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Transcript of Paper1 (Precautionary Savings)
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The volatility of income in exhaustible resource countries has been 2-3 times higher than
in other economies (see panel a in Figure 1 ). This finding remains valid in sample sub-periods
(see panel a in Figure 2) . Although income volatility has decreased in recent decades,
exhaustible resource countries continue to stand out. As of 2007, the 10-year rolling income
volatility in exhaustible resource countries was more than twice the volatility in other economies
and substantially larger than in major non-fuel commodity exporting countries.
The finding of high income volatility in exhaustible resource countries is consistent with
other results in the literature. Easterly et al. (1993) and Broda (2004) among others report a
significant correlation between output volatility and terms of trade volatility, while Baxter andKouparitsas (2006) find that terms of trade volatility is the highest in fuel-exporting countries.
Heightened income volatility in exhaustible resource countries stems from a combination of
more volatile exhaustible resource prices, even when compared to other commodities, and a
larger share of the volatile oil and gas component in total income. It should also be noted that
exhaustible resource prices exhibit considerably larger variation than extraction quantities. At an
annual frequency, prices over the most recent oil price cycle, i.e., 1980-2007, were 2-3 time
more volatile than country-level extraction quantities. 2
In contrast to income volatility, differences in the volatility of consumption for
exhaustible resource countries are less pronounced. Panels a-b in Figure 1 show that over the
last half-century, the difference in the volatility of income of exporters of exhaustible resources
and other countries has been larger than the difference in the volatility of consumption.
Moreover, the difference in the volatility of consumption has altogether disappeared from 1990s
2 If one excluded the two Gulf Wars, prices are 4 times more volatile than extraction quantities (British Petroleum,2008).
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onwards (see panel b in Figure 2 ), as the volatility of consumption in exhaustible resource
countries decreased to levels comparable to the other economies. Panels c in Figures 1 and 2
present further quantitative evidence for the gap between income and consumption volatilities in
exhaustible resource countries. This group of countries has exhibited historical ratios of
consumption volatility to income volatility in the range of 0.5-0.7. In other economies the same
ratios have been close to 1. Finally, panel d in Figure 1 reports the correlation between income
and consumption. Again, exhaustible resource countries exhibit lower income-consumption
correlations than other economies. These empirical results indicate that countries with
exhaustible resources have been able to smooth consumption in face of large income shocks. Next we investigate the channels through which volatility of consumption is mitigated. In
theory, a country could insure against exhaustible resource income volatility by locking in future
sales prices or by altogether selling the remaining stock of the resource. But usage of such tools
remains very limited. Contrary to the prescriptions of economic theory, domestic ownership of
exhaustible resources in major oil producing countries has been on the rise in recent decades and
markets for hedging resource price fluctuations remain very small. As of April 2009, the total
open interest in exchanges and over-the-counter markets for hedging resource price fluctuations
was estimated at only 4 weeks of world oil consumption and 0.18 percent of proven oil reserves
(see Borensztein et al., 2009). Daniel (2001) argues that political constraints have held back
governments from using explicit insurance.
Another approach would be to vary resource extraction quantities in a manner that offsets
the effect of price changes on exhaustible resource revenues or reduces the dependence on such
resources. An extensive literature has studied the supply-side of exhaustible resources under
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different market structures, but has not reached any consensus. 3 For the purpose of this paper, we
note that price variation accounts for 85-90 percent of the 1-year changes in exhaustible resource
revenues. 4 Longer horizons exhibit higher cross-country variation for contributions of prices and
quantities, but average contributions for the sample of oil countries remain unchanged price
changes account for 80-95 percent of the variation in revenues for horizons of up to 10 years.
To further assess the relationship between the exhaustible resource price and extraction
quantities, we consider the response of extraction quantities to the oil price boom of 1999-2008,
which was not expected prior to 1999. EIA (1998) forecasted that the real price of oil in 2005
would remain broadly unchanged at 24 USD/barrel (in 2005 prices), while the actual price in2005 was 56 USD/barrel (in 2005 prices). Despite the surge in the price, EIA (1998) projections
for total extraction of oil in the sample countries were only 1% below the observed extraction
quantities for 2005. Over that 7-year horizon, oil production exhibited very limited response to
the changes in the price. A similar comparison of forecasts and realizations for the period from
1998 to 2008 would suggest an even smaller price elasticity of supply.
A possible explanation for the lack of response in extraction quantities consistent with
the model of this paper is that changes in extraction capacity are very costly and their
implementation requires large time lags. This property of resource extraction, when combined
with the observation that historically exhaustible resource price follows a persistent trendless
process, implies that extraction quantities cannot diversify exhaustible resource risk either at
3 See, e.g., Griffin (1985) and Ramcharran (2002). A survey of the literature on the structure of the oil market byCremer and Salehi-Isfahani (1992) concludes that the level of disagreement is unsettling.4 Computed for country i and year t as .
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short or long horizons. Such a diversification strategy is prohibitively expensive in the short run,
while the nature of the resource price limits its benefits in the long run.
An alternative to explicit insurance and adjustments in extraction quantities is income
diversification, with an aim to counter income fluctuations over the oil price cycle and reduce
exposure to the volatile exhaustible resource revenues over longer horizons. One potential
channel for such diversification is external savings, whereby conversion of exhaustible resource
revenues into foreign assets smoothes consumption and gradually increases the share of income
from foreign sources. The presence of this diversification channel would be consistent with
exhaustible resource countries on average running current account surpluses, with larger surpluses when exhaustible resource prices are high.
In the absence of reliable data on the evolution of net foreign asset positions, we examine
this channel using current account balances, depicted in Figure 3 . Exhaustible resource countries
have been running sizable current account surpluses in periods with high exhaustible resource
prices and less-than-offsetting deficits when prices are low. In particular, an average current
account deficit of 1.2 percent of GDP during the 90s was followed by an average surplus of 13.7
percent of GDP during 2000-2007. Foreign asset accumulation during the price boom of 1974-
1981 was similar in magnitude, with an average surplus of 15.4 percent of GDP.
Another potential diversification channel operates through the conventional domestic
economic activity that is not directly related to the extraction of exhaustible resources. Expansion
of conventional economic activity lowers the share of volatile exhaustible resources in total
income and may provide additional diversification, depending on the correlation of conventional
income with the price of exhaustible resources.
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As shown in Figure 4 , with the exception of Venezuela and Libya, exhaustible resource
countries have experienced significant growth in conventional economic activity over the most
recent oil price peak-to-peak cycle, i.e., 1980-2007. Panel b in Figure 4 reports a decomposition
of the growth rate into contributions of labor input and labor productivity. All exhaustible
resource countries in our sample have experienced a sizable increase in labor force, which
accounts for the bulk of observed output growth. At the same time, there is no systematic
positive contribution from labor productivity to output growth for this group of countries. The
latter result is in line with the findings of the 'resource curse' literature (see e.g. Sachs and
Warner, 2002), recaptured in Figure 5 . Over the most recent oil price cycle, per capita income inexhaustible resource countries on average grew at a slower pace then in other economies.
Furthermore, for the group of countries heavily dependent on exhaustible resources, the average
growth in per capita income was close to zero. We also find that annual growth rates in the
conventional sector exhibit a small positive correlation with growth rates in the exhaustible
resource sector (see panel c in Figure 4 ). The average correlation in the sample of twelve
exhaustible resource countries is 0.19. Thus, the conventional sector does not contribute to the
diversification of income over the oil-price cycle.
Overall, empirical evidence indicates that income diversification in exhaustible resource
countries takes place through two main channels. First, exhaustible resource countries
accumulate foreign assets. By doing so they smooth consumption relative to income and reduce
the share of volatile exhaustible resources in aggregate income. Second, domestic conventional
economic activity in countries with exhaustible resources is increasing in tandem with the
expanding labor force, reducing the share of volatile exhaustible resources in aggregate income.
In our study of precautionary savings, we include both of these channels.
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To gauge the importance of precautionary savings, while controlling for the other
important drivers of savings behavior the desire to smooth consumption of the temporary
exhaustible income over time regardless of uncertainty we need a model. The construction and
application of such a model is the central task of the rest of the paper.
III. M ODELING F RAMEWORK
This section presents a model that captures the savings decision facing producers of exhaustible
resources with volatile prices.
