Master Thesis
Faculty of Economics and Business
University of Amsterdam
Intergenerational Equity Issues and Financing Problems Following a
Public Investment Strategy of Resource Revenue Spending
Student name: Andreas Jordheim Myhre
Student ID: 6026958
Supervisor: Prof. Dr. Sweder van Wijnbergen
Second reviewer: Prof. Dr. Casper van Ewijk
Contents
1 Introduction 2
2 Background and literature review 4
2.1 Typical challenges with natural resources . . . 4
2.2 Resource curse . . . 5
2.2.1 Structural effects . . . 8
2.3 Spending the resource wealth . . . 10
2.3.1 Timing . . . 10
2.3.2 What to spend on . . . 13
2.4 Overlapping generations . . . 14
2.5 Example of Ghana . . . 15
2.6 Summary of the background . . . 16
3 Model 17 3.1 Households . . . 18 3.2 Firms . . . 19 4 Analysis 21 4.1 Intergenerational equity . . . 23 4.2 Financing problems . . . 25
5 Summary and conclusion 25
1
Introduction
The discovery of a non-renewable resource can pose challenges for a country and there can be numerous solutions to the various problems presented with the new found assets. The discovery can be big or small, generating revenues for hundreds of years or only boosting wealth temporarily. The country in this situation can be a modern democracy with high quality institutions or a corrupt society that will not be able to convert the resource wealth into growth and prosperity. Many factors play in when deciding the appropriate spending strategy. This thesis will consider how temporary resource revenues in a capital scarce country can be used as a "Big push" towards higher growth by implementing a strategy of public investment spending. It will then focus on the intertemporal fairness issue associated with the spending of resource revenues and financing problems that can arise in the case of investments with a high social return but a low commercial return.
Countries that discover natural resources are faced with the resource curse which is explained by institutional and structural effects. The structural effects can be explained with Dutch disease and real exchange rate effects. The adverse effects can be isolated by the proper management and timing, such as raising consumption permanently, only to spend when the funds become available and thereafter smoothing it over all generations, or skew consumption towards the present poor generation. Despite the challenges and risks of mismanagement, it is wanted to spend the windfall at some point and the question then is what to spend on. The resource wealth should be converted to other productive assets such as public infrastructure which will boost private capital in the future. This raises two concerns. What are the intergenerational effects of such a distribution that deviates from a permanent income approach? As public infrastructure has a high social return but low cash return, will it run into financing problems?
Some of the recent literature on optimal management of resource revenues has focused on deviations from a standard permanent income strategy. There are several arguments for this; for example, if a country is faced with imperfect access to capital markets, and have to pay a premium on its debt, using some of the revenues to repay debt could bring down this premium and boost private sector investment. Another reason is that it can be optimal with public investments
in infrastructure that will increase private sector productivity in the longer run. This requires an increase in spending early on, which means a deviation from the permanent income approach. Furthermore, public investments can have positive externalities with a potential high social return, but these investments do not necessarily generate any cash flow. A typical example is education, an educated population increases overall productivity, but it can be difficult to capitalize on the investment in a slave free society, as there is little or no cash return. The government has to borrow ahead of time and rely on future earnings to repay the debt, but most of the benefits will fall on the private sector which leaves the government with financing problems. Therefore it makes it hard to implement a strategy of public infrastructure investments. Individuals and firms might not internalize the effects of public capital in their decision making process. It can be a role for a government that levies taxes and invests in infrastructure, and by unlocking this productivity gain the economy can be pushed to a higher level of output.
In order to model the distributional consequences of a deviation from a perma-nent income solution, it can be beneficial to implement an overlapping generations structure. In this setting, the welfare effect for individuals can be different based on which period they are born in. This will enable us to analyze the distribu-tional consequences and the growth prospects when a windfall is spent on public investments. A large part of the literature focuses on real exchange rate effects of a resource discovery, such as the pull between traded and non-traded goods or home and foreign final goods. It is not necessary to model these effects explicitly as the focus is on intergenerational equity and financing problems, or the distri-bution and transfer between generations, and between public and private capital. The structural effects of exchange rate fluctuations are therefore not taken into account in this thesis.
The rest of the thesis is organized as follows. Section 2 provides insight on the background of the challenges of natural resources, such as the resource curse, and reviews some of the literature on this topic. Section 3 sets up the analytical framework and section 4 presents a simple numerical simulation of the model. Section 5 provides a summary and conclusion.
2
Background and literature review
In this section, the typical problems that resource rich countries face, such as the infamous resource curse, will be discussed. Then, the possible options that are available to smooth consumption and what to spend the resources on will be presented. The goal of this thesis is to model these issues in an overlapping generations framework so this will also be discussed. Finally, there will be some key facts about Ghana mentioned as an example.
