Jeffrey Frankel (HKS, Harvard University ) & Dan Xie (Peterson Inst. for Internatl. Econ.)

1. Estimation of De Facto Flexibility Parameter and Basket Weightsin Evolving Exchange Rate Regimes Jeffrey Frankel (HKS, Harvard University ) & Dan Xie(Peterson Inst. for Internatl. Econ.) Annual Meeting of the American Economics Association, Atlanta. Session on International Financial Markets, Ken West presiding; January 4, 2010, 2:30; Atlanta Marriott Marquis, Marquis Ballroom – Salon C

2. As is by now well-known, the exchange rate regimes that countries follow in practice (de facto) often depart from the regimes that they announce officially (de jure). • Many countries that say they float in fact intervene heavily in the foreign exchange market. [1] • Many countries that say they fix in fact devalue when trouble arises.[2] • Many countries that say they target a basket of major currencies in fact fiddle with the weights.[3] [1] “Fear of floating:” Calvo & Reinhart (2001, 2002); Reinhart (2000). [2] “The mirage of fixed exchange rates:” Obstfeld & Rogoff(1995).Klein & Marion(1997). [3] Parameters kept secret: Frankel, Schmukler & Servén(2000).

3. Economists have offered de facto classifications, placing countries into the “true” categories • Important examples include Ghosh, Gulde & Wolf (2000), Reinhart & Rogoff (2004), Shambaugh (2004a), and more to be cited. • Tavlas, Dellas & Stockman (2008) survey the literature. • Unfortunately, these classification schemes disagree with each other as much as they disagree with the de jure classification! [1] • => Something must be wrong.[1]Bénassy-Quéré, et al(Table 5, 2004);Frankel(Table 1, 2004); and Shambaugh(2004b).

4. Correlations Among Regime Classification Schemes GGW =Ghosh, Gulde & Wolf. LY-S = Levy-Yeyati & Sturzenegger. R-R = Reinhart & RogoffSample: 47 countries. From Frankel (2004).

5. Several things are wrong. 1) Attempts to infer statistically a country’s flexibility from the variability of its exchange rate alone ignore that some countries experience greater shocks than others. That problem can be addressed by comparing exchange rate variability to foreign exchange reserve variability, • Calvo & Reinhart (2002); Levy-Yeyati & Sturzenegger (2003, 05).

6. First approach to estimate de facto regimes: estimate degree of flexibility,typically presuming, e.g., anchor currency = $ • Calvo & Reinhart (2002): Variability of Exchange Rate (E) vs. Variability of Reserves. • Levy-Yeyati & Sturzenegger (2005): cluster analysis based on Variability of E & Δ E, and of Δ Reserves

7. This 1st approach can be phrased in terms of Exchange Market Pressure: • Define EMP = Δ value of currency + Δ reserves. • EMP represents shocks in demand for the currency. • Flexibility can be estimated as the propensity of the central bank to let shocks show up in the price of the currency (floating) ,vs. the quantity of the currency (fixed), or in between (intermediate exchange rate regime).

8. Several things are wrong, continued. 2) Those papers impose the choice of the major currency around which the country in question defines its value (often the $). • It would be better to estimate endogenously whether the anchor currency is the $, the €, some other currency, or some basket of currencies. • That problem has been addressed by a 2nd branch.

9. Second approach in the de facto regime literature estimates implicit basket weights: Regress Δvalue of local currency against Δ values of major currencies. • First examples: Frankel(1993) and Frankel & Wei(1994, 95). • More: Bénassy-Quéré(1999), Ohno (1999),Frankel, Schmukler, Servén & Fajnzylber(2001), Bénassy-Quéré, Coeuré, & Mignon(2004)…. • Example of China, post 7/05: • Eichengreen (2006) , Shah, Zeileis, & Patnaik (2005), Yamazaki (2006), Ogawa (2006), Frankel-Wei (2006, 2007), Frankel (2009) • Findings: • RMB still pegged in 2005-06, with 95% weight on $. • Moved away from $ (weight on €) in 2007-08 • Returned to approximate $ peg in mid 2008.