A. Small Open Endowment Economy
Consider a small open economy with two sectors: one is conventional and the other is an
exhaustible resource extracting sector. The aggregate production technology for the conventional
sector is:
t t ALY , (1)
where Y t is output, A is a measure of productivity and Lt is labor input, which grows at a constant
rate:
1 (1 )t t L n L , (2)
and is the only source of growth in the conventional sector. In the baseline model the
conventional sector facilitates income diversification only through the exogenous growth in the
labor force. The model abstracts from domestic investment/savings decision and the only
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endogenous channel of diversification is the external sector. 5 The effect of time-varying
productivity is examined in a subsequent section on sensitivity analysis.
In the exhaustible resource sector, the extraction technology requires no factor inputs and
output follows an exogenously specified sequence:
0 for
0 for t t T
Z t T
, (3)
where Z t is the quantity extracted. Future extraction quantities, 0 0T
t t Z , are known at time t
and such resources are exhausted in period T . The model does not address the question of
optimal extraction quantities and instead takes the available projections for future extraction as
given. The focus is on the uncertainty surrounding the prices of the exhaustible resource instead
of its extraction quantities, which historically have exhibited a considerably smaller variation.
The aggregate per-period resource constraint of the economy is:
t t p
t t t Y Z e Br BC t )1(1 . (4)
In (4) C t represents aggregate consumption. The difference between aggregate production and
absorption is the trade balance, Bt+ 1 - (1 +r ) Bt , where Bt stands for the stock of net foreign assets
as of the end of period t -1 and r is the risk-free rate of return. We assume, in line with the
empirical evidence, that the economy cannot lock in future prices of the exhaustible resource in
insurance markets and the ownership of the stock of the exhaustible resource is non-transferable.
Hence, in each period the extracted amount, t p t e Z , is the only source of exhaustible resource
related revenue.
5 In a more general model with endogenous capital, investment would provide an alternative diversification channelonly when the domestic return on capital exceeds the return on foreign assets. This could be the case if, for example,the economy is credit constrained or experiences a positive productivity shock. Exhaustible resource revenues canthen be used to exploit the temporarily higher domestic returns. However, on the balanced growth path, the return ondomestic capital has to equal the world interest rate, limiting the long-run impact of this diversification channel.
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The log of the relative price of the exhaustible resource which is determined outside
this economy follows a covariance-stationary AR (1) process:
11 1 t t t p p p , (5)
where p0 is given and p is the unconditional mean of p. In line with empirical findings (e.g.,
Krautkraemer, 1998, Lin and Wagner, 2007, and references therein), the relative price of the
exhaustible resource in the model is assumed to be trendless in the long run.
The economy is inhabited by a representative household with the following CRRA
preferences:
)/(0
t t t t
t
LC U L , (6)
where
1for )(log
1or 10for 1)/(
1
/LC
/LC LC U
t t
t t
t t . (7)
In (6), is a subjective discount factor, determines the degree of risk aversion and
intertemporal elasticity of substitution and Lt is the number of members in the representative
household.
B. Optimal Solution
To solve the model, it is instructive to recast all quantities in terms of ratios to the non-
exhaustible resource sector output, where variables expressed in terms of effective units of labor
are denoted by lowercase letters, e.g.t
t
L AY
t y . Then the maximization problem can be
formulated as:
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)(~
max0
0},{ 1t
t
t
bccU E
t t
, (8)
subject to:
1
1 1
(1 ) (1 ) ,
(1 ) ,
1lim 0,
1
t pt t t t t
t t t
S
S S
c n b r b e z y p p p
nb
r
(9)
where )1(~
n and 0b , 0 p are given6.
It is further assumed that 1 / 1r , which puts the model solution on a balanced
growth path after exhaustible resources run out. The balanced growth path is characterized by a
common constant growth rate, n, for consumption, output and the net foreign asset position,
which allows output shares, ct / yt and bt /yt, to remain constant over time.
Deterministic case
In the deterministic case, the expression for optimal consumption is:
t pt
t
z er n
r nr
bnr yc t 11
1 00 . (10)
Per-period consumption equals the sum of conventional output, the annuity value from the initial
net foreign assets and the annuity value from the discounted steam of future exhaustible resource
revenues. For a given income stream, the consumption-output ratio is therefore set at a constant
optimal level and the external balance is used to smooth out any variation in income over time.With the expression for consumption-output ratio in hand, it is straightforward to derive the
optimal solution for all the other variables of interest.
6 The problem in (8)-(9) has a solution if the growth rate of the non-exhaustible resource sector is less than the realinterest rate: n < r.
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Stochastic case
In addition to considerations covered by the deterministic case, the risk-averse representative
household now faces uncertainty about the future price of the exhaustible resource and wants to
insure against variation in future income. In the absence of explicit insurance, the household
solves a simple self-insurance problem. Holdings of net foreign assets are used to lower the
exposure to the uncertain income from exhaustible resources.
In the model, precautionary savings are defined as the change in net foreign assets due to
this self-insurance motive and for any given period they can be calculated as the difference innet foreign asset positions between the deterministic and stochastic versions of the model. 7
The exhaustible nature of the resource plays a crucial role in models solution. It makes
the model deterministic from period T onwards and ensures a finite optimal value for expected
consumption at the infinite horizon. To accommodate the precautionary savings motive, the
optimal consumption in the stochastic model is upward tilting (until resources are exhausted and
uncertainty is resolved) and accompanied by gradual accumulation of a buffer stock of net
foreign assets. In initial periods, consumption is lower than in the deterministic case, but as
savings accumulate and the interest income from foreign assets grows, it eventually exceeds the
consumption path from the deterministic case. The stochastic version of the model does not have
a closed form solution, but it can be solved numerically. Details of the solution method are
presented in Appendix A .
7 This definition of precautionary savings differs from the one used by studies of precautionary savings in modelswith idiosyncratic shocks, as in e.g. Carroll (2001), where precautionary savings are usually defined as change in thedistribution of savings in a stationary steady state.
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IV. P ARAMETERIZATION AND BASELINE M ODEL R ESULTS
This section applies the model to selected exporters of exhaustible resources. The gist of the
exercise is to set model parameters and initial values and then solve for the optimal behavior in
the model from the perspective of year 2007. The results reported in this section focus on the
quantitative estimates of the size of precautionary savings for parameterized model economies.
The section also compares the outcomes of the model with actual data.
A. Model Parameterization
The model is applied to thirteen exhaustible resource economies Algeria, Iran, Kazakhstan,
Kuwait, Libya, Nigeria, Norway, Oman, Qatar, Russia, Saudi Arabia, United Arab Emirates and
Venezuela. Model economies differ in terms of their labor growth rate, stock of initial net
foreign assets, share of exhaustible resource revenues in total output and projected future
exhaustible resource extraction path.
To parameterize the model, one period is taken as one year in the data. For all sample
economies the subjective discount rate is assumed to take a value of )04.1/(1 and the
curvature in CRRA utility is set to 2 . Both values are in the range of what is considered
standard in the literature.
The parameterization of the price process for exhaustible resources in (5) is based on our
estimates of the annual price process for the price of oil with annual data for the period 1970-
2007. The choice of the AR(1) specification was based on the Akaike Information Criterion. The
relevant parameter values are 0.89 [S.E. = 0.10] and 0.30 [S.E. = 0.02]. The initial
value for the price process is set equal to the 2007 average price in US dollars, exp( p2007 ) =
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69.04, which is above the unconditional mean of 37.59 (expressed in 2007 prices) implied by the
AR(1) process. All countries in the sample face the same price process.
The remaining country-specific model inputs are either data for 2007 or projections going
forward. Growth in labor force, n , is set at each countrys average projected growth rate in
working age population from the United Nations (2008) population projections over 2010-2050.
The initial net foreign asset stock, b2007 , is calculated as the end-of-2006 share of net foreign
assets over total output and obtained from the most recent update of the External Wealth of
Nations data set (Lane and Milesi-Ferretti (2007)). The initial size of the exhaustible resource
sector,2007
2007
p
e z , is obtained from the trade balance for oil and gas, as a share of GDP in 2007.