2.1
Typical challenges with natural resources
One of the most typical challenges for countries discovering natural resources is how to avoid the infamous resource curse. It was noticed that resource discoveries tended to be followed by slower or even negative growth in many countries. Nigeria for example experienced negative growth from the late 1960s to early 1970s and again between the 1980s to 1990s despite vast natural resources being discovered. Only since the 2000s have they begun a stable and high growth environment, as seen in figure 1. Explanations can be the role of institutions and structural ef-fects on the economy. Institutions are considered to be one of the most important factors of economic growth1, but a sudden windfall of natural resources can give rise to cronyism and rent-seeking behavior among government agents which skew the allocation of wealth towards a small and powerful elite. This fight over re-sources further weakens democratic institutions, induces corruption and gives rise to destructive conflicts.
The other category of explanation focuses on the structural effects resource revenues have on the economy. Ploeg (2011) mentions real exchange rate appreci-ation, deindustrialization and low growth prospects, all results deriving from the Dutch disease literature. Increased spending out of resource income raises demand for non-traded goods, drives up wages and prices, and thus appreciates the real exchange rate. This makes the traded goods sector less competitive and leads to deindustrialization. Since the traded goods sector tends to be more productive, this results in lower growth prospects. Another damaging effect on growth is the
200
300
400
500
600
GDP per capita (constant 2000 USD)
1960 1970 1980 1990 2000 2010
Year
Figure 1: Nigerian GDP per capita 1960-2010 (constant 2000 US$). Source: World Bank
volatility of the exchange rate, which acts as a tax on investments and reduces productivity growth.
2.2
Resource curse
The term “Resource curse” was first used in Auty (1993) and the literature focuses around whether the curse indeed exists, what the causes are and if there is a cure so that it can be turned into a blessing. In their influential study, Sachs and Warner (1995) demonstrated the existence of the resource curse by showing a negative relationship between the ratio of the level of natural resource exports to GDP in the base year 1970 and the growth rates in the following 20-year period (1970-1990). Thus, countries with a high ratio of natural resource exports to GDP in the base year experienced lower growth rates than countries with a low ratio in the following years.
The scatterplot illustrating this relationship is reproduced in figure 2. The estimates remained significant also after including several other variables that are
-3.635 -3.635 -3.635 5.771 5. 771 5.771 Growth rate G row th r at e Growth rate 0.0064 0.0064 0.0064 0.8856 0.8856 0.8856 Primary exports/GNP in 1970 Primary exports/GNP in 1970 Primary exports/GNP in 1970
Figure 2: Growth and natural resource intensity. Reproduced from Sachs and Warner (1995).
identified by Barro (1991) to be important for economic growth. Their paper thus concludes that a resource curse did indeed exist during the period; a resource boom can be associated with subsequent low growth rates in GDP.
Later papers by the same authors draw similar conclusions. In Sachs and Warner (1999) they present evidence from seven Latin American countries that had experienced natural resource booms, and showed that in some cases the boom was followed by a slowdown in growth, while in other cases there were no permanent increase in growth. The paper is based on a “Big push” reasoning which implies that countries that are trapped in a low-income equilibrium need a big push such as large public spending programs, foreign aid, resource discovery or an increase in the world price of natural resources in order to grow and develop (Sachs and Warner, 1999). The big-push theory rests on an assumption of increasing returns to scale (IRS) in one industry (Murphy et al., 1989) and in their model they show that only if the IRS is in the non-tradeables sectors can a resource boom set off a dynamic growth process. Otherwise it will suppress growth through Dutch disease
effects.
Sachs and Warner (2001) is a summary of the research and it concludes that “[the] curse is a reasonably solid fact”. They base this conclusion on several studies that show a negative correlation between resource intensity and economic growth that also survive introduction of several control variables. They also argue against critiques that claim that the results are biased due to factors such as geography, climate and the magnitude of economic rents from the natural resource. They thus conclude with an existence of the natural resource curse. Other studies that confirm the resource curse include Arezki and Van der Ploeg (2010), Bleaney and Halland (2009) and Gylfason et al. (1999).
On the other side of the literature, there are also studies that refute the curse. Brunnschweiler (2008) finds that natural resources have a positive association with real GDP growth by using a different measure of resource abundance than Sachs and Warner (1995), thus contradicting the curse. This paper also finds no negative effects of resources on growth through the institutions channel, so that resources do not affect institutional quality. Manzano and Rigobon (2001) re-estimate the findings in the cross-sectional analysis in Sachs and Warner (1995), but by using a panel data instead. The results from the cross-section analysis were no longer present when using panel data, which they blame on omitted variable bias in the cross-section estimations. They further conclude that the negative impact on growth observed in other studies is not due to the dependence on natural resources itself, but a debt overhang problem that arises as a result of collateralizing oil revenues that increase due to a bubble.
