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The Share of Systematic Variation in Bilateral Exchange Rates by Adrien Verdelhan Nelson C. Mark, Discussant University
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The Share of Systematic Variation in Bilateral Exchange Rates by Adrien Verdelhan Nelson C. Mark, Discussant University of Notre Dame and NBER NBER Summer Institute 2013
Exchange Rate Disconnect Puzzle • Describes the “exceedingly weak relationship (except, perhaps, in the longer run) between the exchange rate and virtually any macroeconomic aggregates.” --Obstfeld and Rogoff (2000) • Characterize as low adjusted R-square in typical exchange rate regressions – A finance approach towards solving the puzzle?
Contributions ∆si,t+1 = f (dollar factort+1 , carry factort+1 ) + !i,t+1
• Identifies a two-factor model with high explanatory power • Provides some structure on the factors: A story about what the factors represent • Shows how global risks are priced in bilateral exchange rates. CD/USD exchange rate depends on more than US and Canadian variables • Shows cross-country heterogeneity is key to understanding the data. Different countries respond differently to global shocks due to differences in underlying economic structure. 2
and 19% (cf. the Brandt et al.the (2006) puzzle). Moreover, are small, cross-sectional variation in equity R currencies is small, and the carry factors ross-sections of carry in andlocal dollar beta-sorted excess returns 2beta-sorted portfolios; a large share of the dollar mall, the cross-sectional variation in equity R s measured Identification outcomes are carry at oddsfactors with theexplain data. a ocal currencies is small, and the ∆si,t+1 = f (dollar factort+1 , carry factort+1 ) + !i,t+1 e share of the dollar beta-sorted portfolios; all of these • Dollar factor-natural II. S CRATCH AREA omes are at odds with the data. – Cross-sectional average of bilateral exchange rates – Naturally mimics the dominant i factor. ! Is how you ∆s (αi + θt + ui,t ) t = xi,t βin+ II.forScross-sectional CRATCH AREA control correlation error components model
∆sit = x!i,t β + (αi + θt + ui,t )
θt = δft
• Carry factor-insightful – Sort countries by interest rate. Is the average exchange rate between groups of high and low interest rate countries. 3
cd/$
∆st+1
SF /£
= δ∆st+1 Carry
Difference between Swiss and UK global component of SDF. Is nonzero only if Switzerland and UK SDFs respond differently to global shocks
+τ
!
# " 1 ∆sit+1 + #t+1 N Dollar
US specific and global components of US and foreign SDFs Cross country variaCon in loadings means heterogeneity across SDF global components
Two sources of global risks 4
Structure on factors • Plays with reduced form models try to identify these two global risks – Dollar: global growth risk – Carry: global volatility risk
• Global risk idea still pretty general. Maps exchange rates into exchange rates. • Future challenge: Link the risks to exogenous shocks. • Suggest a macro approach
5
Macroeconomic structure ∆st+1 =
m1t+1
−
m2t+1
! 1 " 2 = γ ∆ct+1 − ∆ct+1
• New Keynesian model with Calvo price stickiness, Taylor rules, 3 countries – Heterogeneity between 1 and 2, a shock from 3 moves the exchange rate between 1 and 2 because they respond differently to the shock
• Source of heterogeneity? – Monetary policy reaction functions – Duration of nominal contracts
6
+4
∆sit+4
i" ∆s t+4 i
! i " i = β1 st + pt − pt + "i,t + αi
! i = β1 st + pt − pt + "i,t + αi
" $PPP Exchange #! iMeani R¯ 2 from key key 5: iMonte Rate Regressions ! iTablei ∆s " = Carlo s β s + p − p + β + p − pt + "i,t + αi key key 2 1 t t t+4 t t t = β1 st + pt − pt + β2 st + pt − pt + "i,t + αi #
$
Deviation from PPP relative to Table 5: Monte Carlo Mean R¯ 2 Country from PPP Regressions 1 Exchange CountriesRate 1 and 3 ¯2 ¯2 Horizon Environment R R Deviation from PPP relative to 1 II 0.018 1 Countries 0.059 1 and 3 Country 1 III Horizon Environment 11 IVII 41 IIIII 41
0.014 R¯ 2 0.012 0.018
0.057 R¯ 2 0.065 0.059
0.171 0.014 0.157 0.012
0.349 0.057 0.337 0.065
0.140 0.171
0.345 0.349
44
IIIIV IVII
4
III
0.157
0.337
4
IV
0.140
0.345
7
sit+4
Great Britain Indonesia Japan !
