The Choice of Exchange Rate Assumption in the Process of Forecasting Inflation

Bernhardsen, Tom; Holmsen, Amund Research Report The Choice of Exchange Rate Assumption in the Process of Forecasting Inflation Staff Memo, No. 2005/3 Provided in Cooperation with: Norges Bank, Oslo Suggested Citation: Bernhardsen, Tom; Holmsen, Amund (2005) : The Choice of Exchange Rate Assumption in the Process of Forecasting Inflation, Staff Memo, No. 2005/3, ISBN 82-7553-291-4, Norges Bank, Oslo, https://hdl.handle.net/11250/2508133 This Version is available at: https://hdl.handle.net/10419/210164 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by-nc-nd/4.0/deed.no NO2005/3 Oslo April 25, 2005 Staff Memo Monetary Policy Department The choice of exchange rate assumption in the process of forecasting inflation by Tom Bernhardsen and Amund Holmsen ISSN 1504-2596 (online only) ISBN 82-7553-291-4 (online only) Publications from Norges Bank can be ordered by e-mail: [email protected] or from: Norges Bank, Subscription service, P.O.Box. 1179 Sentrum N-0107Oslo, Norway. Tel. +47 22 31 63 83, Fax. +47 22 41 31 05 Publications in the series Staff Memo are available as pdf-files on the bank’s web site: www.norges-bank.no, under "Publications". Staff Memos present reports on key issues written by staff members of Norges Bank the central bank of Norway - and are intended to encourage comments from colleagues and other interested parties. Views and conclusions expressed in Staff Memos can not be taken to represent the views of Norges Bank. © 2005 Norges Bank The text may be quoted or referred to, provided that due acknowledgement is given to source. Publikasjoner fra Norges Bank kan bestilles over e-post: post[email protected] eller ved henvendelse til: Norges Bank, Abonnementsservice Postboks 1179 Sentrum 0107 Oslo Telefon 22 31 63 83, Telefaks 22 41 31 05 Utgivelser i serien Staff Memo er tilgjengelige som pdf-filer på www.norges-bank.no, under «Publikasjoner». Staff Memo inneholder utredninger som inngår i bankens arbeid med sentrale problemstillinger. Hensikten er å motta kommentarer fra kolleger og andre interesserte. Synspunkter og konklusjoner i arbeidene representerer ikke nødvendigvis Norges Banks synspunkter. © 2005 Norges Bank Det kan siteres fra eller henvises til dette arbeid, gitt at forfatter og Norges Bank oppgis som kilde. The choice of exchange rate assumption in the process of forecasting inflation by Tom Bernhardsen and Amund Holmsen Monetary Policy Department, Norges Bank (the central bank of Norway)1 The paper was presented at the conference “Exchange rate and monetary policy”, BIS 28 – 29 October 2004. 1The first author is senior advicer at the Monetary Policy Department and the second author is Director of the Monetary Policy Department. Thanks to colleagues at Norges Bank for comments and discussion, No one mentioned, no one forgotten. The views expressed in the paper are the responsibility of the authors alone and cannot be taken as the view of Norges Bank. 1 Abstract In the process of forecasting inflation the central bank needs to make assumptions regarding the future path of the interest rate and the exchange rate. This paper focuses on the exchange rate assumption. In particular, three alternative assumptions are discussed. First, the random walk hypothesis suggests a constant exchange rate over the forecast horizon. While being theoretically appellant and frequently chosen across central banks, the level of the exchange rate implied by the assumption remains to be determined. Moreover, assuming the exchange rate to be constant may imply a change in the real exchange rate if the inflation target differs from the target among the trading partners. Second, central banks frequently assume the exchange rate to evolve in line with uncovered interest rate parity. Combined with the assumption of using forward rates for the interest rate, this seems theoretically consistent. However, due to a possible risk premium UIP-predictions may imply a path for the exchange rate far away from market expectations, a path with which the central bank is not necessarily comfortable. Third, the central bank could base the exchange rate assumption on its best prediction of the exchange rate in the future. This would require some analytical tools for the exchange rate. In this paper we focus on mean-reversion in the real exchange rate as a guide to future nominal exchange rate movements. Exchange rate paths implied by the three alternatives are compared with actual exchange rate outcomes. 