Projections for the path of extraction of exhaustible resources for the next 30 years are taken
from the reports on oil and gas extraction quantity projections for 2010, 2015,...,2030 from the
EIA (2008). To project beyond the initial 30-year span of that report, we assume that resource
extraction proceeds at a constant level until reserves of oil and gas, as estimated by the US
Geological Survey (2000), are exhausted. 8
In summary, each sample country is parameterized using standard values in the
neoclassical growth literature with one add-on: in addition to the conventional output, the model
economy has access to revenue from the exhaustible resource sector which amounts to a
substantial share of total output and will be exhausted at some point in the future. Country-
specific model inputs, summarized in Table 1 , exhibit considerable variation across the 13
sample countries. For example, with an initial exhaustible resource output share of 0.19, Russia
8 The model parameterization in this paper contains three significant differences from an earlier working paper Bems and de Carvalho Filho (2009). First, the assumed curvature in the utility function is lowered from =6 to =2to reflect the standard choice in the RBC literature. Second, the amount of remaining reserves is now based onestimates from the US Geological Survey (2000) rather than British Petroleum (2008). We judge the former sourcesdefinition of reserves as more appropriate for the purpose of this paper. Third, results are updated from 2006 to 2007and the sample is extended to include Oman and Russia. These changes did not alter papers main findings.
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in 2007 is the least dependent on exhaustible resource revenues. At the other end of the
spectrum, Libyas exhaustible resource output share exceeds that of the conventional sector. In
terms of the exhaustible resource lifespan, Oman is assessed to be the first to run out of
exhaustible resources, by 2057. On the other end of the spectrum, in Russia, Iran, Saudi Arabia
and Venezuela, extraction is projected to continue beyond 2150. Similarly, there is significant
variation in the extraction time profiles, as depicted in Table 2 . By 2030 extraction quantities in
Norway are projected to decrease by 20 percent relative to the 2007 levels, while in Kazakhstan
extraction quantities are projected to more than double.
B. Baseline Model Results
To convey the intuition behind the papers results, this section first presents a detailed optimal
model solution for one of the countries in the sample Oman. Since Oman is a very small and
heavily oil and gas dependent economy that is expected to exhaust its resources over a relatively
short horizon, its economy fits quite well the assumptions of the modeling framework. Next,
relevant results for the rest of the sample countries are summarized. Finally, the model outcomes
are compared with data.
The Case of Oman
The models solution in the case of Oman is summarized in Figure 6 . Panels (a) and (b) show
the parameterized process for the price of the exhaustible resources and the projected future
extraction quantities, both of which were discussed above. Panel (c) shows the resulting revenues
from exhaustible resources as a share of conventional output. Note that Y t on y-axis is
conventional output , which equals total output only after exhaustible resources are depleted.
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Solid lines in panels (d), (e) and (f) present the optimal solution to the deterministic
version of the model. In this case, per capita consumption is smoothed perfectly over time, as
derived in equation (10). To support this constant level of consumption, the representative
household accumulates wealth in periods with exhaustible resource revenues, and consumes
interest income from the accumulated assets once exhaustible resource revenues run out. The
ratio of foreign assets-to-output increases during the period of asset build-up and stays constant
thereafter. To achieve this when labor force is growing over time, Oman must run current
account surpluses on its balanced growth path. Since constant per capita consumption is
achieved, the curvature in the utility function does not play any role in this deterministic case.How does the optimal solution change when uncertainty about the exhaustible resource
price is added to the model? Combined with the CRRA utility, price uncertainty introduces an
additional consideration -- the precautionary savings motive -- to the model. The representative
consumer will now save more resources to insure against the proverbial rainy day in the future.
To accommodate additional savings, the path of expected consumption initially slopes upwards
and then converges to a constant expected level (see panel d). In panels (e) and (f) precautionary
savings lead to a higher level of net foreign assets, Bt , and a more positive current account
position. The difference in the level of net foreign assets and the current account between the two
model solutions, i.e., the size of precautionary savings, is displayed separately in panels (g) and
(h). To maintain the higher net-foreign-asset-to-output ratio on the balances growth path, the
model with uncertainty requires slightly higher current account surpluses.
Quantitatively, in the model economy parameterized for Oman, the precautionary savings
motive induces an additional current account surplus of about 2 percent of conventional output in
the initial year, with surpluses gradually decreasing thereafter. The expected accumulated
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savings due to the precautionary motive on the balanced growth path amount to around 30
percent of output, as reported in panel (g).
Other exporters of exhaustible resources
The optimal size of precautionary savings in other sample model economies is driven by the
same considerations the uncertainty about future income induces the build-up of a buffer stock
of savings and leads to an upward tilting consumption path. At the same time, the dynamics of
the current account and foreign asset accumulation depend crucially on the exhaustible resource
extraction profile and can therefore differ substantially across sample countries. In Norway,where extraction quantities are decreasing over time (see Table 2 ), consumption smoothing
requires larger current account surpluses during the initial periods, while in Kazakhstan, where
extraction quantities are projected to more than double, consumption smoothing dictates lower
current account surpluses or even deficits in the initial years. Although uncertainty increases the
size of the current account balances (relative to the deterministic case) in all sample countries,
the sign and time profile of aggregate external savings is determined foremost by the resource
extraction profile and consumption smoothing considerations.
The model derived optimal 2007 current accounts for sample countries are presented in
Table 3 . The first column reports the optimal current account balance for year 2007 from the
baseline model parameterization. To understand the driving forces behind the reported balances,
it is instructive to decompose them into two additive components presented in the second and
third columns. The consumption smoothing component of the current account is the optimal
current account from the deterministic model, while the precautionary savings component is
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calculated as the difference between optimal external savings in stochastic and deterministic
versions of the model.
For a given time profile of the exhaustible resource income, values for the consumption
smoothing component of the 2007 current account can be derived analytically using equation
(10) and depend crucially on the shape of the assumed profile. To see this, consider the following
two scenarios that increase total exhaustible resources by the same amount. In the first scenario,
all additional resources are added to the 2007 income. The larger the exhaustible resource
income in 2007, ceteris paribus , the greater the 2007 value of the consumption smoothing
component of the current account. This is the case, since out of the additional current periodrevenues, only its annuity value should be consumed, with the remainder saved (see equation
(10)). In the second scenario, all additional resources are used to extend the lifespan of
exhaustible resources. In this case, the longer the lifetime of exhaustible resources, c eteris
paribus , the smaller the consumption smoothing component. At the extreme, if exhaustible
resource income is permanent (and constant over time), its entire value is consumed in each
period and consumption smoothing component of the current account is zero. In these two cases,
the same increase in the exhaustible resource wealth generates opposite effects on optimal
external savings in 2007.
To help evaluate the contributions of the different aspects of the time profile, Figure 7
shows the current and future exhaustible resource weights in output for each of the sample
countries. The sizable differences in the 2007 consumption smoothing component of the current
account across sample countries is a result of the large cross-country variation in these weights.
Precautionary savings in the model cannot be derived analytically, but are largely also
driven by the current and future exhaustible resource shares in output, as reported in Figure 7 . In
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this case, both larger output shares and longer lifespan of exhaustible resources increase the
share of households total wealth that is exposed to the uncertain exhaustible resource income.
Consequently, precautionary savings increase in both factors - the output share and the lifespan
of the exhaustible resources. Applying these criteria to Figure 7 explains why among the thirteen
sample countries, precautionary savings as a share of output are the largest in Qatar and the
smallest in Norway and Nigeria.
Quantitatively, for the baseline parametrization, precautionary savings add anywhere
between 0.3 to 3.9 percent of total output to the optimal 2007 current account balance. The
median size of precautionary savings in the sample is 1.1 percent of GDP and the mean is 1.2 percent of GDP. When aggregated over the thirteen sample countries, savings induced by the
precautionary motive in 2007 add up to 26 billion dollars, which amounts to 0.8 percent of the
total GDP of the countries in the sample.
How do optimal current account balances for 2007 in the model compare with the actual
outcomes? Figure 8 presents the answer to this question for the sample countries: its x-axis
depicts actual 2007 current account balances and its y-axis represents model outcomes, with and
without uncertainty. For the full-fledged precautionary savings model, correlation between actual
and model outcomes is 0.73, while for the deterministic model the correlation is 0.70.
Overall, results from the baseline model offer several findings. First, the main
determinant of the optimal external sector balances for exhaustible resource countries is the
consumption smoothing motive. Second, despite its more marginal role, optimal outcomes from
the parameterized model prescribe economically significant precautionary savings for exporters
of exhaustible resources. Third, optimal model outcomes for external sector savings are broadly
in line with data, as indicated by the positive correlation of 0.73 between the two variables.
