Assessing terms of trade volatility in Argentina 1810 - 2010. A Fourier approach to decycling .
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Assessing terms of trade volatility in Argentina
1810 - 2010. A Fourier approach to decycling.
Alberto M. Díaz CafferataJosé Luis Arrufat
María Victoria AnauatiSantiago Gastelu
Instituto de Economía y Finanzas. Facultad de Ciencias Económicas
Universidad Nacional de Córdoba
Arnoldshain Seminar XIMigration, Development, and Demographic Change –
Problems, Consequences, SolutionsJune 25 – 28, 2013, University of Antwerp, Belgium
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I. Introduction
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I. Introduction
II.Modeling and estimating uncertainty
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I. Introduction
II.Modeling and estimating uncertainty
III. Analysis of the results
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I. Introduction
II.Modeling and estimating uncertainty
III. Analysis of the results
IV. Concluding remarks
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IIntroduction
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Argentina TOT index. Problems for developing countriesWeak evidence of Prebisch – Singer 1950 declining trend hypothesis. Focus shift towards large shocks and volatile fluctuations.
20
40
60
80
100
120
140
160
1825 1850 1875 1900 1925 1950 1975 2000
TOTTOT index 1993=100 (1810-2010)
1909: 146
1987: 852000: 1062010: 141
1948: 150
1922: 71
Quiebres estructurales
1839
*1917
*1950
*
*
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High and irregular fluctuations
TOT moves irregularly through time.
TOT volatility in emerging countries is 3 times higher than in industrial countries (Aizenman et al. 2011, Mendoza 1995)
Our perspective: volatility in Argentina is HIGH and presumably COSTLY.
Our problem: concept and measure of volatility
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Our goal
Review alternative definitions of volatility in the literature.
Improve on frequently used methods:SD of a time series
SD of detrended residuals
We model additionally cycles, assuming that people perceive not only trends, but also cycles in economic
variables
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IIModeling and
estimating uncertainty
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How much “volatility”?Volatility analytical interpretation:
associated with uncertainty.
Volatility in standard empirical practice,proxyed by:
a)Variability b)Unexpected portion, the unpredictable component of variability. Agents perceive regular but not irregular movements of economic time series:
• SD of Hodrick Prescott (HP) filtered residuals• SD of polynomial detrending residuals.
c)Our approach.
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Modeling and estimating uncertainty (1)
Original Series
Volatility
Standard Deviation
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Modeling and estimating uncertainty (2)
Original Series
Detrended Residuals
Volatility
HP Filter / Polynomial Detrending
Standard Deviation
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Modeling and estimating uncertainty (3)
Original Series
Detrended Residuals
Detrended + Decycled Residuals
Volatility
HP Filter / Polynomial Detrending
Fourier Decomposition
Standard Deviation
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Empirical proxies for volatility in the literature
SD of raw series
• Aizenman et al. (2011), “Adjustment patterns to commodity terms of trade shocks: the role of exchange rate and international reserves policies”, NBER WP 17692.
• Larrain & Parro (2006), “Chile menos volátil”, Instituto de Economía, Universidad Católica de Chile.
• Mendoza (1994), “Terms-of-trade uncertainty and economic growth. Are risk indicators significant in growth regressions?”, International Finance Discussion Papers (Vol 491).
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SD of detrended residuals
Distinguish between predictable (regular part) and unpredictable (uncertainty) components of a variable.
• Kim (2007), “Openness, external risk, and volatility: implications for the compensation hypothesis”, Cambridge Univ Press.
• Wolf (2004), “Volatility: Definitions and Consequences”, Draft Chapter for Managing Volatility and Crises.
• Dehn (2000), "Commodity price uncertainty in developing countries”, World Bank (Series 2426)
• Baxter (2000), “International trade and business cycles”, in Grossman and Rogoff .