2 1. Introduction and background Inflation projections in central banks are commonly based on the assumption that future exchange rates and interest rates are in line with market expectations or remain constant over the forecast horizon. These assumptions are frequently referred to as technical, meaning that the central bank does not necessarily expect them to materialize. Alternatively, the central bank can base its exchange rate and interest rate assumptions on its best prediction of the future. The purpose of this paper is to discuss these two conceptually different assumptions. Particular focus will be placed on the exchange rate assumption. Independent of whether the assumptions are technical or reflecting the bank’s best prediction of the future, some basic criteria should be satisfied: • The exchange rate and the interest rate assumptions must be theoretically consistent. This would be satisfied if, for example, both the exchange rate and the interest rate are assumed to follow market expectations. • The assumptions must be transparent and intelligible. • In alternative scenarios, the key assumptions must be internally consistent and consistent with those in the main scenario. Table 1 shows the bank’s exchange rate and interest rate assumptions taken from the inflation reports since 1999. In the period 1999-2003 inflation projections were based on a constant future exchange rate. The level of the exchange rate implied by the assumption was calculated as an average of the exchange rate in the past. As from late 2003 inflation projections have been based on UIP-implied forward rates.2 The interest rate assumption has also changed correspondingly over time. In comparison, Table 2 shows the exchange rate assumption in other selected central banks. 2 In Inflation Report 2003/2, two alternative projections were presented, one based on a constant future exchange rate and one based on UIP-implied forward rates. 3 In a small open economy, the exchange rate plays a paramount role in the inflation process. Figure 1 shows, based on data from the inflation reports in the period 1999–2003, the relationship between the exchange rate assumption error four quarters ahead and the corresponding inflation gap (deviation from the target) eight quarters ahead. The lags reflect the inertia in the exchange rate pass-through. As an example, compared to the exchange rate assumption in Inflation Report 2001/2, one year later the exchange rate turned out to be 8 percent stronger, while the core inflation two years later took the value 1.3 percentage point below target (marked in the figure).3 The pairs in the scatter plot should be concentrated in the first (north-west) and the third (south-east) quadrant, as exchange rate outcomes stronger (weaker) than assumed will normally be associated with inflation outcomes lower (higher) than predicted. In fact, out of the 13 dots, 10 are located in the second and the third quadrant. Moreover, apart from one outlier (IR 2002/3) the few observations outside the second and the third quadrant are border line observations, close to the second and the third quadrant. As expected the correlation coefficient is positive, 0.45. The overall message from the chart is that the exchange rate assumption is of crucial importance in the process of forecasting inflation.4 Thus, seeking for better methods in forming the exchange rate assumption may reduce the inflation forecast errors significantly. A paramount question is whether we are able to substitute the technical assumption with a reasonable forecast. Against this background we discuss three alternative principles for determining the exchange rate in the projections, (i) a constant exchange rate, (ii) UIP-implied forward rates and (iii) an assumption reflecting the central bank’s best prediction of the future exchange rate, where in particular mean-reversion in the real exchange rate will be emphasized. The ex post paths 3 In the Inflation Report 1999/1 the krone exchange rate was assumed to “return to its initial range against European currencies in the course of the next six months. Subsequently, the exchange rate is assumed to remain unchanged through the remainder of the projection period”. To simplify we concentrate on two kinds of assumptions, a constant exchange rate or UIP-implied forward rates. Hence in the following analysis we exclude the data from Inflation Report 1999/1. 4 Of course, inflation and exchange rate outcomes are interdependent and determined simultaneously in a complex economic environment. Hence the univariate considerations attached to figure 1 are far too simple to explain inflation outcomes as such. 4 implied by the three different assumptions are compared with actual exchange rate outcomes in the case of Norway. 