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Adding precautionary savings motive to the deterministic model increases this correlation and
reduces mean square error for the fit between current accounts in the model and data.
V. S ENSITIVITY ANALYSIS
The modeling framework of this paper is a relatively simple one. The price of this simplicity
comes in the form of several exogenous sequences (i.e., labor force, exhaustible resource
quantities) and an exogenous stochastic process for the price of exhaustible resources, all of
which can significantly affect model results. Another important parameter with scarce empirical
motivation is the curvature in the CRRA utility, which governs the size of precautionary savings.
In view of such concerns, our approach in baseline parameterization has been to lean on the
available data as much as possible.
This section, in turn, presents extensive sensitivity analysis of the baseline model results.
The examination covers four areas: (i) consumer preference parameters, (ii) the source and the
size of growth in the non-exhaustible resource sector, (iii) exhaustible resource extraction
quantities and (iv) parameters of the exhaustible resource price process. The results of sensitivity
tests are summarized in Table 4 . The first column in this table numbers the sensitivity test. The
second column describes the type of deviation from the baseline that a particular sensitivity test
considers. For example, row 2 looks at the case when risk-aversion parameter in higher than in
the baseline while all other parameters and initial values are kept unchanged. The remaining
columns report the size of consumption smoothing and precautionary savings components of the
current account for each sensitivity test. Results are compared with the baseline case, reported in
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row 1. To conserve space, for each test only mean and median values for sample countries are
reported. 9
A. Preference Parameters
The size of precautionary savings depends crucially on the value of the coefficient of relative
risk aversion in the utility function, . To see this, note that if 0 , utility is linear and the
optimal model solution exhibits no precautionary savings. In order to assess the sensitivity of
baseline results to this curvature parameter, the model is solved for cases of 6 and 1 . As
expected, changes in precautionary savings are substantial. The lower curvature parameter
decreases the size of mean and median precautionary savings for sample countries from 1.2 and
1.1 percent of GDP to 0.8 and 0.7 percent of GDP respectively. The higher curvature parameter
increases the same statistics to 2.6 and 2.3 percent of GDP respectively (see rows 1, 2 and 3 in
Table 4 ). Since curvature of the utility function does not affect the optimal solution in the
deterministic case, the consumption smoothing component of the current account is unalteredand any change in total 2007 current account is entirely due to changes in precautionary savings.
Next, consider the effect of a change in the subjective discount factor, , reported in rows
4 and 5 of Table 4 . Heavier discounting lowers the net present value of exhaustible resource
wealth, but at the same time increases the risk-free interest rate that puts the economy on a stable
growth path. The net effect for model economies is an increase in the annuity value of
exhaustible resource wealth, which increases consumption and lowers savings, as captured by the
lower consumption smoothing component of the current account (see row 5 in Table 4 ). Higher
9 More detailed tables with country-by-country results for each sensitivity test are available from the authors uponrequest.
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levels of consumption and lower savings imply that a larger share of total income is derived from
the uncertain exhaustible resources (instead of the risk free foreign asset). In response to this
increased uncertainty about future income, the optimal level of precautionary savings rises.
Within the range of considered values of the discount factor, sensitivity tests show
relatively minor changes in the consumption smoothing and precautionary savings components
of the current account. Furthermore, since the effect on the two current account components
comes with the opposite sign, the overall impact on the current account balance is muted.
B. Growth in Conventional Output
In the model of Section 3, labor is the only source of growth in the conventional sector. The
effect of changes in the growth rate of the labor force on the two current account components is
similar to that of the subjective discount factor (see rows 6-7 in Table 4 ). In the deterministic
model, lower labor force growth rate increases the per worker return on exhaustible resource
wealth, thus rising the level of consumption and lowering the consumption smoothing
component of the current account. At the same time, it increases the share of future income from
the uncertain exhaustible resources, which leads to larger precautionary savings. The opposite
forces are at work when the labor force growth rate is reduced.
How accurate is the models assumption of zero productivity growth in the non-
exhaustible resource sector? During 1970-2006, the average growth rate for real output per
worker in Norway was close to 2 percent, suggesting that this assumption is not completely
accurate.
To address such concerns, row 8 in Table 4 presents results for the case when time-
varying productivity is added to the modeling framework of Section 3. This is done by
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substituting A with At in (1) and assuming that At +1 = (1+ g ) At , where g = 0.02 is the productivity
growth rate. With this specification, the interest rate on the stable growth path needs to satisfy R
= (1+ g ) / , which for baseline parameter values implies an 8 percent risk free annual return.
Although productivity growth affects external savings though several channels, quantitatively,
for this specification, the higher output growth rate on the stable growth path induces additional
savings so as to sustain a constant consumption-output ratio. As a result, the consumption
smoothing component of the current account increases. In contrast, the precautionary savings
component decreases because of the reduced weight for exhaustible resources in future income.
As it is hard empirically to justify an 8 percent risk-free interest rate, an alternativespecification is also considered. Assume that instead of the utility specified in (6), the household
maximizes consumption per effective unit of labor, U( C t /Y t ). Under this specification, the interest
rate on the stable growth path satisfies R=(1+ g )/ , which with baseline parameters amounts to 6
percent.
Results for this sensitivity test are presented in row 9. In this case, the lower interest rate
further increases the amount of additional savings that are required to attain a constant
consumption-output ration on the balanced growth path. As a result, we see a further increase in
the 2007 consumption smoothing component and a further decrease in the 2007 precautionary
savings component of the current account (see row 9 in Table 4 ).
Both productivity growth scenarios show that, although levels of precautionary savings
can be significantly altered, the main finding from the baseline model economically non-
negligible levels of precautionary savings survives introduction of productivity growth into the
model.
Furthermore, Norway has outperformed the rest of the sample in terms of labor
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productivity growth. For the sample as a whole, in line with the findings of the literature on the
resource curse (see e.g. Sachs and Warner (2001) and Figure 5 ), the average labor productivity
growth rate over the most recent oil price cycle is close to zero and, thus, more in line with the
baseline parameterization.
C. Path and Lifespan of Exhaustible Resource Extraction
The exhaustible resource extraction path in the model is obtained by combining estimates from
the 2000 US Geological Survey for oil and gas reserves and EIAs projected future extraction
quantities until 2030. These underlying estimates and projections are subjected to significant
uncertainty, primarily with regards to reservoir characteristics, future extraction technologies and
costs, but also related to limitations in the coverage of available exhaustible resource reserve
estimates.
The sensitivity analysis with respect to exhaustible resource quantities covers two
scenarios. In the first one, the size of the exhaustible resource reserves are changed by varying
the weight of exhaustible resource income in total output in all periods, keeping the lifespan of
resources fixed. In the second scenario, the size of the exhaustible resource reserves is changed
by varying the lifespan of reserves, while keeping the exhaustible resource share in output
constant. In both cases we consider a 10 percent increase/decrease in total reserves of exhaustible
resources.
Results for the two scenarios are reported in rows 10-13 of Table 4 . As already conveyed
in the discussion of the results in the baseline model, an increase in per-period quantities of
exhaustible resources should increase precautionary savings as well as the consumption
smoothing component of the current account. In contrast, an increase in the lifespan of
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exhaustible resources should increase precautionary savings, but decrease the consumption
smoothing component. Overall, a 10 percent change in total exhaustible resource reserves leads
to relatively minor deviations from the baseline results. Notice that a change in reserves has a
smaller effect when introduced by varying the lifespan of exhaustible resource, because
intertemporal discounting substantially lowers the net present value of additional revenues to be
extracted from period T onwards.
D. Process for Exhaustible Resource Prices
The parameterized process for the exhaustible resource price is another crucial input in the
baseline model. Taking as given the appropriateness of the AR(1) process for our exercise, rows
14-17 in Table 4 report sensitivity results with respect to two key inputs the persistence of the
AR(1) process and its expected mean value.
A higher expected mean value of the price process decreases the 2007 consumption
smoothing component of the current account, but increases precautionary savings. The
consumption smoothing component decreases because higher expected mean price implicitly
lowers the size of the initial positive 2007 price shock, or could even reverse its sign. With a
smaller positive shock it is optimal to consume more of the current periods exhaustible resource
income. In contrast, the precautionary savings component increases, as a higher expected mean
price raises the weight of exhaustible resources in total output and thus increases uncertainty
about the future wealth.