Empirical proxies for volatility in the literature
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How to determine the residuals: warnings about proper detrending
“Much care has to be dedicated to the detrending procedure since a wrong specification can bias severely the subsequent analysis” (Bee Dagum)
“Different detrending procedures are alternative windows which look at the series from different perspectives” (Canova)
• Bee Dagum et al. (2006), “A critical investigation on detrending procedures for non-linear processes”, Journal of Macroeconomics (vol 28).
• Kauermann et al. (2008), “Smoothing parameter selection for spline estimation”,
• Kauermann et al. (2011), "Filtering time series with penalized splines", Studies in Nonlinear Dynamics and Econometrics, (vol 15(2))
• Canova (1998), “Detrending and business cycle facts: A user’s guide”, Journal of Monetary Economics (vol 41).
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Data and procedureData:Argentina TOT and GDP logged from index1993=100. 1810 – 2010 (Ferreres & INDEC)
Detrending:a. Cubic polynomial detrendingb. HP filter detrending (lambda = 100)
Decycling:a. Fourier decomposition
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TOT and GDP cubic polynomial detrending
-.6
-.4
-.2
.0
.2
.4
.6
3.2
3.6
4.0
4.4
4.8
5.2
1825 1850 1875 1900 1925 1950 1975 2000
Residual Actual Fitted
-.4
-.2
.0
.2
.4
.6
6
8
10
12
14
1825 1850 1875 1900 1925 1950 1975 2000
Residual Actual Fitted
TOT Cubic DetrendingTrend and Residuals
GDP Cubic DetrendingTrend and Residuals
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Fourier decompositionFollowing Bolch and Huang, the decomposition of a series into its periodic components is done using:
where
and
101 101
0 0
cos 2 sin 2at i ii i
t tZ i iT T
ˆat at atZ Y Y
1 logt tY TOT 2 logt tY GDP
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Fourier decomposition
Relative Cumulative
7 28.86 -0.074277 -0.100609 26.52 26.525 40.40 -0.048533 0.049061 8.08 34.593 67.33 -0.011200 0.060851 6.49 41.098 25.25 0.032471 -0.048437 5.77 46.8515 13.47 0.001766 -0.053962 4.94 51.811 18.36 -0.028542 -0.037448 3.76 55.5617 11.88 0.019214 -0.039233 3.24 58.7932 6.31 0.033478 -0.027366 3.17 61.9612 16.83 0.039866 -0.004198 2.72 64.692 101.00 0.011674 0.036616 2.5 67.1910 20.20 0.019372 -0.030821 2.25 69.4421 9.62 -0.015295 0.030226 1.95 71.38
Contribution to TSS(in percentage)
Note: TSS stands for Total Sum of Squares. Source of data are provided in the Appendix. Own calculations base on Bolch and Huang (1974), Chapter 8, Section 8.2 The Fourier series and the correlogram, pp. 275 – 283.
iPeriod(T/i)
Estimates of cyclical patterns of log TOT: Argentina 1810-2010.
ˆi
i
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Comments on TOT decomposition I. The most important cycle:• period: 28.86 years • frequency: observed only seven times in 202
years • acounts for 26.52% of the total sum of squares.
II. The first five most important cycles account for 51.8% of the total sum of squares
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Relative Cumulative
2 101.00 0.166078 0.007773 57.70 57.703 67.33 -0.033491 0.047847 7.12 64.8210 20.20 0.045337 -0.007748 4.42 69.245 40.40 0.041753 0.006052 3.72 72.951 202.00 -0.035759 -0.002552 2.68 75.6312 16.83 0.031626 -0.011927 2.38 78.024 50.50 0.030783 -0.001724 1.98 80.006 33.67 0.022053 -0.021532 1.98 81.9914 14.43 0.026946 -0.003827 1.55 83.537 28.86 0.019666 -0.018753 1.54 85.0716 12.63 0.023526 -0.010475 1.38 86.4623 8.78 0.000847 -0.023375 1.14 87.60
Contribution to TSS(in percentage)
Note: TSS stands for Total Sum of Squares. Source of data are provided in the Appendix. Own calculations base on Bolch and Huang (1974), Chapter 8, Section 8.2 The Fourier series and the correlogram, pp. 275 – 283.
iPeriod(T/i)
Fourier decompositionEstimates of cyclical patterns of log GDP: Argentina 1810-2010.
