Assessing terms of trade volatility in Argentina 1810 - 2010. A Fourier approach to decycling .

1. 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

2. Introduction

3. Introduction • Modeling and estimating uncertainty

4. Introduction • Modeling and estimatinguncertainty • Analysis of the results

5. Introduction • Modeling and estimatinguncertainty • Analysis of the results • Concluding remarks

6. I Introduction

7. Argentina TOT index. ProblemsfordevelopingcountriesWeakevidence of Prebisch – Singer 1950 decliningtrendhypothesis. Focusshifttowardslarge shocks and volatilefluctuations. TOT index 1993=100 (1810-2010) * Quiebres estructurales 1909: 146 1948: 150 1922: 71 1987: 85 2000: 106 2010: 141 1950 * 1839 * 1917 *

8. 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

9. 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

10. II Modeling and estimatinguncertainty

11. How much “volatility”? Volatility analytical interpretation:associated with uncertainty. Volatility in standard empirical practice, proxyed by: • Variability • 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. • Our approach.

12. Modelingand estimatinguncertainty (1) Original Series Volatility Standard Deviation

13. Modeling and estimatinguncertainty (2) Original Series Detrended Residuals Volatility HP Filter / Polynomial Detrending Standard Deviation

14. Modeling and estimatinguncertainty (3) Original Series Detrended Residuals Detrended + Decycled Residuals Volatility HP Filter / Polynomial Detrending Fourier Decomposition Standard Deviation

15. Empiricalproxiesforvolatility in theliterature SD of raw series • Aizenmanet 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 menosvolátil”, 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).

16. Empiricalproxiesforvolatility in theliterature 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 .

17. 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 Dagumet al. (2006), “A critical investigation on detrending procedures for non-linear processes”, Journal of Macroeconomics (vol 28). • Kauermannet al. (2008), “Smoothing parameter selection for spline estimation”, • Kauermannet al. (2011), "Filtering time series withpenalizedsplines", 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).

18. Data and procedure Data: Argentina TOT and GDP loggedfromindex 1993=100. 1810 – 2010 (Ferreres & INDEC) Detrending: • Cubicpolynomialdetrending • HP filterdetrending (lambda = 100) Decycling: • Fourier decomposition

19. TOT and GDP cubicpolynomialdetrending

20. Fourier decomposition Following Bolch and Huang, the decomposition of a series into its periodic components is done using: where and

21. Fourier decomposition Estimates of cyclical patterns of log TOT: Argentina 1810-2010.

22. Commentson TOT decomposition • The most important cycle: • period: 28.86 years • frequency: observed only seven times in 202 years • acountsfor 26.52% of the total sum of squares. • The first five most important cycles account for 51.8% of the total sum of squares

23. Fourier decomposition Estimates of cyclical patterns of log GDP: Argentina 1810-2010.

24. Commentson GDP decomposition (1) • The most important cycle: • period: 101 years • frequency: observed twice in 202 years • acountsfor 57.70 percent of the total sum of squares. • Another important cycle: • Period: 202 years • frequency: observed once in 202 years • acounts for 2.68 percent of the total sum of squares.

25. Commentson 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

26. How many of the cycles are to be removed from the detrendedseries? • 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

27. Decycled TOT Decycled GDP Removed cycles and decycled residuals GDP Removed Cycles TOT Removed Cycles

28. A scalar measure of volatility (1810-2010) This measure drops monotonically when more knowledge on cycles is attributed to the economic agents

29. A proxy for volatility Volatility = SD in a five-year rolling sample of the decycled residual series

30. TOT and GDP volatility (1815-2010) SD (five years) of cubic detrendingand Fourier decycling TOT volatility (extracting 55% of variability) GDP volatility (extracting 80% of variability)

31. 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)

32. III Analysis of the results

33. Is TOT volatility overestimated in empirical analysis?

34. Is GDP volatility overestimated in empirical analysis?

35. 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?

36. Insights of TOT volatilityeffects 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

37. TOT index positive trend, and largefluctuations.Irregular GDP growth TOT index 1993=100 (1810-2010) GDP growth (1811-2010) 1909: 146 1948: 150 1890: -8% Baring Crisis 1922: 71 1987: 85 2000: 106 2010: 141 2001: - 13% 1897: -21%

38. Possible presence of causality Contemporaneous correlation = 0.14 Higher correlation is observable between TOT volatility and GDP growth volatility

39. 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:

40. Exerciseon 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.

41. VAR impulse response function Once-and-for-all 1-standard deviation shock to TOT volatility on GDP volatility

42. IV Concluding remarks

43. 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.

44. 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.

45. 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.

46. ExtensionsContinued • 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.

47. Thank You

48. 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

49. References Aizenman Edwards Riera-Crichton (2011) Larrain, Parro (2006) Mendoza (1994) Kim (2007) Wolf (2004) Dehn (2000) Baxter (2000)