∆sit+4 = β1 Korea
0.042
0.024
-0.010
-0.007
i 0.045 0.035 " ∆s t+4 = β1 i
New Zealand
-0.008
-0.006
0.024
-0.010
0.027
! i " i st + pt − pt + "i,t0.033 + αi
sit + pt − pt + "i,t + αi 0.013
0.061**
0.111**
-0.004
-0.004
0.093** #
-0.026 $ ! i "$ # -0.004 key key0.054** i i ! i Norway " 0.033** 0.008 s p − p + β + p − pt + "i,t + αi i ∆st+4 = β1keyst + key t = β1 st + pt − pt + β2 st + pt t − ptt + "2i,t +t αi Philippines -0.021 0.038 0.070** 0.029 ¯ 2 of Deviation Singapore -0.021 -0.029 0.045** -0.025 Table 1: R from PPP Exchange Rate Regressions Sweden 0.016 0.010 0.058** 0.019 Deviation from PPP relative to Switzerland -0.018 -0.033 0.041** USD USD & euro USD & yen USD & SF Thailand -0.016 0.000 0.065** -0.008 (1) (2) (3) (4) B: One-period Four-periodhorizon horizon A:
Australia Australia Brazil Brazil
-0.006 -0.020 0.038 -0.016
-0.024 -0.040 0.488** 0.097**
0.115* -0.025 0.032 -0.036
0.065* 0.018** 0.429** 0.088**
Canada Canada Denmark Denmark
0.009 -0.015 0.070 -0.003
0.042 -0.006 0.126 0.000
0.013 -0.030 0.485** 0.124**
0.100** 0.013* 0.062 -0.024
Great Great Britain Britain Indonesia Indonesia
0.250 0.042 0.216 -0.010
0.254 0.024
0.346** 0.061**
0.243 0.024
0.273 -0.007
0.336** -0.010
0.324* 0.027
Japan Japan Korea Korea
0.045 0.199 0.013 0.244
0.035 0.219 -0.006 0.243
0.033 0.258** -0.004 0.249
-0.004 0.266
8
Conclude • Shows how global risks, stuff beyond bilateral country pair, matters for bilateral exchange rates • Importance of cross-country heterogeneity • Still doesn’t solve the disconnect puzzle. Exchange rates on exchange rates • Challenge for future work: Model global risks generated by exogenous shocks. • There is contact between this paper and ongoing macro style research. Berg and Mark (2013), Evans (2012). • Great paper. 9
: This table reports country-level results from the following regression: st+1 = ↵ + (i?t
it ) + (i?t
it )Carryt+1 + Carryt+1 + ⌧Dollart+1 + "t+1 ,
Table 2: Carry and Dollar Factors: Monthly Tests in Developed Countries
st+1 denotes the bilateral exchange rate in foreign currency per U.S. dollar, and i?t it is Table 2: Carry and Dollar Factors: Monthly Tests in Developed Countries di↵erence between the foreign country and the U.S., Carryt+1 denotes the dollar-neutral averag 2 Country ↵ ⌧ R2 R$2 Rno W N nge rates obtained by going long a basket of high interest rate currencies and$ short a basket of Australia -0.44 0.16 0.74 25.59 20.05 *** 312 27.71 Country ↵ ⌧ R$2 rates Rno W N urrencies, and Dollart+10.07 corresponds to0.77the average change inR2exchange against the U.S. $ (0.60) (0.49) (0.13) (0.13) [5.77] [5.72] [4.31] 0.07 -0.44coefficients 0.77 0.16 20.05as the 7.71adjusted *** 312 reports Australia the constant ↵,(0.23) the slope , , ,0.74 and 25.59 ⌧, as well R2 of thi Canada -0.11 -0.02 (0.49) -0.61 (0.13) 0.21 (0.13) 0.34 19.38 13.11 [4.31] 8.14 *** 312 (0.23) (0.60) [5.77] errors [5.72] ercentage points) and the number of observations N. Standard in parentheses are Newe (0.11) (0.63) (0.42) (0.06) (0.07) [6.94] 13.11 [4.34] [4.97] Canada -0.11 -0.02 -0.61 0.21 0.34 19.38 *** (1991). 