ˆi
i
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Comments on GDP decomposition (1)I. The most important cycle:• period: 101 years • frequency: observed twice in 202 years • acounts for 57.70 percent of the total sum of
squares.
II. Another important cycle:• Period: 202 years • frequency: observed once in 202 years • acounts for 2.68 percent of the total sum of
squares.
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Is it meaningful to assume that the 202-year super-cycle exists as a long run
process of GDP?
•Cycles should not be taken mechanically
•Their economic relevance has not a clear interpretation
For analytical purposes we have kept all cycles
Comments on GDP decomposition (2)
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How many of the cycles are to be removed from the detrended series?
• For TOT we extracted approximately 55% of variability
• For GDP we extracted approximately 80% of variability
The results obtained proved to be robust to different choices of end points
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Removed cycles and decycled residuals
-.3
-.2
-.1
.0
.1
.2
.3
.4
1825 1850 1875 1900 1925 1950 1975 2000
TOT Removed Cycles
-.3
-.2
-.1
.0
.1
.2
.3
.4
1825 1850 1875 1900 1925 1950 1975 2000
GDP Removed Cycles
-.3
-.2
-.1
.0
.1
.2
.3
.4
1825 1850 1875 1900 1925 1950 1975 2000
Decycling TOT
-.3
-.2
-.1
.0
.1
.2
.3
1825 1850 1875 1900 1925 1950 1975 2000
Decycling GDPDecycled TOT Decycled GDP
TOT Removed Cycles GDP Removed Cycles
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This measure drops monotonically when more knowledge on cycles is attributed to the
economic agents
TOT GDP
SD SD
0 0.172 0.152
1 0.146 0.099
2 0.137 0.089
3 0.130 0.084
4 0.124 0.079
5 0.118 0.074
6 0.112 0.071
7 0.108 0.068
8 0.104 0.065
9 0.101 0.062
10 0.097 0.059
Number of cycles removed
Note: SD stands for standard deviation.Source of data: Own estimations
A scalar measure of volatility (1810-2010)
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Volatility = SD in a five-year rolling sample
of the decycled residual series
A proxy for volatility
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TOT and GDP volatility (1815-2010) SD (five years) of cubic detrending and Fourier decycling
.00
.05
.10
.15
.20
.25
1850 1900 1950 2000
TOT Volatility
.00
.05
.10
.15
.20
.25
1850 1900 1950 2000
GDP VolatilityTOT volatility
(extracting 55% of variability)GDP volatility
(extracting 80% of variability)
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TOT and GDP volatility (1815-2010) SD (five years) of HP detrending and Fourier decycling
TOT volatility (extracting 55% of variability)
GDP volatility (extracting 80% of variability)
.00
.04
.08
.12
.16
1850 1900 1950 2000
SD of log tot detrending (HP) and decycling(extrancting 55% of variability)
.00
.04
.08
.12
.16
1850 1900 1950 2000
SD of log GDP detrending (HP) and decycling(extrancting 80% of variability)
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IIIAnalysis of the results
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Is TOT volatility overestimated in empirical analysis?
SD of TOT HP residuals
SD of TOT detrendig (HP) and decycled
Mean 0.087 0.064Std. Dev. 0.044 0.031
.00
.04
.08
.12
.16
.20
.24
1825 1850 1875 1900 1925 1950 1975 2000
SD of TOT HP residualsSD of TOT detrendig and decycling
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Is GDP volatility overestimated in empirical analysis?
.00
.02
.04
.06
.08
.10
.12
1825 1850 1875 1900 1925 1950 1975 2000
SD of GDP detrendig and decyclingSD of GDP HP residuals
SD of GDP HP
residuals
SD of GDP detrendig (HP) and
decycled
Mean 0.039 0.023 Std. Dev. 0.027 0.010
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Does TOT volatility Granger-cause GDP volatility?
