Appendix: A. On Public Investment Efficiency, Rates of Return, and Growth
This Appendix elaborates on the concept of “efficiency” and the closely related concept of the rate of return to public capital. It serves as background information for the calibration of efficiency and the rate of return. The bottom line is that the operator needs to be thoughtful when calibrating efficiency, particularly in considering what it might imply for the marginal product of effective capital. A change in the calibration of efficiency has two different interpretations: as a level change that applies to the past and the future, as when comparing two countries at a point in time; or as a change that applies to future investment but not the past, as for example because of an improvement in public financial management. It is up to the operator to decide which applies and whether other adjustments to the calibration are necessary in light of that interpretation.
In the analysis to follow, for simplicity, we assume that there is only one productive sector in the economy and set the long-run growth rate equal to zero.
“Efficiency” refers to the rate at which spending on public investment translates into public capital. The model distinguishes between the efficiency of steady-state public investment (
where iz,t is public investment (measured in real dollars), δ is the rate of depreciation of public capital,
The only nonstandard feature here is that s and
Consider first the marginal product of effective public capital (
That is, the marginal product of effective public capital is proportional to the production function parameter ψ and the output/public capital ratio. The production function embodies decreasing returns to public capital, holding other factors constant, and given the value of the parameter ψ.
Efficiency has a simple direct effect:
It would seem straightforward to obtain the growth impact of public investment. In calibrating the model, the operator chooses directly a value for the rate of return to effective public capital R0, and thus of the marginal product of public capital. The computer can solve for the implied value of ψ, given the other parameters of the model. Meanwhile, assumptions about the efficiency parameters s and
There is an important potential complication, however: efficiency and the marginal product of public capital may be related. Whenever—as with the Cobb-Douglas specification of equation (45)—the marginal product of public capital is declining with larger stocks of public capital, this marginal product will tend to be higher when efficiency has been low in the past. A country with a low value of
In the specific but widely-used case of the Cobb-Douglas production function, which is that used in the model in the text, the
This inverse relationship between
The upshot is that the operator needs to be thoughtful when calibrating efficiency, particularly in considering what it might imply for the marginal product of effective capital. In particular, a different calibration of s can be understood in two different ways. It is thus up to the operator to decide which interpretation applies and whether it calls for other recalibrations:
According to one interpretation, different calibrations of the value of s represent a time-invariant level difference in efficiency, e.g. between two countries. Higher steady-state efficiency will imply a higher marginal product of public investment in the model, because the marginal product of public capital is given by assumption.61 However, the operator should consider whether this makes sense in a particular case. How is it that the country wastes less public investment, and thus presumably has a higher public capital stock, and yet still has the same marginal product of public capital?
The second interpretation is that this represents a change in efficiency relative to the past. Such a change in efficiency through time will have an unambiguous effect on the marginal product of public investment. This is because it raises the effect of investment spending on the growth rate of public capital, with no potentially offsetting effect on the size of the stock. Thus, if the idea is that the country is improving its efficiency relative to its own history, then there is no need to reflect on possible implications for the marginal product of public capital.
Similar thoughtfulness would seem to apply in the application of the Fund’s policy on nonconcessional borrowing (IMF, 2009b). The policy emphasizes the role of efficiency framed as the capacity to manage public resources well—along with debt levels—in determining whether non-concessional borrowing for public investment is warranted. But from equation (46), the
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We thank Valerio Crispolti, Raphael Espinoza, Giovanni Ganelli, Andrew Jewell, Alvar Kangur, Chris Papageorgiou, Jens Reinke, Carlo Sdralevich, Susan Yang, and participants of the MMDG seminar of the African department at the IMF, the 2011 AERC/UNU-WIDER Macroeconomics of Foreign Aid Meeting, and the 2012 CSAE conference in Oxford for useful comments. All errors remain ours. This working paper is part of a research project on macroeconomic policy in low-income countries supported by the U.K.’s Department for International Development (DFID). Edward Buffie: Department of Economics, Indiana University, Wylie Hall Rm 105, 100 S. Woodlawn, Bloomington, IN 47405.
For example, Redifer (2010) points out that the four East African countries with new Fund’s Policy Support Instrument Programs (Mozambique, Rwanda, Tanzania, and Uganda), official aid has on average not increased in line with public investment spending and is not projected to do so in the next three years; therefore new financing sources, such as external commercial borrowing, must be tapped if public investment is to be scaled up.
A recent survey by Citigroup describes the new borrowing environment: “Knowing they want to borrow money to spend on projects to close the infrastructure deficit, governments in SSA have faced a wave of lenders looking to get money out of the door and into their pockets: whether investment bankers extolling the virtues of issuing Eurobonds; apparently cheap BRIC country loans, but with long-term catches on payment implications …” (Cowan, 2010, p.9). A call to borrow for development neeeds is endorsed by UNCTAD (2004) and EURODAD (2001, 2009), in the context of the human development approach to debt sustainability.