312 ) standard errors computed with the optimal number of lags according to8.14 Andrews Th Denmark -0.01 -0.20 0.53 -0.16 1.51 86.08 83.63 3.97 *** 312 (0.11) (0.63) (0.42) (0.06) (0.07) by[6.94] [4.34] [4.97]R2 denotes the adj for the R2 s are reported in brackets; they are obtained bootstrapping. $ (0.07) [1.67] 83.63 [2.03] [3.99] Denmark -0.01 (0.38) -0.20 (0.13) 0.53 (0.03) -0.16 (0.04) 1.51 86.08 3.97 *** 312 ilar regression with only0.07 the Dollar factor (i.e., without the conditional and unconditional Car Euro Area -0.52 (0.13) 0.10 (0.03) -0.28 (0.04) 1.62 80.60 76.22 [3.99] -0.05 *** 143 (0.07) (0.38) [1.67] [2.03] 2 denotes the adjusted R(0.11) of a similar (0.23) regression without the [3.58] Dollar[3.99] factor.[4.81] W denotes the resul Euro Area 0.07 (0.86) -0.52 0.10 (0.05) -0.28 (0.08) 1.62 80.60 76.22 -0.05 *** 143 the nullFrance hypothesis is that the loadings and (0.05) on the(0.08) conditional and unconditional -0.15 -0.10 (0.23) 0.80 -0.13 1.38 90.97 87.58 12.30 *** carry 181 factor (0.11) (0.86) [3.58] [3.99] [4.81] Three asterisks to a rejection of the (0.04) null at the12.30 1% confidence (0.07) (0.14) [1.48] 87.58 [1.93] [5.90] France (***) correspond -0.15 (0.34) -0.10 0.80 (0.03) -0.13 1.38 hypothesis 90.97 *** 181 level; t ne asterisk correspond to the 5% 10% levels.91.00 Data [1.93] are monthly, a Germany -0.21 -0.03and (0.14) 0.79 confidence -0.03 (0.04) 1.42 88.35 22.83 from *** Barclays 181 (0.07) (0.34) (0.03) [1.48] [5.90] stream).Germany All variables are in percentage points. The (0.04) sample period is 11/1983–12/2010. (0.09) (0.34) (0.04) [1.36] 88.35 [1.75] [6.20] *** 181 -0.21 -0.03 (0.17) 0.79 -0.03 1.42 91.00 22.83 Italy Italy Japan Japan New Zealand
-0.03 (0.09) (0.22) -0.03 (0.22) -0.44 -0.44 (0.24) (0.24) 0.10
0.26 (0.34) (0.69) 0.26 (0.69) -1.13 -1.13 (0.86) (0.86) -0.58
0.68 (0.17) (0.20) 0.68 (0.20) -0.10 -0.10 (0.45) (0.45) 0.76
-0.07 (0.04) 1.24 (0.04) (0.11) -0.07 (0.10) 1.24 44 0.83 (0.11) -0.39 (0.10) -0.39 (0.12) 0.83 (0.11) (0.11) -0.11 (0.12) 0.95
68.97 [1.36] [5.25] 68.97 [5.25] 29.52 29.52 [5.51] [5.51] 29.80
64.59 [1.75] [6.92] 64.59 [6.92] 23.58 23.58 [5.45] [5.45] 26.96
2.16 [6.20] [6.13] 2.16 [6.13] 5.34 5.34 [3.47] [3.47] 3.43
*** 177 *** 177 10 *** 325 *** 325 *
312
the idiosyncratic component. The orthogonality restrictions that we imposed for identification implies that the total depreciation variance is the sum of the component variances, o V ar(∆sit ) = V ar(δi,1 ∆f1,t )Table + V ar(δ ∆f ) + V ar(δ ∆f ) + V ar(∆s i,2 2,t i,3 3,t i,t ). 2: Variance Decomposition by Factor
Nominal
(8)
Real
Table 2 shows the results of this decomposition, from which the first factor is seen to account for
Countryof exchange FirstrateSecond Total common Firstfactor Second nearly half of the variance changes. Third Taken together, variationT Australia 0.71 0.06 and 0.0564 percent 0.82 of real0.70 0.06variexplains 66 percent of nominal depreciation variation depreciation ation. We note also that the proportion the nominal Brazil 0.19 of variance 0.39 in 0.00 0.57depreciation 0.16 explained 0.40 by each factor is very close to that explained real depreciation which again offers qualitative Canada 0.45 in the 0.08 0.07 0.60 0.41 0.06 support for our identifying assumptions.