2. A constant exchange rate The assumption of a constant exchange rate is supported by the random walk hypothesis. If today’s exchange rate is the best prediction of the future, a constant exchange rate over the forecast horizon emerges as the best possible assumption. Starting with Meese and Rogoff (1983), the stock of the literature now indicates that a random walk is hard to beat.5 Figure 2 shows the nominal effective exchange rate for Norway from 1971 (an increase indicates a depreciation). Calculated on the whole sample, formal tests clearly reject mean reversion in the data. However, based on the sub-sample from the beginning of 1990, both eye ball econometrics and formal test indicate that mean reverting has takes place.6 Formal tests aside, we will point to two problems regarding the constant exchange rate assumption. First, while the constant exchange rate assumption is frequently based on some average of the exchange rate in recent history, the time span over which to average the exchange rate remains to be determined. This issue will be further discussed below. Second, as the domestic inflation target may differ from the average of trading partners, a constant nominal exchange rate over the next 2-3 years could imply an expected change of the real exchange rate. In the case of Norway, the inflation target is slightly above corresponding targets abroad. Thus, a constant nominal exchange rate would normally imply a real appreciation over a three years horizon. Though not necessarily a substantial change compared to yearly exchange rate fluctuations, the constant exchange rate assumption does contain a systematic – and not necessarily wanted – change in the real exchange rate. 5 In the long run, however, there is a tendency for purchasing power parity to hold (Taylor and Taylor, 2004). 6 As will be shown below, the real exchange rate is stationary. Then, a stationary nominal exchange rate requires that domestic inflation evolves in line with foreign inflation. The tests are based on the unit root test available in EViews. 5 3. Exchange rate assumption based on uncovered interest rate parity As from late 2003 Norges Bank has based the exchange rate assumption on UIP. The parity states that due to arbitrage across markets interest rate differentials compensate for expected changes in the exchange rate. More formally, let it = it* + Et[Δe] + rpt, where it and it* are the domestic and the foreign interest rate in period t respectively, Et[Δe] is the expected percentage change in the exchange rate between period t and t+1 and rp is a risk premium. The equation holds by definition (of the risk premium), and UIP is defined by setting the risk premium equal to zero. Hence given some assumption of the future interest rate differential, UIP implies a path for the exchange rate which would make domestic and foreign investments equal in terms of expected return. In practice the expected future interest rate differential is calculated on the basis of implied forward rates from the yield curve. Exchange rate assumptions based on UIP are appellant for a variety of reasons. First, it goes without saying that the parity has a strong theoretical foundation and is a cornerstone in financial and macroeconomic literature, linking domestic and foreign financial markets. Second, used in combination with forward interest rates, this seems theoretically consistent as the central bank in this case would build its inflation forecast on market expectations for both the two key variables determined in financial markets. Third, using markets expectations for the exchange rate and the interest rate provides a communication channel between the central bank and market participants. Suppose for instance that the central bank’s contingent inflation forecast is higher than the inflation target. This could initiate a correcting mechanism as the bank implicitly conveys the message that is finds current forward rates too expansionary. As the market anticipates that the central bank sooner or later needs to tighten policy, it will – by the logic of rational expectations - adjust its expectations accordingly. In this case, however, the bank does not provide precise information on its preferred interest rate path. A well-known argument against basing the exchange rate assumption on UIP-predictions is its empirical failure due to the existence of a risk premium. There is a large literature discussing empirical UIP tests and the main result is, overall, that UIP is empirically rejected. 