The thresholds depend on the quality of policies and institutes as measured by the Country Policy and Institutional Assessment (CPIA) index of the World Bank.
For this evidence see Celasun et al. (2007), among others. In the current review of the DSF, Fund and World Bank staff are proposing the inclusion, on an optional basis, of a new stress test reflecting dynamic linkages between macroeconomic variables.
The Fund acknowledges the need for strengthening analysis of the investment/growth nexus in DSAs, including through development and operationalizing models to provide a consistent way to assess the complex interlinkages (IMF and World Bank, 2009).
Thus we disagree with Wyplosz (2007): “If external borrowing is growth enhancing, the risk of over borrowing is small, possibly inexistent. If, instead, external borrowing does not exert any favorable growth effect, and possibly stunts growth, DSA is moot …(p.14)”.
The IMF has recently modified its policies on nonconcessional borrowing by LICs in the context of IMF-supported programs to reflect better the diversity of LICs and their financing patterns, and offer more flexibility depending on countries’ debt vulnerabilities and public financial management capacity. See IMF(2009b) for the guidelines on debt limits in Fund-supported programs.
The IMF and World Bank Boards have stated that until the investment-growth nexus is incorporated concerns will persist that “the DSF has unduly constrained the ability of LICs to finance their development goals.” See IMF and World Bank (2009).
As in Berg et al. (2010b), we also introduce learning-by-doing externalities in the production of both sectors, defined in terms of sectoral outputs. These externalities capture the Dutch-disease (Dutch-vigor) notion that real exchange appreciation (depreciation) may harm (help) productivity growth in the traded sector, which is a major concern in LICs that face aid surges, including substantial increases in concessional borrowing. Nevertheless, in this paper we do not elaborate on the implications of these externalities for debt sustainability.
In the long run all variables, including real GDP, grow at the same exogenous growth rate g. However, in the short to medium term, significant public and private capital accumulation, resulting from scaling up investment, implies that the growth rate of the economy can go above g.
We are currently working on a version that includes money and nominal price rigidities along the lines of the model in Berg et al. (2010b).
We assume Cobb-Douglas technologies but, to some extent, we do not expect significant changes in our results by considering CES technologies.
The convention for detrending the capital stocks differs from that for other variables. Because
For simplicity, we assume that adjustment costs are zero when the capital stock grows at the trend growth rate g. This ensures that adjustment costs are zero across steady states as in models that ignore trend growth.
From a technical point of view, the portfolio costs also help to ensure stationarity of
For instance the 2009 Steadman Survey finds that 62 percent of Ugandans do not have access to financial services.
To understand the role of efficiency, it may be useful to imagine that all the available public investment projects at a given point in time are ranked from highest to lowest rate of return. In an efficient investment process, an additional dollar is spent on the best available project. It is possible, though, because of incompetence, corruption, or imperfect information, that a government may choose worse projects. A lower efficiency is a measure of the degree of deviation from the optimal process. A complementary way to think about efficiency is simply that a fraction of spending is simply wasted, e.g. misclassified as investment when it in fact just covers transfers to civil servants.
We model natural resources revenues as a net foreign transfer, following Dagher et al. (2012). As such the measure of GDP used below corresponds to non-oil GDP. For a more comprehensive analysis of oil production, foreign investment, and managing natural resources in LICs see Berg et al. (2012).
Development agencies report that cost overruns of 35% and more are common for new projects in Africa. The most important factor by far is inadequate competitive bidding for tendered contracts. See Foster and Briceño-Garmendia (2010).
For instance, to introduce discrete jumps in the cap on taxes we can respecify the rule as
The nontradables sector comprises trade and transport, private services, dwellings, and construction. The tradables sector consists of agriculture and manufacturing.
The average factor shares cited here conceal tremendous variation. For example, the value added share of capital in the services sector is 59% in Zambia but only 27% in Malawi. See Thurlow et al. (2004) and Thurlow et al. (2008).
The net social return to capital, evaluated at a steady state is (r + δ)(1 + ξj)—δ. To set ξj so that the social return is 30% above the private return, solve (r + δ)(1 + ξj/αj)—δ = (1.30)r for ξj.
ψn and ψx are linked to other parameters and variables through Rz = (ψnVAn + ψxVAx)(δ+g)/izy, where Rz = R+δ is the gross return on infrastructure, VAj is the share of sector j production in GDP, and izy is the ratio of infrastructure investment to GDP.
In each sector j,the first-order condition for investment reads
The production function parameters ψx and ψn that govern R0 are deduced from the calibration of R0, given the rest of the calibration.
Some growth regressions suggest low or insignificant returns, but these are dominated by studies that use cumulative public investment instead of physical indicators to measure the stock of instructure.
Thirty percent may raise some eyebrows, but it is not as big as some of the numbers thrown around in the literature and in policy work. See for instance the scaling-up exercise in Box 4.1 in Barkbu et al. (2008) and Gupta, Powell, and Yang (2006).
