Transcript Diaz Cafferata

Arnoldshain Seminar XI
Migration, Development, and Demographic Change –
Problems, Consequences, Solutions
June 25 – 28, 2013, University of Antwerp, Belgium
Assessing terms of trade volatility in Argentina
1810 - 2010.
A Fourier approach to decycling.
Alberto M. Díaz Cafferata
José Luis Arrufat
María Victoria Anauati
Santiago Gastelu
Instituto de Economía y Finanzas. Facultad de Ciencias Económicas
Universidad Nacional de Córdoba
I. Introduction
I. Introduction
II. Modeling and estimating
uncertainty
I. Introduction
II. Modeling and estimating
uncertainty
III. Analysis of the results
I. Introduction
II. Modeling and estimating
uncertainty
III. Analysis of the results
IV. Concluding remarks
I
Introduction
Argentina TOT index. Problems for developing countries
Weak evidence of Prebisch – Singer 1950 declining trend hypothesis.
Focus shift towards large shocks and volatile fluctuations.
TOT index 1993=100 (1810-2010)
*
Quiebres estructurales
1909: 146
1948: 150
1922: 71
1987: 85
2000: 106
2010: 141
1839
1917
1950
*
*
*
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
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
II
Modeling and estimating
uncertainty
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.
Modeling and estimating uncertainty (1)
Original Series
Standard Deviation
Volatility
Modeling and estimating uncertainty (2)
Original Series
HP Filter / Polynomial
Detrending
Detrended Residuals
Standard Deviation
Volatility
Modeling and estimating uncertainty (3)
Original Series
HP Filter / Polynomial
Detrending
Detrended Residuals
Fourier
Decomposition
Detrended + Decycled Residuals
Standard Deviation
Volatility
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).
Empirical proxies for volatility in the literature
SD of detrended residuals
Distinguish between predictable (regular part)
unpredictable (uncertainty) components of a variable.
and
• 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 .
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).
Data and procedure
Data:
Argentina TOT and GDP logged from index
1993=100. 1810 – 2010 (Ferreres & INDEC)
Detrending:
a.
b.
Cubic polynomial detrending
HP filter detrending (lambda = 100)
Decycling:
a.
Fourier decomposition
TOT and GDP cubic polynomial detrending
GDP Cubic Detrending
Trend and Residuals
TOT Cubic Detrending
Trend and Residuals
5.2
14
4.8
12
.6
4.4
.4
4.0
.2
3.6
.0
10
.6
.4
8
.2
6
-.2
3.2
.0
-.4
-.2
-.6
-.4
1825
1850
1875
Residual
1900
1925
Actual
1950
1975
Fitted
2000
1825
1850
1875
Residual
1900
1925
Actual
1950
1975
Fitted
2000
Fourier decomposition
Following Bolch and Huang, the decomposition of a series
into its periodic components is done using:
101