6 UIP-errors is in fact caused by a risk premium, and (ii) the market bases exchange rate projections on some sort of equilibrium value for the exchange rate (nominal or real) and mean reversion towards that value. 6. Conclusion In small open economies with free capital movements the exchange rate plays a significant role in the inflation process. The exchange rate assumptions underlying the inflation projections vary across countries. Typically, the assumptions are constant exchange rate, uncovered interest parity (UIP) or some projection reflecting the bank’s best guess on the interest rate assumption. Even though constant exchange rate or UIP may be in accordance with best guess, exchange rate assumptions are frequently referred to as technical. Economic theory and empiric studies unambiguously suggest a strong link between the interest rate and the exchange rate. In this respect, the exchange rate does not principally differ from other variables that are endogenous in the projections. The role of the exchange rate in the inflation process is supported by Norwegian data. During the past four years, part of the inflation forecast errors can be attributed to deviations between the actual exchange rate and the assumption. Ex post studies suggest that, in this particular period, a PPP-based approach could have predicted better, based on a gradual move in the exchange rate to restore relative PPP. Whereas the principle of treating the exchange rate as en endogenous variable seems uncontroversial, the practical implementation of it is far from settled. Even though different equilibrium approaches and estimated models should be explored, forecasting the exchange rate is by nature difficult. Even if the exchange rate is not presented as a best guess, central banks should therefore scrutinize different reasonable exchange rate scenarios and communicate the uncertainty in its projections 13 Appendix: The property of real exchange rates across countries A precondition for basing the exchange rate assumption on deviation from PPP is mean reversion in the real exchange rate. The higher the degree of mean reversion, the more it is plausible to base the exchange rate assumption on deviations from PPP. Mean reversion in an economic time series is directly related to the concept of stationarity. For a stationary variable an equilibrium value exists and over time the variable will tend to approach the equilibrium (though the speed of the process may be slow or fast). This means that shocks are temporary. A widespread method used to estimate the degree of mean reversion is to run the simple Dickey-Fuller regression, Δqt = α + βqt-1 + εt , where q is the variable in question and ε is an unsystematic (white noise) error term. If β is less than one, the variable is mean-reverting with a half life given by ln(½)/ln(β). The Dickey- Fuller test examines the null hypothesis that the variable in question is non-stationary (β=0). If the null is rejected, one concludes that mean reversion exists. A huge literature on stationarity tests exists, and there are several problems attached to the simple test above.12 In one recent study from IMF (Cashin, P. and J. McDermott, 2003) several methods to estimate the half life of real exchange rates are discussed. Figure A1 shows the half life of real exchanges rates for a selected group of developing countries, for each country calculated as the average of three different methods discussed in Cashin, P. and J. McDermott (2003).13 The half life of real exchange rates varies considerably across countries. For some countries, Iceland, Norway, New Zealand and Switzerland the half life is estimated to around 1-2 years. For several countries in the euro area half life varies between 4 and 6 years, for UK it is 5-6 years, while for Australia, Japan and Finland half life is 7-8 years. For some countries, notably Portugal, Sweden, Canada, United States and Belgium the real exchange rate is considered to be non-stationary.14 Figures A2-A6 show the real exchange rate and PPP-based exchange rate prediction paths based on the half life in figure 6 for the countries with a half life of 5-6 years and less.15 To 12 See Banerjee, A. et. al (1993) for details. 