Is it the level, trend, cycles, volatility or other statistical property of TOT relevant?
Do TOT affect the level, the volatility, the growth rate or some other characteristic of GDP?
If there is a relation between them, which is its sign?
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Insights of TOT volatility effects
Evidence related to causality is very heterogeneous
Many variables (degree of openness, concentration of X and M, the financial system, etc.) may explain the heterogeneous empirical
results
Direct relationship between TOT volatility and GDP volatility seems to prevail in the
literature
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TOT index positive trend, and large fluctuations.Irregular GDP growth
20
40
60
80
100
120
140
160
1825 1850 1875 1900 1925 1950 1975 2000
TOT
-.3
-.2
-.1
.0
.1
.2
.3
1825 1850 1875 1900 1925 1950 1975 2000
GDPTOT index 1993=100 (1810-2010)
GDP growth (1811-2010)
1909: 146
1987: 852000: 1062010: 141
1948: 150
1922: 71
1897: -21%2001: - 13%
1890: -8% Baring Crisis
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Possible presence of causality
Contemporaneous correlation = 0.14
Higher correlation is observable between TOT volatility and
GDP growth volatility
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Volatility by subperiodsWe can associate subperiods of higher (lower) TOT volatility with higher (lower) GDP volatility. Breaks from Bai Perron algorithm on the original series:
GDP SD
TOT SD
1815 – 1882
CC = 0.19
1950 – 2010
CC = -0.06
1883 – 1949
CC = 0.15
Low
(0.019)
Medium
(0.024)
High
(0.027)
Low
(0.059)
Medium
(0.061)
High
(0.071)
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Exercise on VAR estimationSpecifications:
• Assumption of small open economy – SOE
• Variables (in order):
SD (five years) of TOT detrending and decycled residuals
SD (five years) of GDP detrending and decycled residuals
• Sample: 1815 – 2010
• Control variables: grade of openness, export price index, investment.
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VAR impulse response functionOnce-and-for-all 1-standard deviation shock
to TOT volatility on GDP volatility
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IVConcluding remarks
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Concluding remarks• Alternative definitions of volatility may be used to measure the degree of uncertainty in the evolution of an economic variable.
• From a methodological point of view the variability of an economic time series overestimates its volatility.
• The choice of a specific method might impinge on the magnitude, and other statistical properties of the volatility of a variable.
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• Relevant structural features of the Argentine economy determined by its land abundance: concentration of exports on agricultural commodities generates volatility on TOT.
• Impact on income distribution, external liquidity and solvency, instability of fiscal budgets, preference for flexibility on investment.
Policy implications
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Extensions• Identification of statistical breaks in TOT volatility. Cubic Splines Detrending.
• Further modeling with regard to the relationship between TOT volatility and GDP volatility. Channels of transmition. Control variables (Investment, Grade of Openness, Balance of Payments, etc). Not readily available over such long time span.
• We use barte TOT. Berlinski (2003) documented a wide gap between internal and external terms of trade.
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Extensions Continued• Sudden TOT changes bring about severe distributive conflicts because Argentina is a big exporter of wage goods.
• Wolf (2004): uncertainty proxied by SD might be better measured by a weighting procedure which does not rely on symmetry.
• Wolf (2004): the relationship between TOT and GDP may be subject to threshold effects not captured by a linear model.
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Thank You
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Assessing terms of trade volatility in Argentina
1810 - 2010.A Fourier approach to decycling.
José Luis ArrufatAlberto M. Díaz Cafferata
María Victoria AnauatiSantiago Gastelu
Instituto de Economía y Finanzas. Facultad de Ciencias Económicas
Universidad Nacional de Córdoba
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ReferencesAizenmanEdwardsRiera-Crichton (2011)Larrain, Parro (2006)Mendoza (1994)Kim (2007)Wolf (2004)Dehn (2000)Baxter (2000)