Finally, there are the studies that conclude that resources can be both a curse and a blessing, or more specifically that the curse can be turned into a blessing. Ploeg and Poelhekke (2009) argue that the curse is due to an indirect negative effect from volatility that dominates a positive direct effect of resources on growth, so that the curse is mainly a problem of volatility. Thus, when volatility is controlled for, they argue that the curse can be turned into a blessing. In a survey by Ploeg (2011) he argues that the evidence shows that natural resources can be either a curse or a blessing. Examples of important factors that turn the curse into a blessing are good institutions and reduced impact of volatile commodity prices, for example by improving the financial system.
2.2.1 Structural effects
The structural effects of the resource curse can be explained by Dutch disease and volatility. The term Dutch disease was first used in an article in The Economist in 1977 at a time when the Dutch economy was going through painful restructuring after spending too much gas revenues on unsustainable public projects and welfare systems. The large demand for the Dutch currency had led to an appreciation of the exchange rate which made the traditional export sector less competitive on the world market. The government spending on public projects crowded out investments in other sectors and led to de-industrialization.
The mechanism underlying the Dutch disease is thus as follows. Increased demand for a natural resource increases the disposable income in terms of foreign currency. When this foreign currency is converted into domestic currency, demand for both traded and non-traded goods will increase. The increased demand for traded goods is offset through a deterioration in the non-oil trade balance, but in order to restore the equilibrium in the non-traded goods market, the real exchange rate appreciates.2 The increased demand puts upward pressure on wages and makes the traded goods sector less competitive and it consequently shrinks (van Wijnbergen, 1984a).
Corden and Neary (1982) modeled the phenomenon by considering a small, open economy consisting of three sectors; two traded good sectors and one non-traded good sector. They show that when a boom occurs in one of the non-traded good sectors, the sector that is lagging behind is crowded out by the two other sectors. This result draws from two effects, the resource movement effect and the spending effect. An increased demand for capital and labor in the booming sector bids up the factor prices, which makes the other sectors less competitive and they consequently shrink. This is the resource movement effect. The spending effect occurs when revenues from the booming sector is converted into domestic currency and spent within the country on the non-traded good. The conversion leads to an appreciation of the exchange rate and thus a further weakening of the competitiveness of the traded sector that is lagging behind (Corden and Neary,
2Either through higher inflation if there is a fixed exchange rate, or through a nominal
1982). The main result from both Corden and Neary (1982) and van Wijnbergen (1984a) is thus a decline in the traded goods sectors.
However, the purpose of the traded goods sector is to export its products in order to earn foreign currency, so whether this is achieved through a traditional manufacturing sector or by selling the natural resources does in principle not really matter. It can be seen as a self-correcting mechanism, the higher exchange rate is a signal that the economy should be doing something else (The Economist, 2011; Ebrahim-zadeh, 2003). The problem is that exhaustible resources will eventually be depleted so the inflow of foreign currency will come to a halt. When the economy goes from being an exporter of manufactured goods to dependence on natural resources, workers will find new jobs in the non-traded sectors (resource movement effect) and there will be certain irreversible processes such as closing of factories. When the resources are depleted, foreign currency again needs to be earned by other means. Reopening of factories and retraining of staff implies adjustment costs in order to restore manufacturing capacity, and unless the economy is highly flexible enabling the resource factors to quickly move to the sectors where they are most efficient, this readjustment will be harmful. Additionally, if the traded sectors provide positive externalities for economic growth, for example if they generate Learning by Doing, a shift of resources into other sectors will be damaging to growth as they are less productive (van Wijnbergen, 1984b).
Another structural effect is volatility. Volatility is the fluctuations observed over time in a variable, such as commodity prices, exchange rates and economic output. Volatility affects growth through at least two channels for resource rich economies. First of all, volatile commodity prices mean that government revenues are uncertain. If income from resources make up a large share of government revenues, it means that government spending will be volatile as well. Volatile government spending is in the end damaging to economic growth. Secondly, refer-ring to the Dutch disease explanation above, volatile commodity prices also imply a volatile real exchange rate. This acts as an indirect tax on investment, thus discouraging investment and trade.
The seminal contribution to the relationship between volatility and growth can be found in Ramey and Ramey (1995). In their paper they argue that growth theory and business cycle theory have traditionally been considered unrelated, until
new theories were introduced in the 1980s that explained output fluctuations with stochastic variations in technology. Their contribution however, was to investigate the effect of business cycle volatility on economic growth which previously had received little attention. They found that there is a negative relationship between economic growth and the volatility of economic fluctuations, thus confirming that growth and business cycles are not unrelated. Countries with higher volatility typically had lower growth rates, and the results were significant both in a panel of 92 countries and a narrower selection of the OECD countries when controlling for other growth related variables.