13 The authors of the IMF-study go through several methods to estimate the half life of real exchange rates. For our purpose, we have chosen to take the average of three of them, 1) simple and biased Dickey Fuller regressions, 2) Augmented median unbiased Dickey-Fuller regressions and 3) Phillips-Perron median unbiased regressions. The difference between the tests is related to the degree of biasness in the estimate of the regression coefficient in the regression above and to what extent autocorrelation and heteroscedasticity in the error term are accounted for. 14 One should note that the estimated half life depends strongly on the method used to calculate it. As noted above, we have calculated the half life as the average of three different methods suggested by Cashin, P. and J. McDermott (2003, 2004). By this measure half life of real exchange rates in Portugal, Sweden, Canada, United States and Belgium is estimated to 19, 25, 29, 29 and 35 years respectively, interpreted to be infinite. 15 For each point in the figure where a new PPP-adjusted path begins, the equilibrium value of the real exchange rate is calculated by the historical average from 1979 (start of IMF data available on the data base EcoWin) and up to the starting point of the PPP-based path. This means that more and more data is used to calculate the 14 measure the prediction errors in the figures, table A1 shows the percentage deviation between the real exchange rate and the two years “end-point prediction” implied by the PPP-based path. As an example, for Iceland the actual real exchange rate in 1997 deviated from the prediction for 1997, made in 1995, by 10.2 percent. Figure A8 depicts the two last rows of table A1, showing, for each country, the average deviation and the standard deviation. Overall, the half life for Norway seems to be relatively low compared to most other countries. This result is broadly independent of the method used to calculate the half life. equilibrium value as time evolves. For the euro area, half life is calculated as the average numbers for Germany, France and Italy, resulting in a half life of around 5 years. 15 Appendix: The real exchange rate based on relative wage costs In the main text the real exchange rate was based on relative consumer prices, reflecting developments in relative purchasing power or cost of living. Alternatively, the real exchange rate could be measured in terms of relative wage costs, reflecting developments in competitiveness. Figure A9 shows the real exchange rate deflated by relative wage costs, as deviation from the mean since 1970 (similar to figure 4). Based on simple eye-ball econometrics the chart indicates that this measure of the real exchange rate also tends to vary around the average level. However, formal tests like the augmented Dickey-Fuller test do not reject the null hypothesis of non-stationarity. On the other hand, it is well documented in the literature that the power of these standard tests is rather low and that large samples may be necessary to detect mean reversion in a statistical sense. This means that the tests could fail to reject the null even if the series is stationary. Proceeding with the working hypothesis that the real exchange rate is stationary, the simple AR(1) regression turns out to be Qt = constant + 0.8 Qt-1 where Q is the real exchange rate based on relative wage costs. The standard deviation of the regression coefficient is equal to 0.12. The equation implies a half life of log(-½)/log(-0.8) = 3.11 years, a reasonable estimate and somewhat higher than for the real exchange rate deflated by relative consumer prices. As of mid February 2005 the real exchange rate deflated by relative wage costs is estimated to be around 8 per cent stronger than the average level. A half life of around three years implies that the real value of the Krone should fall by around 4 per cent over a three years period. 16 References Akram, Q. F. (2005) "PPP in the medium run: The case of Norway" Journal of Macroeconomics, forthcoming, see also Working Paper 2002/04, Norges Bank. Banerjee, A., Dolado, J., Galbraith, J. W. and Hendry, D. F. (1993) “Co-Integration, error correction, and the econometric analysis of non-stationary data”, Oxford University Press, 1993 Cashin, P. and McDermott, C. J. “An unbiased appraisal of purchasing power parity”, IMF Staff Papers, 2003, vol 50, pp 321-351 Cashin, P. and McDermott, C. J. “Parity Reversion in real exchange rates: Fast slow, or not at all?”, IMF Working Paper 128, 2004. Lohrman, H. “Evaluation of Norges Bank’s projections for 2001 and 2002”, Economic Bulletin, 2003/1, Norges Bank, 2003. Meese, R. and Rogoff, K. (1983) “Empirical exchange rate models of the seventies: Do they fit out of sample?”, Journal of International Economics, 14, pp.3-24. Taylor, A. M. and M. P. Taylor (2004) “The purchasing power debate”, National Bureau of Economic Research, Working Paper 10607. 