10. Some currencies have basket anchors, often with some flexibility that can be captured either by a band or by leaning-against-the-wind intervention. • Most basket peggers keep the weights secret. They want to preserve a degree of freedom from prying eyes,whether to pursue • a lower degree of de facto flexibility, as China, • or a higher degree, as with most others.

11. Implicit basket weights method -- regress Δvalue of local currency against Δ values of major currencies -- continued. • Null Hypotheses: Close fit => a peg. • Coefficient of 1 on $ => $ peg. • Or significant weights on other currencies => basket peg. • But if the test rejects tight basket peg, what is the Alternative Hypothesis?

12. Several things are wrong, continued. 3) The 2nd approach (inferring the anchor currency or basket) does not allow for flexibility around that anchor. • Inferring de facto weights and inferring de facto flexibility are equally important, • whereas most authors have hitherto done only one or the other.

13. The synthesis technique • A synthesis of the two approaches for statistically estimating de facto exchange rate regimes:(1) the technique that we have used in the past to estimate implicit de facto weights when the hypothesis is a basket peg with little flexibility. + (2) the technique used by others to estimate de facto exchange rate flexibility when the hypothesis is an anchor to the $, but with variation around that anchor. • A majority of currencies today follow • variants of Band-Basket-Crawl or a managed float. • => We need a technique that can cover both dimensions: inferring weights and inferring flexibility.

14. Several things are wrong, continued. 4) All these approaches, even the synthesis technique are plagued by the problem that many countries frequently change regimes or (for those with intermediate regimes) change parameters. • E.g., Chile changed parameters 18 times in 18 years(1980s-90s) • Year-by-year estimation won’t work, because parameter changes come at irregular intervals. • Chou test won’t work, because one does not usually know the candidate dates. • Solution: Apply Bai-Perron econometric technique for endogenous estimation of structural break point dates.

15. Statistical estimation of de facto exchange rate regimes Estimation of implicit weightsin basket peg: Frankel(1993), Frankel & Wei (1993, 94, 95); Ohno (1999), F, Schmukler & Servén(2000),Bénassy-Quéré (1999, 2006)… Estimation of degree of flexibilityin managed float: Calvo & Reinhart (2002); Levi-Yeyati & Sturzenegger (2003)…; also Reinhart & Rogoff … Synthesis: “Estimation of De Facto Exchange Rate Regimes: Synthesis of the Techniques for Inferring Flexibility and Basket Weights”F & Wei (IMF SP2008) Application to RMB:Eichengreen (06), Ogawa (06), Frankel&Wei (07) Application to RMB: Frankel(2009) Econometric estimation of structural break points: Bai & Perron(1998, 2003) Allow for parameter variation: “Estimation of De Facto Flexibility Parameter and Basket Weights in Evolving Exchange Rate Regimes”F & Xie (2010)

16. The technique that estimates basket weights • Assuming the value of the home currency is determined by a currency basket, how does one uncover the currency composition & weights? This is a problem to which OLS is unusually well suited. We regress changes in the log of H, the value of the home currency, against changes in the log values of the candidate currencies. • Algebraically, if the value of the home currency H is pegged to the values of currencies X1, X2, … & Xn, with weights equal to w1, w2, … & wn, then ΔlogH(t) =c+ ∑ w(j) [ΔlogX(j)] (1)

17. Δ log Ht = c + ∑ w(j) [Δ logX(j)t ] = c + β(1) Δ log $t+ β(2) Δ log ¥t + β(3) Δ log €t + α Δ log £t • If the exchange rate is truly governed by a strict basket peg, then we should recover the true weights, w(j), precisely; and the equation should have a perfect fit.