Building on these results, Turnovsky and Chattopadhyay (2003) develop a model where they analyze volatility and growth for developing countries that have imperfect access to world capital markets. When tested empirically, they found that terms of trade volatility, government expenditure volatility and monetary volatility all have strong negative effects on growth. An explanation as to why volatility in government spending is negative to growth is that due to imperfect capital markets governments are unable to smooth consumption. When they can-not do this, all income has to be spent as they are earned. This means that consumption and investments are high when revenues are high, but when revenues decrease there will no longer be funding to maintain this high level. That makes the business cycle more volatile, which has a negative effect on growth. Further on the expenditure volatility issue, Furceri (2007) finds a negative relationship between government expenditure volatility and economic growth.
2.3
Spending the resource wealth
2.3.1 Timing
As documented in the previous section, there will be structural effects of resource discoveries but at some point the revenues will have to be spent. The main prob-lems are the timing of spending and what to spend on. To answer this, we can first look at the timeline of resource revenues. In the case of a temporary windfall, the discovery is made at time t and extraction begins in the future period t + 1. This is when revenues are generated. The resources are depleted and revenue streams come to a stop in period t + 2, this distribution can be seen in figure 3.
BIH
PIH
Skewed Consumption
t t+1 t+2 Time
Figure 3: Different consumption strategies for temporary resource revenues The simplest way to smooth out the consumption would be to follow a per-manent income (PI) strategy. This means taking the present value of the future revenue streams and spread it evenly among all generations. This relies on capital markets, as consumption will be financed by borrowing money ahead of the rev-enue streams, then paying off the debt and building up a sovereign wealth fund during the extraction time, and finally spending out of the fund when resources are depleted.
Another strategy is known as the Bird-in-Hand approach. This is a conservative way of consuming the revenue wealth, as revenues are saved in a fund and only the returns on this fund are consumed. This indicates that consumption increases gradually as resources are extracted, sold and converted into foreign currency, and stored in a fund. This is the strategy adopted in Norway, where the government is only allowed to use the estimated long term real return to fund the budget deficit. These two approaches rely on at least one important assumption; access to efficient capital markets. In countries with imperfect capital markets there can be financing issues during the first time period as the borrowing relies on future
resource revenues as collateral. This limits the capital mobility as the value of this collateral goes down precisely when hit by an adverse resource price shock. When the value of the collateral goes down the country might find itself in a debt overhang situation.
Another consumption strategy that has been proposed for low-income, capital scarce countries is to skew the consumption towards the present poor generation. This would mean to borrow more than the PI approach allows for in the first period, where consumption peaks, and then less in the future time periods. Public investments in infrastructure can absorb the revenues, but will usually not yield a high cash return in the future. It will on the other hand, increase productivity of the private sector and hence improve economic growth, which will benefit future generations.
Ploeg and Poelhekke (2009) analyze optimal policies for capital scarce countries that discover temporary natural resources. Crucial to their analyses are the level of debt and the interest rate, as they show that there is a positive correlation between the indebtedness of a country and the interest premium. Using a PI policy as a baseline, they first show that the country should deviate from the PI policy and rather raise the rate of growth of consumption if the interest rate is greater than the time preference rate. They further look at the composition of spending, which should take the form of increased consumption and public investments/debt reduction. Thus, the distribution of spending will be skewed more towards the present poor population in order to accelerate the move towards the long-term level of consumption. Only if the windfall is large enough should a SWF be built up. However, they do not consider the inevitable volatility of resource revenues, which would call for a SWF to smooth out this volatility.
In a study on Angola, Richmond et al. (2013) compares a spend-as-you-go approach to a gradual scaling up of public investments. They point out the coun-tercyclical effects of the volatility, in that investments will be high and perhaps above absorptive constraints in times of rising revenues, and low during down-turns so that old projects are not maintained. This increases the depreciation rate and thus reduces the returns. In the case of Angola, which will benefit from oil revenues in the long term, their simulations show a decrease in volatility by following the gradual scaling up approach, thus a strategy that looks more like the
Bird-In-Hand.
When revenues are only temporary, the approach may look different. Samake et al. (2013) discuss the spending issue in the case of Cameroon, which they as-sume will deplete their resources by 2032. Their simulations suggest that a scaling up approach can benefit the country if reforms that increases the efficiency of pub-lic investments are made. They point out that the key transmission mechanism seems to be the complimentarity with private investments. This is also suggested in Agenor and Moreno-Dodson (2006) who identify three conventional channels of public investments effect on growth. The most common argument is that public investments increases the productivity of private inputs. Secondly is the comple-mentarity effect on private investments, and third is a potentially adverse crowding out effect.
In a comprehensive study on Ghana, van der Ploeg et al. (2012) addresses how they should optimally spend their resource wealth. They use the permanent income rule as a benchmark and find that spending should be skewed more forwards as long as the spending goes to investment. They suggest to first spend the revenues on reducing foreign debt in order to lower the interest rate, which will stimulate investment. Then they propose that the windfall should be spent on domestic capital, but also to build up a sovereign wealth fund in order to smooth out potential absorption constraints.
