preliminary results long-run evolution of fossil fuel prices: evidence from persistence break...

Preliminary Results

Long-run Evolution of Fossil Fuel Prices: Evidence from Persistence Break Testing (Work in Progress)

Aleksandar Zaklan (DIW Berlin), Jan Abrell (TU Dresden) and Anne Neumann (University of Potsdam and DIW Berlin)

Motivation•Fossil fuels are key inputs into electricity generation, industrial processes and transportation. •However, there is no consensus on the persistence properties of non-renewable resource prices in the literature. •Understanding whether prices are stationary is important for:•Testing the validity of certain theoretical approaches (e.g. Hotelling (1931))•Choice of admissible estimation frameworks•Optimizing forecasting performance

Data and Methodology

Data• Long-term price data at annual frequency

• Bituminous coal prices (1870-2009) from Manthy (1978) and U.S. Energy Information Administration (EIA)

• Crude oil prices (1861-2009) from BP (2011)• Natural gas prices (1922-2009) from U.S. EIA

Selected ReferencesAhrens, W.A. and V.R. Sharma (1997): Trends in Natural Resource Commodity Prices: Deterministic or Stochastic? Journal of Environmental Economics and Management, 33(1), pp. 59-74.Berck, P. and M. Roberts, 1996: Natural Resource Prices: Will they ever turn up? Journal of Environmental Economics and Management, 31(1), pp. 65-78.BP, 2011. Statistical Review of World Energy 2010. Historical data available at http://www.bp.com/sectiongenericarticle.do?categoryId=9033088&contentId=7060602Busetti, F. and A. M. R. Taylor. 2004. Tests of Stationarity Against a Change in Persistence. Journal of Econometrics, 123(1), pp. 33-66.Cavaliere, G. and A. M. Taylor. 2008. Testing for a Change in Persistence in the Presence of Non-stationary Volatility. Journal of Econometrics 147(1),

pp. 84-98.Dvir, E. and K. Rogoff. 2010. Three Epochs of Oil. Mimeo, Boston College.Hotelling, H., 1931. The Economics of Exhaustible Resources. Journal of Political Economy 39, 137-75.

References (continued)…Harvey, D. I., S. J. Leybourne, and A. M. R. Taylor. 2006. Modifed Tests for a Change in Persistence. Journal of Econometrics 134(2), pp. 441-469.Kim, J.-Y. 2000. Detection of Change in Persistence of a Linear Time Series. Journal of Econometrics, 95(1), pp. 97-116.Kim, J.-Y., J. Belaire-Franch, and R. B. Amador. 2002. Corrigendum, Journal of Econometrics, 109(2), pp. 389-392.Lee, J., J. A. List, and M. C. Strazicich, 2006: Non-renewable resource prices: Deterministic or stochastic trends? Journal of Environmental Economics and Management, 51(3), pp. 354-370.Manthy, R. S. 1978. Natural Resource Commodities: A Century of Statistics. Baltimore and London: Johns Hopkins University Press. Perron, P. 1989. The Great Crash, The Oil Price Shock, and the Unit Root Hypothesis. Econometrica 57(6), pp. 1361-1401. Pindyck, R. S. 1999. "The Long-Run Evolution of Energy Prices." The Energy Journal, 20(2), pp. 1-27.Slade, M.E., 1982: Trends in Natural-Resource Commodity Prices: An Analysis of the Time Domain. Journal of Environmental Economics and Management, 9(2), pp. 122-137.