Z at    i cos 2 i t
i 0
where
and
   sin  2 i t 

T
T
101
i 0
i
Zat  Yat  Yˆat
Y1t  log TOTt 
Y2t  log  GDPt 
Fourier decomposition
Estimates of cyclical patterns of log TOT: Argentina 1810-2010.
i
7
5
3
8
15
11
17
32
12
2
10
21
Period
(T/i)
ˆi
28.86
40.40
67.33
25.25
13.47
18.36
11.88
6.31
16.83
101.00
20.20
9.62
-0.074277
-0.048533
-0.011200
0.032471
0.001766
-0.028542
0.019214
0.033478
0.039866
0.011674
0.019372
-0.015295
ˆi
-0.100609
0.049061
0.060851
-0.048437
-0.053962
-0.037448
-0.039233
-0.027366
-0.004198
0.036616
-0.030821
0.030226
Contribution to TSS
(in percentage)
Relative
26.52
8.08
6.49
5.77
4.94
3.76
3.24
3.17
2.72
2.5
2.25
1.95
Cumulative
26.52
34.59
41.09
46.85
51.8
55.56
58.79
61.96
64.69
67.19
69.44
71.38
Note: T SS stands for T otal Sum of Squares.
Source of data are provided in the Appendix. Own calculations base on Bolch and Huang (1974), Chapter
8, Section 8.2 T he Fourier series and the correlogram, pp. 275 – 283.
Comments on TOT decomposition
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.
I.
II.
The first five most important cycles account for 51.8%
of the total sum of squares
Fourier decomposition
Estimates of cyclical patterns of log GDP: Argentina 1810-2010.
i
2
3
10
5
1
12
4
6
14
7
16
23
Period
(T/i)
ˆi
ˆi
101.00
67.33
20.20
40.40
202.00
16.83
50.50
33.67
14.43
28.86
12.63
8.78
0.166078
-0.033491
0.045337
0.041753
-0.035759
0.031626
0.030783
0.022053
0.026946
0.019666
0.023526
0.000847
0.007773
0.047847
-0.007748
0.006052
-0.002552
-0.011927
-0.001724
-0.021532
-0.003827
-0.018753
-0.010475
-0.023375
Contribution to TSS
(in percentage)
Relative
57.70
7.12
4.42
3.72
2.68
2.38
1.98
1.98
1.55
1.54
1.38
1.14
Cumulative
57.70
64.82
69.24
72.95
75.63
78.02
80.00
81.99
83.53
85.07
86.46
87.60
Note: T SS stands for T otal Sum of Squares.
Source of data are provided in the Appendix. Own calculations base on Bolch and Huang (1974), Chapter
8, Section 8.2 T he Fourier series and the correlogram, pp. 275 – 283.
Comments on GDP decomposition (1)
The most important cycle:
• period: 101 years
• frequency: observed twice in 202 years
• acounts for 57.70 percent of the total sum of squares.
I.
Another important cycle:
• Period: 202 years
• frequency: observed once in 202 years
• acounts for 2.68 percent of the total sum of squares.
II.
Comments on GDP decomposition (2)
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
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
Removed cycles and decycled residuals
GDP
GDPRemoved
RemovedCycles
Cycles
TOT Removed
Removed Cycles
TOT
Cycles
.4
.4
.3
.3
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
-.3
-.3
1825 1850 1875 1900 1925 1950 1975 2000
1825 1850 1875 1900 1925 1950 1975 2000
Decycling
TOT
Decycled
TOT
DecyclingGDP
GDP
Decycled
.4
.3
.3
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
-.3
-.3
1825 1850 1875 1900 1925 1950 1975 2000
1825 1850 1875 1900 1925 1950 1975 2000
A scalar measure of volatility (1810-2010)
Number of
cycles removed
TOT
GDP
SD
SD
0
1
2
3
4
5
6
7
8
9
10
0.172
0.146
0.137
0.130
0.124
0.118
0.112
0.108
0.104
0.101
0.097
0.152
0.099
0.089
0.084
0.079
0.074
0.071
0.068
0.065
0.062
0.059
No te : S D s ta nds fo r s ta nda rd de via tio n.
S o urc e o f da ta : Own e s tim a tio ns
This measure drops monotonically when more knowledge on
cycles is attributed to the economic agents
A proxy for volatility
Volatility = SD in a five-year rolling
sample
of the decycled residual series
TOT and GDP volatility (1815-2010)
SD (five years) of cubic detrending and Fourier decycling
TOT volatility
(extracting
55%
of variability)
TOT
Volatility
GDP volatility
(extractingGDP
80%Volatility
of variability)
.25
.25
.20
.20
.15
.15
.10
.10
.05
.05
.00
.00
1850
1900
1950
2000
1850
1900
1950
2000
TOT and GDP volatility (1815-2010)
SD (five years) of HP detrending and Fourier decycling
TOT
volatility
SD of log tot
detrending
(HP) and decycling
(extracting 55% of variability)
(extrancting 55% of variability)
volatility
SD of log GDPGDP
detrending
(HP) and decycling
(extracting 80% of variability)
(extrancting 80% of variability)
.16
.16
.12
.12
.08
.08
.04
.04
.00
.00
1850
1900
1950
2000
1850
1900
1950
2000
III
Analysis of the results
Is TOT volatility overestimated in
empirical analysis?
.24
.20
.16
.12
Mean
Std. Dev.
.08
.04
.00
1825
1850
1875
1900
1925
1950
1975
SD of TOT HP residuals
SD of TOT detrendig and decycling
2000
SD of
TOT HP
residuals
0.087
0.044
SD of TOT
detrendig (HP)
and decycled
0.064
0.031
Is GDP volatility overestimated in
empirical analysis?
.12
.10
SD of GDP
SD of GDP
HP
detrendig (HP) and
residuals
decycled
Mean
0.039
0.023
Std. Dev.
0.027
0.010
.08
.06
.04
.02
.00
1825
1850
1875
1900
1925
1950
1975
SD of GDP detrendig and decycling
SD of GDP HP residuals
2000
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?
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
TOT index positive trend, and large fluctuations.
Irregular GDP growth
TOT index 1993=100 (1810-2010)
1909: 146
GDP growth (1811-2010)
1948: 150
1922: 71
1890: -8% Baring Crisis
1987: 85
2000: 106
2010: 141
2001: - 13%
1897: -21%
Possible presence of causality
Contemporaneous correlation = 0.14
Higher correlation is observable between TOT volatility and
GDP growth volatility
Volatility by subperiods
We 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
Low
(0.059)
Medium
(0.061)
High
(0.071)
Low
(0.019)
1815 – 1882
CC = 0.19
Medium
(0.024)
High
(0.027)
1950 – 2010
CC = -0.06
1883 – 1949
CC = 0.15
Exercise on VAR estimation
Specifications:
• 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.
VAR impulse response function
Once-and-for-all 1-standard deviation shock
to TOT volatility on GDP volatility
IV
Concluding remarks
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.
Policy implications
• 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.
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.
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.
Thank You
Assessing terms of trade volatility in Argentina
1810 - 2010.
A Fourier approach to decycling.
José Luis Arrufat
Alberto M. Díaz Cafferata
María Victoria Anauati
Santiago Gastelu
Instituto de Economía y Finanzas. Facultad de Ciencias Económicas
Universidad Nacional de Córdoba
References
Aizenman
Edwards
Riera-Crichton (2011)
Larrain, Parro (2006)
Mendoza (1994)
Kim (2007)
Wolf (2004)
Dehn (2000)
Baxter (2000)