2.3.2 What to spend on
While private investments need to generate a cash flow in order to make profits, this is not necessarily the case with public investments. Public investments in infrastructure such as education, health care and roads may have a potential high social return, but no cash return. Education provides the economy with higher skilled workers, a decent health care system helps these workers to a speedy re-covery in case of injury or illness and a physical infrastructure, like roads and electricity grids, make production and trade more efficient. Now imagine a very basic economy, where households own firms and also provide labor which, together with capital, is used to generate output. By introducing a tax levying government, it can take some of this output and invest in infrastructure. Since this is public
capital, which does not yield a cash return, individuals or firms will not find these projects profitable and will refrain from making these investments themselves. However, the access to infrastructure raises the productivity of the firms, which means that more output is produced. The tax therefore in a way becomes self financing.
This only works up to a certain point, as the government can at a maximum tax what the economy produces. In an equilibrium, a benevolent government will only raise taxes to a point where the marginal cost to households is lower than what they gain by higher output. The economy might therefore still be stuck in a low income equilibrium even though infrastructure projects have been undertaken. If resource revenues become available on the other hand, the government can finance the infrastructure projects with the extra funds. If the revenues are large enough, it can act as a "Big push" towards a high income equilibrium.
It should also be noted that not all investments in infrastructure will help increase productivity and growth. A government should not be building bridges to nowhere, and it will be crucial to have proper institutions in place to perform cost/benefit analyses to determine the appropriateness of an investment.
2.4
Overlapping generations
The spending of resource revenues on infrastructure projects that will increase pro-ductivity in the future means that the consumption will deviate from a permanent income approach. This has distributional consequences among generations and therefore introduces a question of intergenerational fairness. These effects can be captured in an overlapping generations (OLG) framework, where households are made up of a young and an old generation.
The main distinction to consider is whether to spend or to save. As mentioned in van der Ploeg et al. (2012), spending in its purest form is domestic consump-tion, while saving can be thought of as investing in foreign assets as it can yield benefits in the future. But public investments (which means investing in domestic assets) can be considered a bit of both, as the spending occurs now and increases consumption through wage income, while at the same time those investments yield a return that is consumed by future generations.
0 0 0 500 500 500 1000 1000 1000 1500 1500 1500
GDP per capita (current US$)
G D P pe r ca pi ta ( cu rr en t U S$ )
GDP per capita (current US$) 1960 1960 1960 1970 1970 1970 1980 1980 1980 1990 1990 1990 2000 2000 2000 2010 2010 2010 Year Year Year
Figure 4: GDP per capita (current US$) in Ghana. Source: World Bank The present and future generations are therefore faced with the question of what is a fair allocation of the resources. Spending more than the PI approach allows for in the beginning means that the present poor generation will be able to consume more via the wage income, but at the same time leaving less for the future generations in terms of the cash from the windfall. On the other hand, the future generation will enjoy the (social) returns from the public investments which increases the productivity of the private sector. The challenge is therefore to balance these intergenerational equity concerns.
2.5
Example of Ghana
A capital scarce country with a temporary and relatively small resource discovery is Ghana. The International Monetary Fund and World Bank classify Ghana as a lower middle-income country and is advancing towards middle income status. GDP grew by 7.9% in 2012 and is expected to grow by 5-8% annually in the next few years. After a long period of slow growth, the 2000s saw a huge improvement in GDP growth as illustrated in figure 4.
The Jubilee oil field was discovered in 2007 and production started in 2010. The resources are projected to last for 20 years and peak between 2013 and 2015 with production at 120,000 barrels of oil per day. At its peak oil revenues will therefore account for about 30% of government income (van der Ploeg et al., 2012).
Ghana is considered to have strong democratic institutions which is favorable for avoiding the resource curse. The IMF points out that the country has a strong growth momentum, but faces some potentially serious risks due to a large cur-rent account deficit and increased government borrowing (International Monetary Fund, 2013). Thus it is important to implement safeguards to avoid a situation of debt overhang.
Ghana has a large and unproductive agricultural sector, which means that a resource movement effect can potentially pull labor resources out of this unproduc-tive sector without being damaging to growth. These resources can for example be used in public investments or related spill overs. A more capital intensive agricul-tural sector can for example make it more productive and allow Ghana to exploit its comparative advantage in agriculture. As illustrated in figure 5, agriculture account for 42% of employment and only 26% of output. The issues discussed in this thesis can therefore be applied to the case of Ghana.
2.6
Summary of the background
The aim of this section has been to motivate the analysis which follows. To sum up, we have seen that at the top of the problem is the resource curse, which was explained by institutional issues and structural effects. Despite the risks associated with mismanagement of the resources, it is still an opportunity to create welfare and prosperity, so the revenues should be spent somehow and at some point in time. The best strategy of spending depends on the country and ranges from a permanent income approach, to a BIH approach or to skew the spending towards the present in case of a poor, capital scarce country. In the case of Ghana, it is likely beneficial to skew the consumption towards current generations, and let future generations benefit from higher productivity. Based on this background, the following analysis will then focus on the intergenerational equity issues and financing problems of adopting a public investment strategy.