This result offers an interesting insight into the optimal behavior for exhaustible resource
exporters. The recent increase in the price of the exhaustible resource has motivated many
exporting countries (correctly or incorrectly) to increase the expected long-run price of the
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resource, which in turn justifies higher current consumption levels. However, it should be borne
in mind that the higher consumption levels need to be adjusted downwards to account for the
implicitly assumed increase in the long run weight of the more volatile exhaustible resource
revenues in total income, brought about by the assumed increase in the long run price of the
resource.
A more persistent price process also increases the expected long run price of the resource
and, in addition, makes the reversion to the mean following the initial positive price shock more
gradual. As a result, the 2007 consumption smoothing component of the current account
decreases and precautionary savings increase. The quantitative effects from altering the persistence of the price process can be substantial. For example, an increase in the persistence
parameter from =0.89 to =0.94 more than triples the mean and median sizes of precautionary
savings in the sample, while a reduction to =0.84 cuts precautionary savings by a half.
We also examine if the model results under various sensitivity tests preserve the
correlation with data observed in Figure 8 . In this regard two results are noteworthy. First, for all
sixteen sensitivity tests the correlation between the current account in the model and data
remains above 0.68 and in the case of the added productivity growth (rows 8 and 9), the
correlation increases to 0.82. Second, in all sixteen cases the stochastic model exhibits higher
correlation and lower mean square error between current accounts in the model and data than the
deterministic model. This finding indicates that, although consumption smoothing is the main
driving force behind the current account levels in exhaustible resource countries, the
precautionary motive is a valid additional determinant with a non-negligible economic
contribution.
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VI. E XTENSION TO T IME -SERIES OF O PTIMAL OUTCOMES
Each year can potentially bring a new exhaustible resource price shock. In response, the
representative household should re-solve the infinite horizon optimization problem, taking into
account the latest information. The baseline exercises focus on a single year with a particular
exhaustible resource price shock leaves several important questions unanswered: (i) how well
can our model replicate external sector behavior for years other than 2007? (ii) how does the size
of precautionary savings in 2007 compare to other years? (iii) how large are precautionary
savings when accumulated over extended periods? To answer these questions, this section
extends the baseline exercise to incorporate multiple historical price shocks. The model is
applied to a sequence of 1996-2008 price shocks for the above considered oil exporting countries
and the outcomes of the model are compared with data.
A. Setup and Parameterization
To implement the time-series exercise we use all inputs from the parameterization of the baseline
exercise for 2007 and, where time sequences of values are involved, extend the series to cover
the added 1996-2006 period. In particular, using the estimated exhaustible resource price
process, we interpret historical prices as representing positive or negative annual price shocks.
Figure 9 shows the actual exhaustible resource price for years on which our AR(1) estimates are
based. When the actual price is above (below) its mean in the parameterized AR(1) process, it
represents a positive (negative) shock to the exhaustible resource price.
Also, to solve the model from the perspective of years 1996, 1997, , 2006, we extend
the series for exhaustible resource extraction quantities using oil and gas extraction rates for
1996-2006, as reported in British Petroleum (2009). Similarly, labor force series are extended to
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the 1996-2006 period using the average labor force growth rate for 1996-2006, as reported in
WEO 2009. Finally, we set end-of-1995 NFA as the initial 1996 NFA position for each country.
Details of these extended series are reported in Table 5 .
To obtain the optimal model outcomes, the infinite horizon problem is solved from the
perspective of each year from 1996 till 2008. Optimizations for adjacent years are connected
though the choice of net foreign assets, b t+1 . In particular, the optimal choice of bt +1 from the
perspective of year t is taken as the initial value, bt , for the subsequent years problem. To
estimate the size of precautionary savings, both deterministic and stochastic versions of the
model are solved. Note that the setup of the time-series exercise implies that, consistent with themodel of Section 3, we are sequentially solving an entirely deterministic model with the
exception of the price of exhaustible resource, which is shocked each period. An implication is
that the model solution for 2007 should be the same as in the baseline case, except for the
difference in initial NFA, which now is taken from the model rather than data.
B. Results
We start by comparing the share of exhaustible resources in total output in the model and data,
reported in Figure 10 . In data this share is estimated using net exports of oil and gas, as a share
of GDP. 10 By construction, the two shares are identical in 2007. For other years they can deviate
to the extent that changes in the price of the exhaustible resource, extraction quantities and labor
input in the model do not capture all the variation in economic activity in data. For the majority
of sample countries, the results show that the model can capture the trends in the data. This
10 Results are very similar if data on economic activity in the mining sector is used instead.
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finding confirms our earlier empirical results that changes in the labor force and oil and gas
revenues capture the bulk of growth in countries with exhaustible resources.
Model assumptions are more restrictive for Norway and Russia, which have experienced
significant growth in labor productivity, not captured by the baseline model. These two
economies are also the least dependent on exhaustible resources, further limiting the applicability
of the model. Other major discrepancies between model outcomes and data in Figure 10 , i.e.,
Qatar, Nigeria, Kazakhstan and Oman, are driven by differences in exhaustible resource
revenues as measured by the oil price and extraction quantities in the model and net exports of
oil and gas in aggregate data.11
The model results for these countries should be interpreted withcaution.
Next, we examine per capita growth rates for output and consumption, summarized in
Figure 11. In the baseline model per capital output growth in the conventional sector is by
assumption zero, therefore any variation is aggregate output is driven entirely by changes in per
capita revenues in the exhaustible resource sector. As expected, aggregate volatility increases
with the share of exhaustible resources in economic activity.
The optimal consumption choice smoothes the deterministic change in per capita
extraction quantities, so that the remaining variation in consumption is due to the effect of
resource price shocks on the discounted future income. With the assumed price process for
exhaustible resources, such variation is a fraction of the current period variation in the price of
the exhaustible resource. Allowing for uncertainty in the resource price adds precautionary
11 One approach to reconcile the two exhaustible resource revenue series would be to use a country specificexhaustible resource price, as implied by data on extraction quantities and export revenues. We do not follow thisapproach, since it effectively introduced another country-specific sequence of parameters in the model, limiting themodel-imposed discipline for our exercise.
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savings considerations to the deterministic model, which lowers the level of per capita
consumption, but does not have a quantitatively significant effect on consumption growth rates.
Cross-country differences in consumption growth rates are driven by several factors, including
the share of the exhaustible resource sector in GDP and the time-profile of exhaustible resource
extraction quantities. Hence, in line with our earlier discussion of baseline results for 2007,
countries with equal current share of exhaustible resources in GDP can exhibit different
consumption growth rates in response to the same price shock. For example, given a price shock
and an equal current share of exhaustible resources in GDP, consumption will respond more in a
country that expects to exhaust the resource sooner because of a larger effect of the price shock on discounted future wealth.
Table 6 reports standard deviations for output and consumption growth rates as well as
the correlation between the two. As expected, the variation in the model for both consumption
and output is a fraction of what can be observed in data. Consumption variation in the model is
in the range of 20-50% of the variation in output, with a median of 29%. In data the median
value for the same ratio is 50%. At the same time correlation in the model (in 0.69-0.97 range,
with a median value of 0.89) is somewhat higher than in data (0-0.75, 0.38).
Finally, we turn to the model results for the external sector. Figure 12 compares CA
balances in the model and data. The results are mixed. Changes in current account balances in
the model correlate positively with data, more so for countries for which the model can capture
the share of exhaustible resources in GDP. 12 Furthermore, in the post-2000 period the model
captures a significant share of the observed CA surpluses in data. For Norway and Russia the
models fit with data is more problematic, but even for these countries a nontrivial share of post- 12 Correlations are in the 0.6-0.9 range, with exception of Russia (0.3) and Qatar (0.4).
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2000 surpluses is replicated by the model.