18. The question of the numeraire • Methodology question: how to define “value” of each currency.[1] • In a true basket peg, the choice of numeraire currency is immaterial; we estimate the weights accurately regardless. [2] • In practice, few countries take their basket pegs literally enough to produce such a tight fit. One must then think about non-basket factors in the regression (EMP, the trend term, error term):Are they better measured in terms of one numeraire or another? • We choose as numeraire the SDR. • F&Wei checked how much difference numeraire choice makes. • by trying the Swiss franc as a robustness check • and in Monte Carlo studies [1] Frankel(1993) used purchasing power over a consumer basket of domestic goods as numeraire; Frankel-Wei (1995) used the SDR; Frankel-Wei (1994, 06), Ohno (1999), and Eichengreen (2006) used the Swiss franc; Bénassy-Quéré (1999), the $; Frankel, Schmukler and Luis Servén (2000), a GDP-weighted basket of 5 major currencies; and Yamazaki (2006), the Canadian $. [2] assuming weights add to1, and no error term, constant term, or other non-currency variable.

19. Distillation of technique to infer flexibility • When a shock increases international demand for korona, do the authorities allow it to show up as an appreciation, or as a rise in reserves? • We frame the issue in terms of Exchange Market Pressure (EMP), defined as % increase in the value of the currency plus increase in reserves (as share of monetary base). • EMP variable appears on the RHS of the equation. The % rise in the value of the currency appears on the left. • A coefficient of 0 on EMP signifies a fixed E(no changes in the value of the currency), • a coefficient of 1 signifies a freely floating rate (no changes in reserves) and • a coefficient somewhere in between indicates a correspondingly flexible/stable intermediate regime.

20. Synthesis equation Δ logH(t) = c + ∑ w(j) Δ[logX(j, t)] + ß {Δ EMP(t)} + u(t) (2) where Δ EMP(t) ≡Δ[logH(t)] + [ΔRes(t) / MB(t)]. We impose ∑ w(j) = 1, implemented by treating £ as the last currency.

21. Synthesis equation Δ log H t = c + ∑w(j) [Δ logXt] + δ {ΔEMPt } + ut (3’) = c + w(1)Δ log$ t + w (2) Δ log €t + w (3) Δ log ¥t + w (4) Δ log £t + + δ { Δ EMP t } + u t .

22. Now we introduce Bai-Perron technique for endogenous estimation of m possible structural break points (6)

23. Illustration using 5 currencies • These are 5 emerging market currencies of interest all of which now make available their data on reserves on a weekly basis (which is necessary to get good estimates, if structural changes happen as often as yearly) • Mexico (monetary base is also available weekly) • Chile, Russia, Thailand, India (although reserves available weekly, denominator must be interpolated from monthly monetary base data)

24. Overview of findings • For all five, the estimates suggest managed floats during most of the period 1999-2009. • This was a new development for emerging markets. • Most of the countries had some variety of a peg before the currency crises of the 1990s. • But the Bai-Perron test shows statistically significant structural breaks for every currency, • even when the threshold is set high, at the 1% level of statistical significance.

25. Table 1A reports estimation for the Mexican peso • 5 structural breaks • The peso is known as a floater. • To the extent Mexico intervenes to reduce exchange rate variation, $ is the primary anchor, but there also appears to have been some weight on € starting in 2003. • Aug.2006 - Dec.2008, coefficient on EMP is essentially 0, surprisingly, suggesting heavier intervention around a $ target. • But in the period starting Dec.2008, the peso once again moved away from the currency to the north, as the worst phase of the global liquidity crisis hit and $ appreciated.

26. Table 1A. Identifying Break Points in Mexican Exchange Rate Regime M1:1999-M7:2009

27. Tables 1B-1E • Chile (with 3 estimated structural breaks) appears a managed floater throughout. • The anchor is exclusively the $ in some periods, but puts significant weight on the € in other periods. • Russia (3 structural breaks) is similar, except that the $ weight is always significantly less than 1. • For Thailand (3 structural breaks), the $ share in the anchor basket is slightly > .6, but usually significantly < 1. • The € and ¥ show weights of about .2 each Jan.1999-Sept. 2006. • India (5 structural breaks) apparently fixed its exchange rate during two of the sub-periods, but pursued a managed float in the other four sub-periods. • $ was always the most important of the anchor currencies, but the € was also significant in four out of six sub-periods, and the ¥ in two.