Figure 5: Sectoral employment and output share. Source: International Monetary Fund (2013)
3
Model
This section presents a simple model to analyze the two issues discussed in the previous sections. It follows a standard OLG framework as in Diamond (1965) and lecture notes from a course in macroeconomics3. The model is made up of firms and households, which includes an old and a young generation. The young provide labor to the firms and earn wages w, while the old own the firms which yield a return rP. This means that the young consume parts of their income, and invest the rest in the firms for their retirement. Firms produce output by using labor, private capital and public capital (infrastructure). Resource revenues are spent only on publicly available infrastructure, and public capital therefore enters the model exogenously. In a competitive equilibrium, the marginal products of labor and private capital equal the wages and interest rate. The model is open, so the firms produce a single good which is traded freely. Thus there is no distinction between traded and non-traded goods, or home and foreign goods, and therefore no exchange rate effects. The open nature of the model also means that lending and
3Macroeconomics (Master Course) taught spring 2011 at the University of Amsterdam by Dr.
borrowing can be done freely with the consequence that the private capital stock is set independently of domestic savings, but rather relies on the international real interest rate. This separates investments and domestic savings. Each time period is considered to be one generation which lasts for many years, so that there are no investment adjustment costs in between generations.
3.1
Households
The model considers three time periods; the time from discovery to when the revenues start flowing in, the period of extraction, and the post resource time period. In each period, there is an old and a young population. The population is given by N with growth rate n so that Lt+1 = Lt(1 + n). The population derives utility from consumption in each period of their lives. This is given by c1,t when a person is young and c2,t+1 when the person is old. The utility function is given by
Ut= lnc1,t+ 1
1 + ρlnc2,t+1 (1)
where ρ > 0 is a time preference parameter.
People work and consume part of their income while young, and saves the rest (by investing in the firms) to consume in their old days when they have no income. The household budget constraint is therefore given by
c1,t+ 1 1 + rP,t+1
c2,t+1= wt (2)
Maximizing (1) subject to (2) yields the following standard consumption Euler equation
c2,t+1=
1 + rP,t+1
1 + ρ c1,t (3)
Equation (3) can then be inserted to (2) to get period 1 consumption:
c1,t = 1 + ρ
2 + ρwt (4)
and (4) can then be inserted to (3) to get period 2 consumption (for the same individual):
c2,t+1=
1 + rP,t+1
2 + ρ wt (5)
The saving rate is defined as the fraction of the wage that is left for consumption in the second period, so that s = wt−c1,t
wt . By inserting equation (4) and rearranging we get the following expression for saving:
s = 1
2 + ρ (6)
Equation (4), the consumption equation for the young generation, can therefore be rewritten as c1,t+ swt= wt.
3.2
Firms
The firms generate output according to the following production function:
Yt = KI,tα L β tK
1−α−β
P,t (7)
where KI,t is the public capital and KP,t is private capital. This is a similar production function as in Agenor and Moreno-Dodson (2006) and it can be seen from the marginal products of labor and private capital that both increase with a higher stock of public capital:
∂Yt ∂KP,t = (1 − α − β) KI,t KP,t α Lt KP,t β ∂Yt ∂KI,t = α KP,t KI,t α Lt KP,t β ∂Yt ∂Lt = β KI,t KP,t α K P,t Lt 1−β
It can also be seen that the marginal products increase and decrease at a decreasing rate as α < 1. Therefore in the situation where the public capital is very low, the returns will be very high. As it increases, the return gets lower to the benefit of higher private capital returns and wages. In the case of a windfall that is channelled entirely into higher public capital, households are made better
off through an indirect increase in the wage rate. Thus, although not benefiting directly from the windfall, they will be able to increase consumption in both periods due to higher wages as is seen from equations (4) and (5).
Another interesting feature of the production function is if we consider unbal-anced growth outside the steady state. If we assume constant returns to scale in all factors, so that α and β are between 0 and 1, and α + β < 1, then private capital and labor will have decreasing returns to scale if public capital remains fixed. A doubling of private capital and labor will not double output, unless public capi-tal is also increased. Thus there is a kind of complementarity effect so that the economy needs the support of infrastructure in order to be on a balanced growth path.