To quantify the role of precautionary savings and consumption smoothing in model
outcomes, panel A in Table 7 presents a decomposed cumulative current account data for the
2004-2008 period, during which sample countries contributed to the global imbalances by
accumulating a total of 2.2 trillion USD in current account surpluses. For the sample as a whole
the model can generate 85 percent of the external savings in data, although there is significant
variation in the models explanatory power across the individual economies, especially the ones
that were indentified in the discussion of Figure 10 as more problematic. During the period 6
percent (or 111 billion USD) of the external savings in the model are due to the precautionarymotive, while the remaining are induced by consumption smoothing considerations. Panel B in
Table 7 reports comparable results for a period that extends back to 1996. In this case,
accumulated external savings in the data increase further to 2.9 trillion USD. In contrast, total
savings in the model decrease from 1.9 to 1.8 trillion, with the model now generating 63 percent
of savings in data. Savings in the model are de-cumulated, because oil prices during 1996-2003
were below the estimated average price. Note, however, that the size of precautionary savings in
the model is always positive. As a result, over more extended periods that include both high and
low oil prices the relative role of precautionary savings increases. Comparison of the two panels
in Table 7 shows a doubling of the share of savings that can be attributed to the precautionary
motive to 10 percent of total.
To further link the results of this section with the discussion of the baseline results for
year 2007, Figure 13 shows cross sections of current accounts for each sample years, directly
comparable to Figure 8 . In support of baseline results, the correlation between model current
accounts and data is positive for all years, with higher correlations observed during 2005-2008.
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VII. C ONCLUSIONS
This paper introduces the precautionary savings motive into the framework of a
deterministic small open economy model to study the optimal consumption-savings choices in
economies with exhaustible resources. The model fares moderately well at capturing
savings/current account behavior in exhaustible resource countries in both cross-section and
time-series data. The cross-section correlation between current accounts in the model and data
during years 1996 to 2008 is in the 0.1-0.8 range, while correlation of changes in the current
account for each of the thirteen sample countries is in 0.3-0.9 range. When aggregated over the
sample countries and the 1996-2008 period, the model generates 63 percent of external savings
observed in data. According to the model, the sizable contribution of the exhaustible resource
countries to global imbalances over the last decade is justified given the exhaustible nature of the
resource, historically high exhaustible resource prices and uncertainty about future prices. 13
The model results show that, while the desire to smooth consumption is the main
determinant of external sector dynamics, allowing for uncertainty in the price of exhaustible
resources can generate sizable external savings, more so for countries where exhaustible
resources dominate economic activity. Under the baseline parameterization for year 2007 the
median size of precautionary savings in the sample is 1.1 percent of GDP. When aggregated over
all sample countries, precautionary savings in 2007 add up to 26 billion dollars, which amounts
to 0.8 percent of the samples GDP. The size of precautionary savings for other years between
1996-2008 is similar in magnitude. We also find that the introduction of the precautionary
13 This benign view of current account surpluses in oil exporting countries is also espoused by Blanchard andMilesi-Ferretti (2009).
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motive allows the model to more closely match the external sector savings in the data. An
extensive sensitivity analysis shows that the main finding from the model economically non-
negligible levels of precautionary savings is not driven by the parameterization of the baseline
exercise.
There are several important issues that are left for future research. First, the small open
economy assumption is employed throughout the paper. When taken separately, each of the
exhaustible resource economies is likely too small to affect outcomes in the rest of the world.
However, when taken as a group, it is possible that the savings behavior of exhaustible resource
countries affects the world interest rate.Second, we have abstracted from investment requirements for the extraction of
exhaustible resources. For economies in the process of expanding their exhaustible resource
output, e.g., Kazakhstan, this assumption might be problematic, since expansion of the resource
extraction capacity requires large upfront investments. In such instances, current account deficits
might be driven not only by the consumption smoothing and precautionary savings motives, but
also by the required investment in the exhaustible resource sector.
Finally, several aspects of the papers exercise suggest that the estimated precautionary
savings represent a lower bound. There might be more uncertainty about the price of the
exhaustible resource at distant horizons than the assumption of stationary implies. There is also
considerable uncertainty about the remaining stock of exhaustible resources, which we do not
model. As rows 14-17 in Table 4 show, added uncertainty can significantly increase the size of
precautionary savings.
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APPENDIX A: SOLUTION M ETHOD (CASE OF n = 0)
The problem we want to solve is:
000
0 0
1
. .
(1 )
is a random sequence
t t
t
t t C t t
t
t t t t
not t t
t
Max E U C
s t B B
B B r Y C
Y Y Z P
P
This problem does not have a steady-state solution, so one needs a shortcut to solve it.
The shortcut we use is to assume that there is no randomness beyond the exhaustible resource
depletion date ( T-1 ). Then we can solve it recursively. In the first period after depletion, the
consumption-savings decision going forward is:
0
1. . (1 ) 1
t T
t T t t C
t T
t t t
not
V B Max E U C
s t B B r C
Y Y
This problem has a closed-form solution:
1
1 1
N T
T
Y rBV B
For each possible value in a grid for BT (it can be a large positive or negative number), we
can calculate the value of the program going forward. Then we can solve it recursively back to
the initial period. For T -1, the last period with positive output in the exhaustible resource sector,
the problem to be solved numerically over a grid on 1 1,T T B P with a finite number of nodes:
11 1 1 11 1 1 1
, ( )
. . (1 ) 1T T T T T T T C
T T T T T
V B P Max U C V B
s t B B r Z P C
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For all periods up to T-2 , the decision problem incorporates the uncertainty over prices
going forward:
1 1 11
, ( , )
. . (1 ) 1t t t t t t t t t C
t t t t t
V B P Max U C E V B P
s t B B r Z P C
.
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Table 1: Country-Specific Model Parameters and Initial Values
Labor forcegrowth rate, %
Initial NFA position, % of
GDP
Initial Exhaustibleresource revenues,
% of GDP
Exhaustibleresource reserves,
bn brls oilequivalent
Lifetime of exhaustibleresources
Algeria 0.7 64 44 86 2077Iran 0.3 37 27 411 2150Kazakhstan 0.2 -36 24 87 2105Kuwait 1.0 206 54 104 2129Libya 0.9 263 58 64 2117
Nigeria 2.0 26 32 118 2 Norway 0.3 62 24 98 2091Oman 1.3 31 46 25 2057Qatar 0.7 165 56 142 2148Russia -0.9 -4 19 942 2150Saudi Arabia 1.4 97 54 664 2150United Arab Emirates 1.2 156 41 139 2095
Venezuela 0.9 27 27 134 2150 Sources: IMF World Economic Outlook, British Petroleum (2009), US Geological Survey (2000), EnergyInformation Administrations (2008), United Nations (2008), Lane and Milesi-Ferretti (2007).
Note: Parameters and initial values not reported in the table are identical for all sample countries.
Table 2: Projected Production of Liquids (oil and gas, billion barrels oil equivalent per year)
2007 2008 2009 2010 2015 2020 2025 2030 2050
Algeria 1.3 1.4 1.4 1.5 1.7 1.9 2.0 2.2 0.8Iran, I.R. of 2.3 2.3 2.3 2.4 2.5 2.7 2.9 3.2 3.2Kazakhstan 0.7 0.8 0.8 0.9 1.2 1.3 1.5 1.7 1.7Kuwait 1.0 1.0 1.0 1.0 1.2 1.2 1.3 1.3 1.3Libya 0.8 0.8 0.8 0.9 0.8 0.8 0.8 0.8 0.8
Nigeria 1.1 1.2 1.2 1.2 1.4 1.5 1.7 1.8 1.8 Norway 1.6 1.5 1.5 1.5 1.4 1.3 1.3 1.2 1.2Oman 0.4 0.4 0.4 0.4 0.5 0.6 0.6 0.7 0.3Qatar 0.8 0.9 1.0 1.0 1.3 1.6 1.8 2.0 0.8Russia 7.3 7.4 7.4 7.5 7.9 8.2 8.4 8.8 8.9Saudi Arabia 4.4 4.4 4.4 4.5 5.1 5.5 5.8 6.1 6.1United Arab Emirates 1.4 1.4 1.4 1.4 1.5 1.6 1.7 1.7 1.7
Venezuela, Rep. Bol.0.9 0.9 0.9 0.8 0.9 1.0 1.2 1.2 1.2
Source: Data for 2007, 2010, 2015,,2030 from Energy Information Administration (2008). Quantities for other years between 2007-2030 extrapolated using a linear trend. After 2030 production quantities kept constant untilreserves, as reported in column 4 of Table 1, are exhausted.