Chile
2.2
0.29
0.23
0.01
0.52
0.26
0.21
Colombia 0.23 Testing for predictability Czech 0.73
0.31
0.00
0.55
0.19
0.36
0.07
0.01
0.81
0.71
0.06
In this subsection, we conduct an in-sample test of exchange rate predictability by estimating
Denmark
0.81
0.11
0.00
0.93
0.79
0.11
Euro
0.81
0.11
0.00
0.93
0.81
0.11
the factor-augmented PPP predictive regression (6) and testing the null hypothesis that the slope coefficient on the lagged real exchange rate β, is zero. Inoue and Kilian (2004) argue that
0.78 0.03 the 0.82 0.77 sample0.00 in-sample tests of Hungary predictability may be more 0.01 credible than results of out-of tests. Israel 0.00 First,0.01 0.26that the0.26 0.00 We make two points about the0.25 econometrics. we assume slope coefficients βi ∼
iid(β, σβ2 )
11
are randomly β and estimate a common β0.09 by pooling across Japan distributed 0.09 around 0.20 0.35 0.64 0.21
individuals in the panel. Second, 0.44 we control 0.14 for the omitted common 0.15 factors) Korea 0.01 variables 0.60 (the0.42
Identification • Where is Adrien’s third factor? – Carry is dollar neutral: BR/Yen=BR/USD USD/Yen – SF and Yen are source currencies for carry trade.
12
tracted only from the exchange rate data and not from additional
Fi,t =
δi,j fj,t
j=1
change rates {si,t }N driven by pIdentification common factors {f1,t , f2,t , . . . fp,t }. GMSW i=1 be
e common exchange rate component forSulcurrency i. With this notation (Greenaway-McGrevy, Mark, and Wu (2012))
loading for currency i by δi,j and let
• factor Three structure factor model: monthly 1999 to 2010. have the Fi,t =
p !
si,t = Fi,t + soi,t .
δi,j fj,t
j=1
make the standard identifying restriction that the factors {fj,t} are m "
rate component for currency i. With this notation, nominal exchange %*+,-*+./0+12,304+56 $72,-*+./0+12,304+56 o o
are orthogonal to# the idiosyncratic component si,t . si,t can either be a
cture
$
is more likely theFcase, ocan be a unit-root process. We place further si,t = + s (1) i,t i,t . % eded below. &
dentifying restriction that the factors {fj,t} are mutually orthogonal
!% ext, let the log real exchange rate between country i and the U.S. be o o
e idiosyncratic component si,t . si,t can either be a stationary process !$
o case, can be a unit-root process. We place further restrictions on s ∗ i,t !# #62,-*+./0+12,304+56
!" %'''
$&&%
qi,t = si,t + pt − pi,t ,
$&&#
$&&(
$&&)
$&&'
13
country i and and pthe U.S. belog country i price level. S eexchange p∗ is therate logbetween U.S. price level is the i,t Figure 1. Integrated factors estimated from panel of depreciation rates.
ves
∗
GMSW Identification Regress first factor on each exchange rate: select maximum Rsquare
14
Figure 5. First empirical and statistical nominal exchange rate factor.
remaining exchange rate on first and second factor. SwissFigure 5.Regress Firsteach empirical and statistical nominal exchange rate factor. franc has highest R-square
15
gure 6. Second empirical and statistical nominal exchange rate factor
eachempirical remaining exchange rate on first, second, and third factor. Figure 6.Regress Second and statistical nominal exchange rate facto Yen has highest R-square
16
Figure 7. Third empirical and statistical nominal exchange rate facto