In a competitive equilibrium, labor and capital are paid their marginal prod-ucts, w and r. A crucial point is that, as the economy is assumed to be open, it is faced with an interest rate set in the international financial markets. That means that the interest rate is set exogenously, so that the level of capital intensity is determined accordingly. The first order conditions can be written as
βYt Lt = wt (8) (1 − α − β) Yt KP, t = rt (9)
The value of the firms in the beginning of period t is therefore Vt = (1 + rt)KP,t. In each period, the goods market clears, which means that aggregate investment (in KP) is equal to aggregate saving and net exports, or It = S − N X. Assuming no depreciation, aggregate investment is equal to the change in capital stock, or It= KP,t+1− KP,t. The aggregate saving is what is saved by the young minus that which is dissaved by the old. The total saving by the young is swtLt, while the dissaving by the old is what they consume minus their income. The old consume their financial wealth, which is equal to the value of the firm, and earns rent from firms, rtKP,t, as their income. Their dissaving is therefore (1 + rt)KP,t− rtKP,t. The equilibrium It= S − N X can therefore be written as KP,t+1= swtLt− N Xt.
Using equation (8) this can be written
KP,t+1 = sβYt− N Xt (10)
which is the capital accumulation function. To get the capital accumulation func-tion in terms of labor, we divide by Lt and rearrange (keeping in mind that Lt+1= Lt(1 + n)) to get: kP,t+1= sβkα I,tk 1−α−β P,t − nxt (1 + n) (11) where Yt Lt = yt = k α
i kp1−α−β. The system of equations that solve the model can therefore be summarized as follows.
c2,t+1= 1 + rP,t+1 1 + ρ c1,t (12) c1,t + swt= wt (13) c2,t+1= 1 + rP,t+1 2 + ρ wt (14) yt= kI,tα k 1−α−β P,t (15) wt= βyt (16) rt= (1 − α − β)kαI,tk −α−β P,t (17) kP,t+1= sβkI,tα k1−α−βP,t − nxt (1 + n) (18)
4
Analysis
This section presents numerical simulations of the model in order to discuss the questions of intergenerational equity and financing problems that can arise by implementing a strategy of investments in public capital. The parameters are set in order to loosely reflect the case of Ghana and can be seen in table 1.
Parameter Value α 0.1 β 0.6 ρ 0.81 rP 1.5 n 0.72
Table 1: Parameter values.
Each period represents a generation, which can be thought of as 30 years. The parameters for time preference, population growth and interest rate have therefore been discounted to reflect this. That means an annual population growth rate of 1.82%, as in van der Ploeg et al. (2012), and time preference of around 2%. The output elasticities are set to reflect Ghana’s high labor share, which is also estimated in van der Ploeg et al. (2012). With these parameters, an initial steady state can be calculated and is shown in table 2.
Variable Steady state
y 0.327024 kP 0.065405 c1 0.126387 c2 0.174568 w 0.196215 nx -0.042669
Table 2: Steady state calculation of the model
These numbers do not tell much by themselves, but it can be noted that there is already a trade deficit as the net export is negative for the exogenously given interest rate. That means that the country imports more than it exports. The next step will be to simulate a change in the public capital stock due to public investments. The way to think about this increase is that resource revenues enter public investments directly so that the public capital stock increases. There is no depreciation and the level is set exogenously. This can be done in three different
ways, either by making the investments, and thus increase public capital, in the first, second or third period. The numerical simulation of these scenarios can be seen in tables 3, 4 and 5. One thing to notice is that as there is no investment adjustment cost built into the model (since each period is considered to be 30 years, which is plenty of time for investments to adjust) so the model immediately converges to a new steady state following an increase in public capital. The results will further be used to discuss the questions in the following sections.
Initial steady state 1 2 3 End steady state
y 0.327024 0.361064 0.361064 0.361064 0.361064 kP 0.065405 0.072213 0.072213 0.072213 0.072213 c1 0.126387 0.139543 0.139543 0.139543 0.139543 c2 0.174568 0.174568 0.192739 0.192739 0.192739 w 0.196215 0.216638 0.216638 0.216638 0.216638 nx -0.042669 -0.047111 -0.047111 -0.047111 -0.047111 kI 0.05 0.1 0.1 0.1 0.1
Table 3: Simulation of increase in public capital in period 1
Initial steady state 1 2 3 End steady state
y 0.327024 0.327024 0.361064 0.361064 0.361064 kP 0.065405 0.065405 0.072213 0.072213 0.072213 c1 0.126387 0.126387 0.139543 0.139543 0.139543 c2 0.174568 0.174568 0.174568 0.192739 0.192739 w 0.196215 0.196215 0.216638 0.216638 0.216638 nx -0.042669 -0.054379 -0.047111 -0.047111 -0.047111 kI 0.05 0.05 0.1 0.1 0.1
Table 4: Simulation of increase in public capital in period 2
4.1
Intergenerational equity
Deviating from a permanent income approach of revenue spending raises an issue of fair distribution of the wealth over all generations. If all is spent early on
Initial steady state 1 2 3 End steady state y 0.327024 0.327024 0.327024 0.361064 0.361064 kP 0.065405 0.065405 0.065405 0.072213 0.072213 c1 0.126387 0.126387 0.126387 0.139543 0.139543 c2 0.174568 0.174568 0.174568 0.174568 0.192739 w 0.196215 0.196215 0.196215 0.216638 0.216638 nx -0.042669 -0.042669 -0.054379 -0.047111 -0.047111 kI 0.05 0.05 0.05 0.1 0.1
Table 5: Simulation of increase in public capital in period 3
these generations will benefit the most from the direct effects of the spending, while leaving nothing for future generations. But when the spending is invested in public infrastructure the future generations will benefit from higher productivity of private capital and therefore be better off as well. Which scenario benefits all generations the most then according to the model? Clearly, having an increased public capital early on increases consumption for young and old generations in each period as seen in table 3, while the increased consumption is postponed in the two other scenarios in tables 4 and 5. This is a direct result of higher productivity of the private capital that follows the increase in public capital.