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Table 3: Optimal 2007 Current Accounts in the Baseline Model
of which:Consumption
smoothing
Precautionary
savings(1) (2) (3)
Algeria 19.7 18.2 1.4Iran, I.R. of 8.3 7.6 0.7Kazakhstan 1.8 0.6 1.2Kuwait 27.9 26.3 1.7Libya 33.0 31.4 1.5
Nigeria 20.0 Norway 11.9 11.6 0.3Oman 25.9 24.8 1.1Qatar 15.6 11.7 3.9Russia 2.9 2.3 0.6
Saudi Arabia 29.6 28.2 1.4United Arab Emirates 23.0 22.3 0.8Venezuela, Rep. Bol. 13.8 13.5 0.4
Sample mean 18.0 16.8 1.2Sample median 19.7 18.2 1.1
CA in 2007, % of GDP
Source: Authors calculations
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Table 4: Summary of Sensitivity Analysis for Current Account Components
Row
number
Deviation from
baseline
Consumptionsmoothing, % of GDP
Precautionarysavings, % of GDP
Mean Median Mean Median(1) (2) (3) (4)
1 Baseline 16.8 18.2 1.2 1.1
2 ' 4 16.8 18.2 2.6 2.33 ' 1 16.8 18.2 0.8 0.74 ' 0.005 18.7 20.7 1.0 0.85 ' 0.005 15.4 16.4 1.3 1.3
6 ' 0.005i in n i 21.0 22.6 0.8 0.7
7 ' 0.005i in n i 12.8 14.1 1.6 1.5
8 / 0.02 (Case 1)1 A A t t t 20.2 19.8 1.0 0.9
9 / 0.02 (Case 2)1 A A t t t 24.9 25.7 0.6 0.6
10 ' 1.1 z z t t t 18.5 20.1 1.4 1.3
11 ' 0.9 z z t t t 15.3 16.6 1.0 0.9
12 ' 1.1i iT T i 16.5 17.4 1.2 1.1
13 ' 0.9i iT T i 17.4 19.5 1.1 1.0
14 ' 0.25 p p 12.5 13.6 1.6 1.5
15' 0.25 p p
20.6 21.8 0.8 0.716 ' 0.05 11.1 11.6 3.7 3.417 ' 0.05 19.0 20.9 0.6 0.6
Source: Authors calculations Note: In the column reporting the type of deviation from baseline primed parameters represent the deviation andsubscript i indexes sample countries. For definitions of Case 1 and Case 2 in rows 8-9 see Section V.B.
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Table 5: Additional model inputs for the 1996-2006 time-series exercise
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006Algeria 4.2 -71 0.9 1.0 1.0 1.1 1.1 1.1 1.1 1.2 1.2 1.3 1.3Iran, I.R. of 3.4 -9 1.6 1.7 1.7 1.7 1.8 1.8 1.8 2.0 2.1 2.2 2.2Kazakhstan 0.8 -16 0.2 0.2 0.2 0.3 0.3 0.4 0.4 0.5 0.6 0.6 0.7Kuwait 6.0 181 0.8 0.8 0.9 0.8 0.9 0.9 0.8 0.9 1.0 1.0 1.1Libya 2.5 50 0.6 0.6 0.6 0.6 0.6 0.6 0.5 0.6 0.6 0.7 0.8
Nigeria 2.8 -105 0.8 0.9 0.8 0.8 0.9 0.9 0.9 0.9 1.1 1.1 1.1 Norway 1.4 4 1.4 1.5 1.4 1.5 1.5 1.6 1.6 1.7 1.7 1.6 1.6Oman 4.6 -6 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4Qatar 6.5 985 0.3 0.4 0.4 0.4 0.4 0.4 0.5 0.5 0.6 0.7 0.7Russia 0.5 -3 5.7 5.5 5.6 5.6 5.7 5.9 6.2 6.6 7.0 7.1 7.3Saudi Arabia 0.6 40 3.7 3.7 3.8 3.5 3.8 3.7 3.6 4.1 4.3 4.5 4.4United Arab Emirates 8.1 277 1.1 1.2 1.2 1.2 1.2 1.2 1.1 1.2 1.3 1.3 1.4Venezuela, Rep. Bol. 3.5 -1 1.3 1.4 1.5 1.3 1.4 1.3 1.2 1.1 1.2 1.2 1.2
Labor forcegrowth rate,
%
Production of liquids, billion barrels oil equivalent per yearInitial NFAposition, %
of GDP
Sources: IMF World Economic Outlook, Lane and Milesi-Ferretti (2007), British Petroleum (2009).
Table 6: Comparison of per capita output and consumption growth series for 1997-2008
std(Y) std(C) corr(Y,C) std(Y) std(C) corr(Y,C)Algeria 0.08 0.02 0.12 0.07 0.02 0.89Iran, I.R. of 0.06 0.03 0.38 0.04 0.01 0.95Kazakhstan 0.07 0.09 0.61 0.03 0.01 0.90
Kuwait 0.14 0.05 0.23 0.10 0.03 0.79Libya 0.15 .. .. 0.10 0.02 0.97
Nigeria 0.12 .. .. 0.04 0.01 0.96 Norway 0.05 0.01 0.00 0.03 0.01 0.94Oman 0.10 0.05 -0.01 0.09 0.04 0.69Qatar 0.13 0.08 0.28 0.10 0.04 0.85Russia 0.09 0.09 0.76 0.02 0.01 0.94Saudi Arabia 0.09 0.05 0.73 0.08 0.02 0.77United Arab Emirates 0.10 0.04 0.63 0.08 0.02 0.88Venezuela, Rep. Bol. 0.12 0.09 0.82 0.05 0.01 0.79
Data Model
Sources: WB World Development Indicators and authors calculations.
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Table 7: Accumulated external savings in the model and data, billion USD
Precautionary
savings
Consumption
smoothing(1) (2) (3) (4) (5)
Algeria 129 9 108 0.91 0.07Iran, I.R. of 95 8 86 0.99 0.08Kazakhstan -4 5 5 -2.33 0.50Kuwait 224 7 149 0.70 0.05Libya 115 5 85 0.78 0.06
Nigeria 124 2 122 1.00 0.02 Norway 290 3 177 0.62 0.02Oman 21 4 54 2.78 0.06Qatar 88 9 57 0.75 0.14Russia 418 21 158 0.43 0.11Saudi Arabia 469 28 444 1.01 0.06United Arab Emirates 141 7 206 1.51 0.03Venezuela, Rep. Bol. 127 4 147 1.18 0.02Total 2236 111 1797 0.85 0.06
Total (subs ample)1 1300 68 1225 0.99 0.05
Algeria 162 17 95 0.69 0.15Iran, I.R. of 129 13 35 0.37 0.27Kazakhstan -9 6 -21 1.71 -0.44Kuwait 283 13 174 0.66 0.07Libya 152 12 71 0.55 0.14
Nigeria 118 4 115 1.01 0.03 Norway 424 7 177 0.43 0.04Oman 24 8 66 3.07 0.11Qatar 102 14 57 0.70 0.19Russia 599 29 27 0.09 0.52Saudi Arabia 521 57 334 0.75 0.15United Arab Emirates 183 14 274 1.58 0.05Venezuela, Rep. Bol. 171 7 195 1.18 0.03Total 2859 200 1600 0.63 0.11
Total (subs ample)1 1601 132 1179 0.82 0.10
PANEL A: 2004-2008
PANEL B: 1996-2008
Accumulatedexternal
savings in
data2
(2+3)/(1) (2)/(2+3)
Accumulated model savingsdue to:
Sources: IMF World Economic Outlook and authors calculations.
Notes:1 The subsample excludes Kazakhstan, Nigeria, Norway, Oman, Qatar and Russia. For these countries themodel exhibits more limited explanatory power.2 Calculated as the sum of current account balances over the relevant period.
