Paper1 (Precautionary Savings)

8/8/2019 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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R EFERENCES

Bailen G. and V. Kramarenko, 2004, Issues in Medium-Term Management of Oil Wealth,

IMF Country Report No. 04/308 (Washington: International Monetary Fund), pp. 22

36.

Baxter, Marianne and Michael A. Kouparitsas, 2006, What Can Account for Fluctuations in

the Terms of Trade, International Finance, 9:1, pp.63-86.

Bems and De Carvalho Filho, 2009, Current account and Precautionary Savings for Exporters

of Exhaustible Resources, IMF Working Paper No.09/33, March.

Blanchard, Olivier and Gian Maria Milesi-Ferretti, 2009, Global Imbalances: In Midstream?IMF Staff Position Note SPN/09/29; December 22, 2009.

Borensztein, Eduardo, Olivier Jeanne and Damiano Sandri, 2009, Macro-Hedging for

Commodity Exporters, mimeo, John Hopkins University.

British Petroleum, 2009, Statistical Review of World Energy.

Broda, Christian, 2004, Terms of Trade and Exchange Rate Regimes in Developing

Countries, Journal of International Economics, 63, 31-58.

Caballero, Ricardo J., 1990, Consumption Puzzles and Precautionary Savings, Journal of

Monetary Economics , Vol. 25, No. 1, pp. 113-136.

Carroll, Christopher D., 2001, A Theory of the Consumption Function, With and Without

Liquidity Constraints (Expanded Version), NBER Working Paper No. 8387, July.

Daniel, James, 2001, Hedging Government Oil Price Risk, IMF Working Paper No. 01/185,

November.

Davis, Jeffrey, Rolando Ossowski, and Annalise Fedelino, 2003, Fiscal Policy Formulation and

Implementation in Oil-Producing Countries, Washington: International Monetary Fund.


39/60

38

de Carvalho Filho, Irineu, 2007, Medium-Term Fiscal Sustainability in Trinidad and Tobago,

in IMF Country Report No.07/08 (Washington: International Monetary Fund).

Cremer, J., and D., Salehi-Isfahani, 1991, Models of the Oil Market, Harwood Academic

Publishers, New York.

Easterly, William and Michael Kremer, Lant Pritchett, and Lawrence H.Summers, 1993, Good

policy or good luck?: Country growth performance and temporary shocks, Journal of

Monetary Economics , vol. 32, No. 3, pp. 459-483.

Energy Information Administration, 2008, International Energy Outlook.

Energy Information Administration, 1998, International Energy Outlook.Fogli, Alessandra and Fabrizio Perri, 2006, The Great Moderation and the U.S External

Imbalance, Monetary and Economic Studies , Vol. 24, No. S-1, pp. 209-234.

Ghironi, Fabio, 2007, The Role of Net Foreign Assets in a New Keynesian Small Open

Economy Model, Journal of Economic Dynamics and Control , Vol. 32, No. 6,

pp.1721-2060.

Ghosh, Atish R. and Jonathan D. Ostry, 1997, Macroeconomic Uncertainty, Precautionary

Savings, and the Current Account, Journal of Monetary Economics , Vol. 40, No. 1, pp.

121-139.

Griffin, J., 1985, OPEC Behavior: A Test of Alternative Hypothesis, American Economic

Review , Vol.75, No.5, pp. 954-963.

International Monetary Fund, 2009, World Economic Outlook Database.

Krautkraemer, Jeffery, 1998, Nonrenewable Resource Scarcity, Journal of Economic

Literature , Vol.36, Dec, pp2065-2107.


40/60

39

Lane, Philip R. and Milesi-Ferretti, Gian Maria, 2007, The external wealth of nations mark II:

Revised and extended estimates of foreign assets and liabilities, 1970-2004, Journal of

International Economics , Vol. 73, No. 2, pp. 223-250.

Lin, Cynthia C.-Y. and Gernot Wagner, 2007, Steady-state growth in a Hotelling model of

resource extraction, Journal of Environmental Economics and Management , 54, pp68-

83.

Ramcharran, H., 2002, Oil Production Response to Price Changes: An Empirical Application

of the Competitive Model to OPEC and non-OPEC Countries, Energy Economics , 24,

pp. 97-106.Sachs, Jeffrey D. and Andrew M. Warner, 2001, The Curse of Natural Resources, European

Economic Review , vol. 45, No. 4-6, pp. 827-838.

Schmitt-Groh, Stephanie and Martn Uribe, 2003, Closing Small Open Economy Models,

Journal of International Economics , Vol. No. 61, No. 1, pp. 16385.

Takizawa, Hajime, 2005, Fiscal Sustainability and Options for Fiscal Adjustment, IMF

Country Report No. 05/234 (Washington: International Monetary Fund), pp. 2539.

Thomas, Alun H., Jun Il Kim and Aqib Aslam, 2008, Equilibrium Non-Oil Current Account

Assessments for Oil Producing Countries, IMF Working Paper No. 08/198.

United Nations, 2008, World Population Prospects: The 2008 Revision Population Database.

United States Geological Survey, 2000, World Petroleum Assessment.

World Bank, 2008, World Development Indicators Database.


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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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50

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

Documents

Paper1 (Precautionary Savings)