In the first case, when the public capital stock increases in period 1, output immediately adjusts to a new steady state. As is seen from the marginal product equations, an increase in the public capital stock requires the private capital stock to increase in order to keep the interest rate constant. Higher consumption for both young and old follows from a higher wage rate. The net exports also immediately adjusts and becomes more negative, which means that imports increase relative to export and is in line with the expectation that the country borrows to finance the expenditure.
In the second and third case, a similar pattern is seen, but the adjustments take place later as the increase in public capital stock is delayed. Net exports become more negative in the period before the increased public capital stock in anticipation of the higher output levels. It is therefore clearly illustrated that in a situation like this, all generations are better off by skewing the revenue spending
forwards towards the present generations, and let future generations benefit from the indirect effects of higher productivity.
4.2
Financing problems
The second question concerns if a strategy of spending the windfall on public infras-tructure runs into financing problems. Public infrasinfras-tructure raises productivity of the private sector, and such investments therefore implies a transfer from the pub-lic to the private sector. Or in other words, the return on the pubpub-lic investments accrues to the private sector. The windfall is channeled into public infrastructure projects which benefit the private sector, but the nature of such investments makes it hard to generate any cash returns. If consumption is skewed towards the present it means that these projects have to be financed by external borrowing before the oil revenues actually materialize. This can result in financing problems.
The increased productivity is clearly seen in the numerical simulations by look-ing at the increase in output and private capital. It was also discussed in the previous section that net exports become more negative, which implies more for-eign borrowing. As there is no accumulation of or return from public capital other than the investments from resource revenues, there is no way to finance the foreign borrowing that is required to make the investments before the actual revenues are available. In the second and third cases the investment is delayed. The previous section discussed how the increase in public infrastructure benefits all generations, so the borrowing should take place. One way to make this possible is by lump sum taxes of private capital in order to transfer some of the increased productivity back to the foreign lenders. This might be enabled by reforming the tax system as part of implementing the public investment strategy of resource spending.
5
Summary and conclusion
This thesis has on the one hand discussed the intergenerational equity issues asso-ciated with a spending strategy of natural resource revenues that deviates from a permanent income approach, and on the other hand the financing problems that can follow from such a strategy. The various problems associated with natural
resource spending have been discussed, from the resource curse to how and when these revenues should be spent and what they should be spent on.
The problem of a large windfall that natural resources bring with them was discussed as being divided in two parts. One side looks at the institutional prob-lems such as corruption, cronyism and rent seeking, while the other side focuses on structural effects. This thesis focused most on these structural effects, such as Dutch disease and problems of volatility. Different strategies to cope with these problems in order to turn the curse into a blessing were then discussed, such as the timing and what to spend on. It was then argued that a relatively poor country with a low level of infrastructure that discovered a natural resource which will only last temporary, should skew their consumption forward and invest in public infrastructure that will increase private capital productivity in the future.
Such a deviation from a permanent income approach would mean that different generations would be treated differently, thus raising the problem of intergener-ational equity. Furthermore, the nature of such investments in public capital is characterized by a low cash return, but an obvious high social return in terms of higher private capital productivity. This therefore creates a financing problem since investing in infrastructure requires borrowing ahead of when the resource revenues will actually accrue. The investments will not yield a cash return, and the public sector will therefore not be able to borrow in the first place.
An overlapping generations model was then used to discuss these issues with a numerical simulation. The parameters were loosely calibrated to resemble Ghana, and it was concluded that since all generations benefit from early spending, a public investment strategy of resource revenue spending should be complemented with a provision in the tax system that enables a transfer of private capital to service the debt.
What can be learned from the discussion in this thesis is that a country like Ghana, which has been endowed with a temporary oil wealth, should borrow money in the financial markets in order to fund public infrastructure projects that will increase productivity in the future. The debt should be repaid by taxing the private sector who will benefit from this increased productivity. Structural effects are not likely to be an issue as the investments can act as a "Big push" that kick starts more productive industries than the current highly manual agricultural sector.
6
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