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Figure 1: Historical income and consumption volatility in exhaustible resource countries, 1964-2008
-10 0 10 20 30 40 50 600
0.05
0.1
0.15
0.2
0.25
DZA
ARG
AUSAUT
BOLBWABRABFA
BDICMR
CAN
CHL
HKGCOL
ZAR
CRICIV
DNK
DOM
ECU
EGY
SLVETH
FIN
FRA
GAB
GMB
GHA
GTM
HNDHUNIND
IDN
IRN
IRLISR
ITA
JAM
JPN
JOR KEN
KOR
KWT
LSO
MDG
MWI
MYS
MUSMEXMAR
NPL
NLDNZL
NER
NGA
NOR
OMN
PAKPAN
PNG
PRY
PER
PHLPRT
QAT
RWA
SAU
SENZAF
ESPLKA
SDN
SWZ
SWECHE
SYR
THA
TTO
TUR
UGA
ARE
GBRUSA
URYVEN
ZWE
(a)Income volatility
S t . d e v .
o f p e r c a p
i t a
G D P / C P I g r o w
t h
Mean oil&gas balance, percent of GDP-10 0 10 20 30 40 50 600
0.05
0.1
0.15
0.2
0.25
DZA
ARG
AUSAUT
BOLBWA
BRABFA
BDI
CMR
CAN
CHL
HKGCOL
ZAR
CRI
CIV
DNK
DOM
ECU
EGY
SLV
ETH
FIN
FRA
GAB
GMB
GHA
GTM
HND
HUNINDIDN
IRN
IRLISR
ITA
JAM
JPN
JOR KEN
KOR
KWT
LSOMDG
MWI
MYS
MUS
MEX
MAR
NPL
NLDNZL
NER
NOR
OMN
PAK
PAN
PNG
PRY
PER
PHLPRT
QATRWA SAU
SENZAF
ESP
LKA
SDNSWZ
SWECHE
SYR
THA
TTO
TUR
UGA
ARE
GBRUSA
URY VEN
ZWE
(b)Consumption volatility
S t . d e v .
o f p e r c a p
i t a c o n s u m p
t i o n
/ C P I g r o w
t h
Mean oil&gas balance, percent of GDP
-10 0 10 20 30 40 50 600
0.5
1
1.5
2
DZA
ARG
AUS
AUT
BOLBWA
BRABFABDI
CMR
CANCHLHKG
COLZAR
CRI
CIVDNK
DOM
ECUEGYSLV
ETH
FINFRA GAB
GMB
GHA
GTM
HNDHUNIND
IDN IRN
IRL
ISR
ITA
JAM
JPN
JOR KEN
KOR
KWT
LSO
MDG
MWIMYSMUS
MEX
MAR
NPLNLD
NZL
NER
NOROMN
PAK
PAN
PNGPRY
PERPHLPRT
QAT
RWA
SAU
SENZAF
ESP
LKA
SDN
SWZ
SWE
CHE
SYRTHA
TTO
TURUGA
ARE
GBR
USAURY
VEN
ZWE
(c)Ratio of consumption to income volatility
Mean oil&gas balance, percent of GDP-10 0 10 20 30 40 50 600
0.2
0.4
0.6
0.8
1
DZA
ARG
AUSAUT
BOL
BWA
BRABFA
BDI
CMRCAN
CHL
HKG
COLZARCRI
CIV
DNKDOM
ECU
EGY
SLVETH
FINFRA
GAB
GMB
GHA
GTM
HND
HUN
IND
IDN
IRN
IRL
ISR
ITAJAM
JPN
JOR
KENKOR
KWT
LSO
MDG
MWIMYS
MUS
MEXMAR
NPLNLD
NZL
NER
NOR
OMN
PAK
PAN
PNG
PRY
PER
PHL
PRT
QAT
RWA
SAU
SEN
ZAFESP
LKA
SDN
SWZ
SWECHE
SYRTHA
TTO
TUR
UGA
ARE
GBR
USA
URY VEN
ZWE
(d)Correlation of income and consumption
Mean oil&gas balance, percent of GDP
Sources: WB World Development Indicators.
Notes: Sample restricted to countries with at least 25 annual observations and a population of at least 1 million,which limits the sample to 90 countries.
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Figure 2: Output volatility by decade
1975 1980 1985 1990 1995 2000 20050
0.05
0.1
0.15
0.2
0.25 (a)Income volatility
1 0
- y e a r r o
l l i n g s
t . d e v .
o f p e r c a p
i t a
G D P / C P I g r o w
1975 1980 1985 1990 1995 2000 20050
0.05
0.1
0.15
0.2
0.25 (b)Consumption volatility
1 0 - y e a r r o
l l i n g s
t . d e v .
o f p e r c a p
i t a
C / C P I g r o w
t h
1975 1980 1985 1990 1995 2000 20050
0.5
1
1.5(c)Ratio of consumption to income volatility
Exhaustible resource exportersOther commodity exportersAll other countries
Sources: WB World Development Indicators. Notes: Exhaustible resource exporters are defined as economies, where median trade surplus for oil and gas during1964-2007 was at least 10 percent of GDP. This procedure identifies 11 exhaustible resource exporters - Algeria,Gabon, Iran, Kuwait, Nigeria, Oman, Qatar, Saudi Arabia, United Arab Emirates, Venezuela and Trinidad andTobago. Yemen and Norway are excluded from the group, since in both economies sizable oil and gas exportsstarted only during the 1990s. Due to the lack of data prior to 1990, CIS countries (e.g., Russia, Kazakhstan,Azerbaijan) are also excluded from the sample. Other commodity exporters include Iceland, New Zealand, Chile,Costa Rica, Ecuador, Honduras, Malaysia, Ghana, Cte d'Ivoire.
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Figure 3: The c urrent account balance and the oil price
1970 1975 1980 1985 1990 1995 2000 2005-40
-30
-20
-10
0
10
20
30
40
P e r c e n
t o
f G D P
Year
Oil price (right scale)
Current account20
40
60
80
100
$ 2 0 0 7
, l o g s c a
l e
Sources: IMF World Economic Outlook and British Petroleum (2008).
Notes: Current account defined as the sum of CA balances in exhaustible resource countries, normalized by thesample countries GDP, all in current prices. For the definition of exhaustible resource countries see notes to Figure2.
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Figure 4: Growth in conventional output, contributing factors and correlation with exhaustibleresources (1980-2007)
-10 -5 0 5 10
VEN
TTO
BHR
IRN
KWT
OMN
QAT
SAU
ARE
DZA
LBY
NGA
(a) Growth in conventional output
Average annual growth rate, percent-10 -5 0 5 10
VEN
TTO
BHR
IRN
KWT
OMN
QAT
SAU
ARE
DZA
LBY
NGA
(b) Contributions of labor and productivity
Average annual growth rate, percent
Productivity Labor
-1 -0.5 0 0.5 1
VEN
TTO
BHR
IRN
KWT
OMN
QAT
SAU
ARE
DZA
LBY
NGA
(c) Correlation with growth in exhaustible resource sector
ProductivityOutput
Sources: WB World Development Indicators, IMF World Economic Outlook and United Nations (2008).
Notes: Due to lack of sectoral data on economic activity Conventional output defined as GDP less exports of oiland gas. Growth in labor is defined as growth in population of age 15-64 from UN data.
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Figure 5: Per capita real GDP growth rates, 1980-2007
-10 0 10 20 30 40 50-4
-2
0
2
4
6
8
10
USA
GBR
AUTBEL DNK
FRADEUITANLD
NOR
SWE
CHE
CAN
JPN
FIN
GRCISL
IRL
PRTESP
TUR
AUS
NZL
ZAF
ARG
BOL
BRA
CHL
COLCRI
DOM
ECUSLV
GTM
HND
MEX
PAN
PRY
PER
URY
VEN
TTO
BHR
CYP
IRNISR
JOR
KWT
OMN
QAT
SAU
SYR
ARE
EGY YEMBGD
LKA
TWN
HKG
IND
IDN
KOR
MYS
PAK
PHL
SGP THA
VNM
DZA
AGO
BWA
CMR
ETHGHA
CIV
KEN
LBY
MAR
NGASDN
TUN
CHN
HUNPOL
Median oil&gas balance, percent of GDP
A v e r a g e p e r c a p
i t a r e a
l G D P g r o w
t h
y = - 0.052 * x + 2.1(0.027) (0.4)
Sources: WB World Development Indicators and IMF World Economic Outlook.
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Figure 6: Optimal Model Solution for Oman, t 0=2007
2010 2020 2030 2040 20500
50
100
150
(a)Price of exhaustible resources, P t
i n d e x ,
P 2 0 0 6
= 6 5
E(P)90% confidence
2010 2020 2030 2040 20500