28. Future research • Results for other currencies will be published in other papers • Often requiring weekly interpolation between monthly reserve figures. • Including our China updates • And true basket/band/crawl currencies • Econometric extension: use Threshold Autoregression for target zones.

29. Conclusion: It is harder to classify regimes than one would think • It is genuinely difficult to classify most countries’ de facto regimes: intermediate regimes that change over time. • Need techniques • that allow for intermediate regimes (managed floating and basket anchors) • and that allow the parameters to change over time. • Jarko Fidrmuc allows parameters to evolve gradually over time, by means of a Kalman filter (session Jan. 5).

30. Bottom line(s) • The new synthesis technique is necessary to discern exchange rate regimes where both the anchor weights and the flexibility parameter are unknown. • Weekly data are necessary to capture the frequency with which many countries’ exchange rate regimes evolve.

32. Appendix 0: preliminary look at the data • First set of countries examined: • 9 small countries that have been officially identified by the IMF as following basket pegs: Latvia, Papua New Guinea, Botswana, Vanuatu, Fiji, W.Samoa, Malta & the Seychelles. • 4 known floaters: Australia, Canada and Japan. • 3 peggers of special interest: China,Hong Kong & Malaysia.

33. Variances of Δ E & Δ Reserves arecomputed • within the period 1980-2007, • for 7-year intervals • The aim in choosing this interval: long enough to generate reliable parameter estimates, and yet not so long as inevitably to include major changes in each country’s exchange rate regime. • All changes are logarithmic, throughout this research. • We try subtracting imputed interest earnings from reported Δ Reserves to get intervention.

35. Lessons from Figure 1 • The folly of judging a country’s exchange rate regime – the extent to which it seeks to stabilize the value of its currency – by looking simply at variation in the exchange rate.E.g. Var(ΔE) for 1980-86 A$ > 2001-07 ¥. But not because the A$ more flexible. It is rather because Australia was hit by much larger shocks.One must focus on Var(ΔE) relative to Var(ΔRes). • Countries that specialize in mineral products tend to have larger shocks.

36. Lessons from Figure 1,continued • Even countries that float use FX reserves actively. E.g., Canada in the 1980s. • A currency with a firm peg (e.g., Hong Kong) can experience low variability of reserves, because it has low variability of shocks.

37. Appendix 1Testing out the synthesis technique,first on some known $ peggers • RMB(Table 2.5): • a perfect peg to the dollar during 2001-04 ($ coefficient =.99, flexibility coefficient insignificantly different from 0, & R2=.99). • In 2005-07 the EMP coefficient suggested that only 90% of increased demand for the currency shows up in reserves, rather than 100%; but the $ weight & R2 were as high as ever. • Hong Kong $(Table 2.8): • close to full weight on US$, 0 flexibility, & perfect fit.

38. A commodity-producing pegger • Kuwaiti dinar shows a firm peg throughout most of the period: a near-zero flexibility parameter, & R2 > .9 (IV estimates in Table 3.5; IV= price of oil). • A small weight was assigned to other currencies in the 1980s basket, • but in the 2nd half of the sample, the anchor was usually a simple $ peg.

39. A first official basket peggerwhich is on a path to the € • The Latvian lat(Table 2.10) • Flexibility is low during the 1990s, and has disappeared altogether since 2000. R2 > .9 during 1996-2003. • The combination of low flexibility coefficient and a high R2 during 2000-03 suggests a particularly tight basket peg during these years. • Initially the estimated weights include $-weight .4 ¥-weight .3; though both decline over time. DM-weight .3 until 1999, • then transferred to €: .2 in 2000-03 and .5 in 2004-07.

