Appendix. First Order Conditions
Making the relevant substitutions in equation (2), and maximizing the objective function described in (1), it can be shown that the intra- and intertemporal conditions for private consumption are given by the first-order conditions described in equations39 (A.1.)–(A.3.)
Ct, Kt, and the Lagrange operator λt (or shadow price) solve for the representative problem in (1) and satisfy the first order conditions:
The productivity of public capital is given by
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The authors wish to thank Mario de Zamaróczy and Mauro Mecagni for their guidance and very helpful discussions. We also thank Alfredo Baldini, Andy Berg, Katja Funke, Bin Li, Paolo Mauro, Giovanni Melina, Fabien Nsengiyumva, Alex Segura-Ubiergo, Jean van Houtte, Susan Yang and Felipe Zanna for useful comments. Any errors and omissions are the authors’ sole responsibility.
Recent explorations give some indications that oil reserves may not necessarily be fully depleted by 2032. However, this would not fundamentally alter the qualitative assessment that Cameroon’s reserves are on a declining path.
Reflecting complementarities between public and private capital, private investment is expected to increase overtime.
This assumption is consistent with the Cameroonian authorities’ vision expressed in Cameroon’s Growth and Employment Strategy Paper (Government of Cameroon, 2009).
In 2001, the Norwegian government implemented a BIH fiscal rule allowing the government to take out 4 percent of the value of the oil saving fund in the previous year, equivalent to the real return on the fund, to finance the general government budget in the current year (Bjerkholt and Niculescu, 2004; Harding and Van der Ploeg, 2009).
Public investment efficiency is defined as the ratio of public investment spending to the value of resulting installed public capital. In general, in environments of imperfect information and/or governance constraints, projects with the highest returns are not necessarily chosen, and, not always well executed. A complementary way to think about efficiency is that a fraction of spending is wasted through suboptimal project execution processes (e.g., procurement issues).
Gauthier and Zeufack (2009), for example, find that GDP contracted on average by 5 percent a year between 1977 and 1985, or by a cumulative 27 percent during the period. Arbache and Page (2007), using event history analysis, estimate that a growth deceleration occurred in 1986. The methodology and criteria they employ suggest that growth would have been contracting for at least three years before 1986.
According to Essama-Nssah and Bassolé (2010), real GDP in 1990 was 20 percent lower than its 1985 level; and per capita income fell by 50 percent between 1986 and 1993. Gauthier and Zeufack (2009) report that Cameroon was poorer in 2007 than in 1986 in terms of GDP per capita (measured in constant 2000 U.S. dollars).
In 2010, Cameroon’s oil production amounted to 63,800 barrels a day. Oil exports were about half of total exports, while oil revenue was 27 percent of total government revenue. By comparison, in the same year, Nigeria (sub-Saharan Africa’s largest oil producer) produced over 2.4 million barrels a day; oil exports were 96 percent of total exports; and oil revenue was 70 percent of total government revenue.
Cameroon is subject, as a member of the Central African Economic and Monetary Community (CEMAC), to an explicit balanced budget rule for general government, adopted in 1996; and a debt rule, adopted in 2002, limiting the debt-to-GDP ratio to 70 percent. Since 2000, Cameroon has failed to meet the former criterion only once, and it has always met the debt rule since debt relief was granted in 2006. In 2008, CEMAC agreed to start monitoring other (non-binding) fiscal criteria, including one based on a balanced budget excluding oil revenue (Iossifov and others, 2009).
Partly, this appears to have been the result of weak program ownership. In addition, the rule was applied on a cash basis and was circumvented through the accumulation of domestic arrears during 2003–04 (Cossé, 2006).
The “Dutch disease” is defined as a series of negative consequences arising from large increases in a country’s foreign currency income. It is generally associated with a natural resource discovery, but can also arise from any large increase in foreign currency earnings, including foreign direct investment, foreign aid, or a substantial increase in natural resource prices. Typically, the Dutch disease results in a combination of (i) a decline in price competitiveness, and thus exports, of the manufacturing sector; and (ii) an increase in imports. The Dutch disease has generally been characterized as one of the root causes of the “natural resource curse.”
Gupta and others (2011) measure public investment efficiency using the Public Investment Management Index (PIMI) as constructed by Dabla-Norris and others (2011). As such they make the assumption that not all public investment spending translates fully into productive capital assets.
This is also below what researchers found to be optimal. Fosu, Getachew, and Ziesemer (2011) for example, put the optimal level of public investment in SSA between 8 and 11 percent.
