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We are grateful for comments and suggestions from two anonymous referees, Christian Bender, Ben Hambly, Vicky Henderson, Sam Howison, Robert Kaufmann, Rick van der Ploeg, Oral Williams, and seminar and conference participants at Oxford, Princeton, the IMF, the EEA Annual Meeting and the ECB Workshop on Coping with Volatile Oil and Commodity Prices.
A new method based on generalized linear complementarity problems (GLCPs) has recently been proposed by Nagae and Akamatsu (2008).
In several of our applications, we assume that countries extract every year a minimum amount of barrels, in which case extraction occurs indeed over a finite horizon.
kt must be a multiple of the discretization unit that we use and that represents one real option to extract oil.
When γ = 1, the utility function is defined as u(x) = log(x).
In an earlier version of the paper (Aleksandrov and Espinoza, 2011), we used the lower bound of the value function provided by the Monte-Carlo Least Squares method as well as the upper bound of the value function provided by the dual method of Aleksandrov and Hambly (2010) to construct a confidence interval for the value function when risk aversion is set to 0. We compared the upper and lower bound approaches for our baseline model and found that the relative difference between the upper and the lower bound does not exceed 3 percent, which confirms the accuracy of the numerical approximations used.
The oil price is deflated by the US CPI, with index 100 in 2000. The standard errors in Table 1 are the OLS standard errors, which are valid if the series is stationary. However, the augmented Dickey-Fuller test and the Phillips-Perron test were not able to reject the null hypothesis of non-stationarity.
The two factors are not observable, but Schwartz and Smith (2000) estimate them using spot and future prices over the period 1990-1996.
time is a linear trend that takes the value 0 in 1980 and 32 in 2012, which is the first year of the simulations presented in section VI.
Farzin (2001) uses both CUMt–1 and CUMt–2 but the two variables are almost identical in our sample so we dropped CUMt–2.
US CPI inflation between 2000 and 2011 was 30 percent.
The oil price process parameters are as before. We start with oil price S = 54.6. The time horizon in 100 years.
We assume that production capacity is maintained at the highest level after expansion, although production capacity is usually declining with time because of depletion.
We are grateful to an anonymous referee for pointing this to us.
Production data is a monthly average of production, in million barrels per day. The source is Joint Oil Data Initiative.
See individual IMF Country Reports for 2009–2010.
Based on a portfolio of half US 10–year yields (3.7 percent) and half the long-run performance of the Dow Jones (8 percent).
The data on the share of oil revenues is for 2007 and comes from individual country IMF reports. For Brazil, the data is deduced from Gobetti (2010). For Canada, the data is deduced from Ahmad and Mottu (2002). For Denmark, the data is taken from Danish Energy Agency (2008). The data for India is deduced from Table 7 in Segal and Sen (2011). For the UK, the data is from HM Revenues and Customs, 2011. The data for Venezuela comes from an old IMF country report (1999). Data was unavailable for Argentina, Australia, China, Egypt and the U.S.
Kuwait expected production profile and reserves are very similar to those of our large producer and therefore its decision rule should be the same. Algeria, Mexico and Brazil should also have policies comparable with our small producer (threshold around US$90) while Venezuela’s threshold price would lie in between. Norway and Egypt policies should be to extract at prices higher than US$90 only.