40. A 2nd official basket peggeralso on a path to the € • The Maltese lira(Table 2.12) • a tight peg during 1984-1991 and 2004-07 (low flexibility coefficient & high R2). • During 1980-2003, weight on the $ is .2 -.4. • During 1980-1995, the European currencies garner .3-.4, the £ .2-.3 & the ¥ .1. • At the end of the sample period, the weight on the € rises almost to .9.

41. 3rd official basket pegger • Norwegian kroner(Table 2.14) • The estimates show heavy intervention. • Weights are initially .3 on the $ and .4 on European currencies (+ perhaps a little weight on ¥ & £). • But the weight on the European currencies rises at the expense of the $, until the latter part of the sample period shows full weight on the € and none on the $.

42. 4th official basket pegger • Seychelles rupee(Table 2.17) • confirms its official classification, particularly in 1984-1995: not only is the flexibility coefficient essentially 0, but R2 > .97. • Estimated weights: .4 on the $, .3 on the European currencies, .2 on the ¥ and .1 on the £. • After 2004, the $ weight suddenly shoots up to .9 .

43. 2 Pacific basket peggers • Vanuatu(Table 2.19) • low exchange rate flexibility and a fairly close fit. • roughly comparable weights on the $ , ¥, €, and £ . • Western Samoa(Table 2.20) • heavy intervention during the first 3 sub-periods, • around a basket that weights the $ most , and the ¥ 2nd. • More flexibility after 1992. • Weights in the reference basket during 2000-2003 are similar, except the € now receives a large significant weight (.4).

44. A BBC country,rare in that it announced explicitly the parameters: basket weights, band width and rate of crawl. • Chilein the 1980s & 1990s (Table 2.4) • R2 > .9. • The $ weight is always high, but others enter too. • Significant downward crawl 1980-99. • Estimates qualitatively capture Chile’s • shift from $ anchor alone in the 1980s, to a basket starting in 1992. • move to full floating in 1999.

45. Chile,continued • But the estimates do not correspond perfectly to the policy shifts of 1992 & 99 • Possible explanations for gap between official regime and estimates include: • De facto  de jure • Parameter changes more frequent than the 4-year sub-periods. • The Chilean authorities announced 18 changes in regime parameters (weights, width, and rate of crawl) during the 18-year period 1982 -1999. • The difficulty is that we have only monthly data on reserves, for most countries => it is not possible to estimate meaningful parameter values if they change every year or so.

46. Floaters • Australian $ (Table 2.1) • The coefficient on EMP shows less flexibility than one would have expected, given that the currency is thought to have floated throughout this period. • Perhaps the problem is endogeneity of EMP. • World commodity prices are a natural IV.(Table 3.1) • For each sub-period, the estimated flexibility coefficient is indeed higher than it was under OLS, but still far below 1.

47. Appendix 2: Current applicationsusing higher-frequency data • (I) RMB • “New Estimation of China’s Exchange Rate Regime,” Pacific Ec.Rev., 2009. • Updated through early 2009, on my weblog http://content.ksg.harvard.edu/blog/jeff_frankels_weblog/2009/03/11/the-rmb-has-now-moved-back-to-the-dollar/ . • (II) Estimation to allow for frequent parameter shifts • Results for 13 countries offering weekly reserve data, • Therefore allowing estimation intervals shorter than 1 year. • Econometric techniques to estimate parameter shifts endogenously.

48. (2.I)Estimation of RMB with updated technique and data (through early 2008) • This approach reveals that the RMB basket had loosened link to the $ by late 2006, and switched substantial weight onto the € by mid 2007. • An implication is that the appreciation of the RMB against the dollar observed during this period was due to the appreciation of the € against the $, not to any upward trend in the RMB relative to its basket.

49. Table 1: Evolution of RMB Basket Weights from 10-22-2006, 3-month windows of daily data, ending on the month shown Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

50. Table 2:Rolling 12-month regressions of value of RMB Δ (EMP) defined as [res(t)-res(t-1)]/mb(t-1) + [exr(t)-exr(t-1)]/exr(t-1) 12-month windows, ending on the month shown