A large contributor to these losses was the power sector, owing to the underpricing of power and distributional losses.
Note, however, that Cameroon is not EITI compliant as of February 2013.
As in Finn (1998), government expenditure on goods enters nonseparably in the utility function and alters the marginal utility of household consumption, thereby directly affecting household consumption decisions.
By iterating forward the representative household budget constraint, Husted (1992), Pattichis (2010) and Ramsey (1928) show that the intertemporal budget constraint can be expressed as in equation (2) under certain conditions—see the discussion on “Fiscal Policy and the Ramsey Problem.”
An alternative modeling approach is suggested by Van der Ploeg (2012), using Hayashi’s internal cost of adjustment to differentiate the total cost of public investment from the actual increment in public capital. His specification also captures the fact that absorption and other constraints become more severe as the public investment rate increases.
There is no consensus in the empirical literature on the impact of public investment spending on growth. Some reasons for this stem from factors such as differences in methodology, issues in data measurement, collection, and quality, and the consideration of stock vs. flows of investment. Additionally, it has been shown that industry-level (micro), country-specific, and region-level studies also account for differences in empirical results. Chakraborty and Dabla-Norris (2009) show that the quality of investment can explain income gaps or the varying estimates of elasticity of public infrastructure capital to growth between rich and poor countries. This consideration is crucial for countries like Cameroon.
A public good is both nonexcludable (it is not possible to provide that good to some households while excluding others—for instance the police department services of a city) and nonrival (the consumption of a unit does not reduce or diminish the units available for other consumers—for instance, a concert on television is nonrival).
Taking this into account could lead to a different optimal path of public investment. However, we think that in a low-income country like Cameroon, there is ample room for productive public investment before negative effects on private investment would set in.
We believe that this modeling strategy is realistic; however, not applying the ineffectiveness coefficient to the previous year capital stock does not modify qualitatively our results.
Using historical data, we first estimate ρ and κ given the assumed AR (1) process in (11). For 2012–32, ρ is obtained from (12) using the estimated κ in (11). A policy shift (e.g., when resource depletion triggers a change in fiscal policy) could lead to significant differences between ρ estimated from historical data and the projected ρ.
T=21 (assuming depletion of oil reserves by 2032, with 2011 being the base year).
Baunsgaard and others (2012) argue that using a fiscal rule based on the non-resource primary balance (like the NOPD) is relevant for countries with a relatively short horizon for resources, which is the case in Cameroon.
A negative σ would hence be associated with a procyclical fiscal policy.
Although countercyclical fiscal policy generally provides better economic outcome, procyclicality is not necessarily a suboptimal policy. For example, Talvi and Végh (2005) show that running a fiscal surplus may create pressure to increase spending—a government that faces large fluctuations in tax revenue may therefore choose to run a procyclical fiscal policy.
The Ramsey problem and the original optimization problem are linked through applying control theory to solve the problem by substitution, as shown in the Appendix.
Our model specification needs to be considered against two important limitations: (i) there is no explicit modeling of public sector congestion effects nor of a monetary sector; and (ii) we do not consider other possible spending options and objectives of the government (for example redistributive income transfers to reduce inequality).
DSGE estimates are generally considered data driven when they are obtained through maximum likelihood techniques.
Hulten’s φ is an index incorporating “electricity system loss,” “road condition,” “telephone network,” and “railway availability.” With the help of the PIMI, Dabla-Norris and others (2011) calculate an efficiency-adjusted public capital stock and find that, for 40 LICs, only 47 percent of investment translates into productive public capital. This is close to the 0.45 used in Hulten, even though the Hulten figure also includes the use of productive existing capital (one can see this by substituting equation (9) into equation (5)). Pritchett (2000) estimates that the fraction of public investment that is productive averages 0.49 for sub-Saharan African countries. IMF (2012) cautions, however, that these are measures presumably correlated but not direct estimates of the fraction of investment not well spent.
The oil prices are assumed to be in the range of US$95–US$110 a barrel, roughly in line with current IMF World Economic Outlook projections. Also there is some convergence of views among analysts that the current oil prices are expected to fluctuate within that range.
This is consistent with the average for middle-income countries in Hulten (1996) and is similar to what Dabla-Norris and others (2011) find for such countries.
This scenario is run to illustrate the risk of lack of progress in governance, which may make the use of natural resource revenue insufficient to boost growth and provide better social indicators.
We focus on the first-order conditions for optimum solutions based on the Lagrange method, and the knowledge of the value is not necessary in solving the dynamic optimization problem.