of the New Zealand dollar may be an indicator that the financial sector is anticipating inflationary pressures that will require a policy response in the form of a higher domestic interest rate. This result is easily generalised. Suppose the New Zealand rate of interest is expected to be increased to i in n periods time, and to be maintained at that higher level for m further periods. From equation (12):

(18) [e.sub.n]/[e.sub.n] = [[(1+i)/(1+i)].sup.m]

The multi-period UIP condition requires that:

(19) [(1+R).sup.n] = [(1+i).sup.n] * [e.sub.n]/e = [(1+i).sup.n] * [e.sub.n]/e

which implies that:

(20) (e/e) = ([e.sub.n]/[e.sub.n])

Substitute equation (20) into equation (18) to obtain:

e/e= [[(1+i)/(1+i)].sub.m] (21)

Equation (21) is the same expression as equation (12) in section 5 above.

7. Implications and Conclusion

The main results of this paper can be summarised in a few simple statements. Given the world real rate of interest, and assuming the exchange rate is currently at its purchasing power parity value, there exists a unique domestic interest rate that is consistent with maintaining purchasing power parity at the end of the period (equation 5). This domestic interest rate, however, may not produce inflation consistent with the Reserve Bank's policy targets agreement. If financial market participants expect that sometime in the future the Reserve Bank will change the domestic interest rate from the value that produces purchasing power parity, then (ceteris paribus) there is an immediate percentage change in the exchange rate approximated by the expected change in the interest rate multiplied by the number of periods the expected change is anticipated to be in effect (equations 13 and 21). The most important policy implication is the size of this last calculation. Recall equation (13):

(13) [DELTA]e/e [congruent to] m * (i-i)

Suppose the Reserve Bank moved its official cash rate by 3 percentage points (which would be regarded as a very big change), and the financial sector expected this change to endure for 2 years (which would be regarded as a very long time for monetary restraint or expansion). Then equation (13) indicates that the percentage change in the exchange rate caused by this monetary policy initiative would be just 6 per cent. To put this into perspective, 6 per cent per annum was the maximum amount by which the Reserve Bank had discretionary power to adjust the exchange rate during New Zealand's 'crawling peg' exchange rate regime in the late 1970s and early 1980s.

Recent work in the Reserve Bank suggests that a plausible purchasing power parity USD/NZD exchange rate in the 1990s lay somewhere between 52 and 60 cents (Brook and Hargreaves, 2001). Taking the mid-point of these two estimates for illustrative purposes, a 6 per cent band produces a range of 52.6 to 59.4 around a value for e at 56. This range is depicted in Figure 1, along with the actual USD/NZD exchange rate between January 1989 and December 2000. The graph clearly shows that the size of the appreciation of the dollar in 1997 and the size of the depreciation in 2000 were both well outside the range that could reasonably be attributed to monetary policy changes alone. Indeed the peak of the appreciation in December 1997 and the trough of the depreciation in November 2000 represented departures from the illustrative PPP value of 56 by more than one quarter (26.1 and 28.8 per cent respectively).

[FIGURE 1 OMITTED]

This suggests two important policy lessons. First, it is unreasonable to blame monetary policy per se for the size of the swings in New Zealand's exchange rate depicted in Figure 1. Indeed, as the governor of the Reserve Bank at the time observed, `exchange rate fluctuations of that magnitude are just part of the rough and tumble of an economy such as New Zealand's' (Brash, 1999, p. 35). Second, it is surely impractical for monetary policy to be used in an attempt to prevent such wide swings. If the New Zealand exchange rate can depart from its purchasing power parity value by 25 per cent over a reasonably short period, this phenomenon would require far too great a change in domestic interest rates (and hence in the domestic inflation rate) to be offset by monetary policy alone. If it is indeed possible to reduce the amplitude of the cycles in the New Zealand exchange rate, the solution must be found in some other direction.

(1) The property that expected inflation depends on the domestic interest rate is, of course, the necessary condition for monetary policy to be able to use interest rate changes to meet its inflation target. The idea of defining a market equilibrium price in this way was given to me in a completely different context by my PhD supervisor, Richard Manning; see Dalziel (1987).

References

Brash, D. (1999). The New Zealand dollar and the recent business cycle.' Reserve Bank Bulletin, Vol. 62(1), pp. 25-35.

Brook, A. and D. Hargreaves (2001). PPP-based analysis of New Zealand's equilibrium exchange rate. Reserve Bank of New Zealand Discussion Paper, DP2001/01.

Dalziel, P. (1987). Optimal water storage and pricing: the effect of monopoly. New Zealand Economic Papers, vol. 21, pp. 3-16.

Dalziel, P. (1991). Theoretical approaches to monetary disinflation. Journal of Economic Surveys, vol. 5(4), pp. 329-57.

Dalziel, P. (1997). Setting the Reserve Bank's inflation target: the New Zealand debate. Agenda, Vol. 4(3), pp. 285-96.

Dalziel, P. (1998). New Zealand's experience with an independent central bank since 1989. In P. Arestis and M. Sawyer (eds), The Political Economy of Central Banking. Aldershot: Edward Elgar.

Dalziel, P. (2001). Money, Credit and Price Stability. London: Routledge.

Dornbusch, R. (1976). Expectations and exchange rate dynamics. Journal of Political Economy, vol. 84(6), pp. 1161-76.

Easton, B. (1997). In Stormy Seas: The Post-War New Zealand Economy. Dunedin: University of Otago Press.

Grimes, A. (1996). Monetary policy. In B. Silverstone, A. Bollard and R. Lattimore (eds), A Study of Economic Reform: The Case of New Zealand. Amsterdam: Elsevier North-Holland.

Grimes, A. and J. Wong (1994). The role of the exchange rate in New Zealand monetary policy.' In R. Glick and M. Hutchison (eds), Exchange Rate Policy and Interdependence: Perspectives from the Pacific Basin. Cambridge: Cambridge University Press.

Guthrie, G. and J. Wright (2000). Open mouth operations.' Journal of Monetary Economics, Vol. 46(2), pp. 489-516.

Monetary Policy Committee (1999). The transmission mechanism of monetary policy. A report of the Bank of England, London.

Reserve Bank (1996a). The Impact of Monetary Policy on Farming. Wellington: Reserve Bank of New Zealand.

Reserve Bank (1996b). The Impact of Monetary Policy on Exporters. Wellington: Reserve Bank of New Zealand.

Sherwin, M. (1999). Inflation targeting: 10 years on. Reserve Bank of New Zealand Bulletin, Vol. 62(3), pp. 72-80.

Taylor, J. and P. Dalziel (2002). Macroeconomics: New Zealand Edition. Milton: Wiley.

Whitwell, J. (1990). The Rogernomics monetarist experiment. In M. Holland and J. Boston (eds), The Fourth Labour Government: Politics and Policy in New Zealand. Auckland: Oxford University Press.

Paul Dalziel, Professor of Economics, Commerce Division, P.O. Box 84, Lincoln University Post Office, Canterbury, E-mail: dalzielp@lincoln.ac.nz

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Title Annotation: | monetary policy has a relatively small influence on the exchange rate |
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Author: | Dalziel, Paul |

Publication: | New Zealand Economic Papers |

Geographic Code: | 8NEWZ |

Date: | Dec 1, 2002 |

Words: | 3461 |

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