State of the Literature •Empirical literature

• Testing of resource theory (Slade, 1982)• Appropriate model choice (Ahrens and Sharma, 1997)• Improving forecasting performance (Berck and Roberts, 1996; Pindyck, 1999; Lee et al., 2006)

•Recent theoretical literature on persistence break testing • Kim (2000), Kim et al. (2002), Busetti and Taylor (2004) Harvey et al.(2006), Cavaliere and

Taylor (2008)•Dvir and Rogoff (2010) apply this methodology historical crude oil prices, we take it a step further

• Extend their analysis to natural gas and bituminous coal prices• Allow for breaks in persistence and breaks in the trend

Figure 1: Fossil Fuel Prices

Model and Hypotheses•We consider the Gaussian unobserved components model (Busetti and Taylor, 2004)

•We test whether the variance of process determining is greater than zero, i.e. whether there is a switch in persistence from I(0) to I(1) behavior:

•Using the inverse of the test statistic allows us to test for a switch from I(1) to I(0) behavior:

1 ( )

, 1, ...,

t t t t

t t t T t

y d t T

1

20

21

2

: 0

: 0

0

a

H t

H for t T

for t T

20

21

2

: 0

: 0

0

b

H t

H for t T

for t T

Test Statistics•Based on this approach we can derive the ratio test statistic (Kim, 2000; Kim et al.,

2002; Busetti and Taylor, 2004; Harvey et al., 2006):

where are OLS residuals from a regression of on intercept and trend for the periods before and after the proposed break, respectively.•Subject to detecting a break in persistence we can estimate the break point, as follows:

0

0

0

0

2 21,

1

2 20,

1

0, 0 0,

1

1, 0 1,

1

[(1 ) ] ( )

( )

[ ] ( )

( ) , 1, ...,

( ) , 1, ..., ,

T

i

i T

T

i

i

T

t i

i

t

t i

i T

T S

K

T S

S t T

S t T T

2 21,

1

2 20,

1

[(1 ) ] ( )( ) ,

[ ] ( )

T

i

i TT

i

i

T

T

0, 1,, 1, ..., and , 1, ...,

t tt T t T T

Bituminous Coal Prices

MS 14.635 ME 22.187 * MX 52.587 *(0.181) (0.094) (0.093)

MSR 0.111 MER 0.057 MXR 1.195(0.902) (0.916) (0.523)

MSMAX 14.590 MEMAX 22.118 * MXMAX 52.395 *(0.182) (0.095) (0.094)

Estimated change point 1964

Mean Score Statistics Mean-Exponential Statistics Maximum Statistics

*, ** indicate significance at the 10% and 5% levels, respectively. Bootstrap p-values are in parentheses.

Source: Manthy (1978) and U.S. Energy Information Administration*, ** indicate significance at the 10% and 5% levels, respectively. Bootstrap p-values are in parentheses.

Crude Oil Prices

MS 31.7581 ** ME 36.1588 ** MX 82.9016 **(0.04) (0.04) (0.034)

MSR

0.1029 MER

0.0603 MXR

1.8183(0.916) (0.882) (0.334)

MSMAX

31.6238 ** MEMAX

36.0059 ** MXMAX

82.4882 **(0.04) (0.04) (0.034)




Natural Gas Prices

MS 46.4598 *** ME 213.3219 *** MX 474.4185 ***(0.00) (0.00) (0.00)

MSR 0.0486 MER 0.0198 MXR 0.1274(0.99) (0.99) (0.99)

MSMAX 45.9971 *** MEMAX 211.1974 *** MXMAX 468.8506 ***(0.00) (0.00) (0.00)




Summary of Main Results•Coal prices may be stationary over the long term•For oil and natural gas prices stationarity is rejected in favor of a switch from I(0) to I(1) behavior having taken place. •Particularly for natural gas the persistence break point is estimated to be implausibly early

Preliminary Conclusions and Next Steps•The literature strongly suggests the existence of structural breaks in natural resource time series (Perron, 1989; Lee et al., 2006)

This may bias persistence break test statistics if unaccounted for•Our results appear to confirm that a bias exists, cautioning against accepting the result by Dvir and Rogoff (2010) as is•We therefore aim to incorporate structural breaks into the persistence break testing procedure

preliminary results long-run evolution of fossil fuel prices: evidence from persistence break...

Documents