17 Table 1. Exchange rate and interest rate assumptions at Norges Bank Exchange rate assumption Interest rate assumption Inflation Report Constant Forward rates Constant Forward rates 1999 1 2 3 4 X1 X (mean last 3 months) X (last month) X ( mean so far 4th quarter) X X X X 2000 1 2 3 4 X (mean so far 2000) X (mean first 4 months 2000) X (mean so far 2000) X (mean last 3 months) X X X X 2001 1 2 3 X (mean so far 2001) X (mean last 3 months) X (mean last 3 months) X X X 2002 1 2 3 X (mean last month) X (mean last 3 months) X (mean last 3 months) X X X 2003 1 2 3 X (mean last month) X2 (mean 3 - 19 June 2003) X X X X X X 2004 1 2 3 X X X X X X 2005 1 1In the Inflation Report 1999/1 the krone exchange rate was assumed to “return to its initial range against European currencies in the course of the next six months. Subsequently, the exchange rate is assumed to remain unchanged through the remainder of the projection period” 2In Inflation Report 2003/2, two alternative projections were presented, one based on a constant future exchange rate and one based on UIP-implied forward rates. 18 Table 2. Exchange rate assumptions in selected central banks Technical assumptions Best Forecast Other New Zealand Gradual return to an estimated real exchange rate Sweden Uses a variety of models to predict the most like outcome (conditioned on the interest rate assumption) Canada Not publicly available Australia Constant exchange rate Czech Republic Forecast of the koruna/euro rate based on the real exchange rate’s deviation from equilibrium USA FED publishes the central tendency of the FOMC participants’ individual forecasts for key macroeconomic variables. The exchange rate assumption is not discussed. ECB Constant exchange rate UK Average of constant exchange rate and UIP Norway UIP 19 Table 3. Deviation from exchange rate outcomes, averaged over 2 years Random Walk UIP PPP IR 2/99 2.30 1.18 3.57 IR3/99 2.02 1.70 2.95 IR4/99 1.94 2.44 2.28 IR1/00 2.24 3.44 1.83 IR2/00 3.14 7.18 2.60 IR3/00 5.43 8.60 4.01 IR4/00 7.73 10.03 5.84 IR1/01 8.16 10.79 6.58 IR2/01 7.84 11.05 6.75 IR3/01 6.91 9.56 6.11 IR1/02 5.36 7.95 5.29 IR2/02 3.28 3.54 2.66 IR3/02 5.42 3.46 4.43 Average 4.75 6.23 4.22 St.dev. 2.39 3.68 1.73 Table 4. Deviation from exchange rate outcomes, 2 years after publication of IR Random Walk UIP PPP IR 2/99 0.91 3.45 2.80 IR3/99 0.70 4.84 1.16 IR4/99 2.19 5.95 0.20 IR1/00 4.03 7.69 1.85 IR2/00 9.56 15.98 8.08 IR3/00 14.14 19.26 11.26 IR4/00 15.95 19.72 12.70 IR1/01 13.80 18.46 11.25 IR2/01 9.08 14.85 7.36 IR3/01 4.38 9.29 3.47 IR1/02 0.61 3.97 0.51 IR2/02 2.49 3.41 0.02 IR3/02 7.10 3.32 4.61 Average 6.53 10.01 5.02 St.dev. 5.49 6.63 4.59 20 Table A1. The percentage deviation between the real exchange rate and the two years “endpoint prediction” implied by the PPP-based path. Switzerland Norway Iceland Euro area UK New Zealand 1997 1.46 3.22 10.20 0.13 7.86 16.57 1998 1.64 0.66 5.81 8.13 25.49 4.69 1999 4.07 7.05 4.93 1.07 8.13 12.51 2000 3.15 3.67 1.79 9.03 7.39 14.51 2001 1.04 1.94 5.19 12.16 6.68 10.60 2002 6.21 0.70 11.98 2.93 2.06 7.17 2003 8.10 16.34 0.88 9.39 3.92 10.02 2004 1.65 2.00 3.59 18.33 2.44 19.61 Average 3.42 4.45 5.55 7.65 8.00 11.96 Std.dev. 2.56 5.22 3.84 6.11 7.47 4.90 21 Norges Bank 1 -3 -2,5 -2 -1,5 -1 -0,5 0 0,5 1 1,5 Deviation from inflation target, percentage points Deviation from exchange rate assumption, percent -20 -15 -10 -5 0 5 10 Chart 1. Deviation from inflation target against deviation from exchange rate assumption (πt+8 –πIR) against (Vt+4 –V IR) IR 2001/2 (-1.3, -8) IR 2002/3 Correlation = 0.45 Source: Norges Bank Norges Bank 2 Source: Norges Bank Chart 2. Nominal effective exchange rate Increase indicates depreciation 70 80 90 100 110 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 70 80 90 100 110 22 Norges Bank 14 70 80 90 100 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 70 80 90 100 A7. Real exchange rates and PPP-adjusted paths for UK (half time ≈5-6 years) Source: IMF Norges Bank 15 A8. Average deviation and standard deviation between the real exchange rate and the prediction implied by the PPP-based path exactly two years after the prediction took place 0 2 4 6 8 10 12 14 Switzerland Norway Iceland Euro area UK New Zealand Source: IMF Average deviation Standard deviation 29 Norges Bank 17 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 1970 1974 1978 1982 1986 1990 1994 1998 2002 Chart A9. Real exchange rate (deflated by relative wage costs). Deviation from the average from 1970 Source: Norges Bank 30 Tom Bernhardsen and Amund Holmsen: The choice of exchange rate assumption in the process of forecasting inflation Staff Memo 2005/3