But true O+M costs are probably higher, as argued by Briceño-Garmendia et al. (2008). Because of underspending on O+M, 30% of Africa’s infrastructure assets are in need of rehabilitation.
Appendix A describes how calibration of s and
Pritchett’s estimates of s range from 0.08 to 0.49 for SSA and from 0.09 to 0.54 for South Asia. In Africa, large cost overruns stemming from planning/coordination/management problems and low capital budget execution ratios (average = 66%) suggest that absorptive capacity may be a binding constraint in many countries. See Foster and Briceno-Garmendia (2010).
For 2003-2006, consumption, indirect taxes, and trade taxes averaged 81%, 9.6%, and 4.6% of GDP, respectively. If duties on consumer imports accounted for half of trade taxes, then the average consumption tax was 14.7%. (Data from IMF, 2007b). Ideally this rate will also reflect VAT productivity adjustments.
The repayment period is leisurely stretched out over 27 years, after 8 years of grace period. These correspond roughly to the average maturity and grace-period years for new concessional loans to LICs in 2009-2010, based on available IMF-WB’s DSAs. We assume that the country contracts a concessional loan of 20.25% of initial GDP in year 2, with the previously described disbursements. Then we apply an equal principal payment formula, together with these grace and maturity periods and an interest rate of 0%, to obtain the repayment profile. The grant element of this loan is about 62%.
Note that the adjustment in taxes would be smaller if government transfers were cut. But this is not an easy task when public sector employees are pressing for wage increases that match the increase in the private sector wages.
The numerical simulations are free of approximation error. In all scenarios, the simulations track the global nonlinear saddle path. The solutions were generated by set of programs written in Matlab 188.8.131.521 (R2008b) and Dynare 4.1.1. See http://www.cepremap.cnrs.fr/dynare.
To see why the interest rate rises when taxes go up significantly, recall the Euler equation for savers consumption, which can be written as:
It is common practice to discount econometric estimates of the q-elasticity of investment and assign Ω a value of 5-10 to speed up adjustment of the capital stock. That does not work in our case. When Ω = 10, the increases in private capital and real GDP are still small.
When λ> 0, the fiscal adjustment falls on both taxes and transfers. In this case the model can still allow for scenarios with downwardly inflexible expenditure. For instance, transfers can be kept constant until growth generates a fiscal windfall according to
where the initial public wage bill is 5% of GDP and raises of this bill are as large as raises in private sector wages.
In fact, public management capacity constraints in themselves may call for further investments in capacity, i.e. “to invest in investing” in the words of Collier (2007).
Note that this is equivalent to say that taxes and transfers are determined by the reactions functions (27)-(30), where x = dc and the gap 𝔊𝔞𝔭t is defined in (23); while the path of external commercial debt is determined by equation (24), which is a different way to express the government budget constraint.
Note that this is equivalent to say that taxes and transfers are determined by the reactions functions (27)-(30), where x = b and the gap 𝔊𝔞𝔭t is defined in(23); while the path of domestic debt is determined by equation(24), which is a different way to express the government budget constraint.
Interest payments on the internal debt are usually several times larger than interest payments on the external debt, exceeding 5% in some countries. Barkbu et al. (2008) also note that empirical studies find that rising domestic debt significantly increases the likelihood of external debt distress.
This is analogus to a spend-and-don’t-aborb response to aid surges and creates similar macroeconomic challenges, as analyzed in detail in Berg et al. (2010a)
For a discussion on importance of these external shocks in explaining the instability of output and the macroeconomic fluctuations in LICs, see Kose and Riezman (2001) and Raddatz (2007) and references therein.
Neumeyer and Perri (2005), Uribe and Yue (2006) and Fernandez-Villaverde et al. (2011) discuss how country risk premia, country spread and the volatility of the real exchange rate, respectively, affect business cycles in emerging economies.
Kraay and Nerhu (2006) find that shocks to real GDP growth are highly significant predictors of debt distress.
Because in our analysis there is perfect foresight, to model unexpected shocks we have to paste two dynamic systems. Consider, for instance, how to model unexpected TOT shocks. In this case, the first system ignores TOT shocks and gives us the dynamic paths for all the endogenous variables under the public investment scaling up. This allows us to retrieve the values of these variables for any particular time when we want to hit the economy with the TOT shock. Assume that, without loss of generality, this time corresponds to t = 9. Then we run a second system that (i) has as initial conditions for endogenous and exogenous variables the values retrieved from the first system at t = 9, (ii) includes the TOT shocks and (iii) appropriately incorporates the continuation values for the rest of exogenous variables such as public investment, grants, and concessional borrowing. The final path for each variables is then constructed by pasting the series of the first system up to t = 9 and the series of the second system beyond this point. Note that by our perfect foresight assumption, this methodology implies that the initial decrease in TOT shocks is the unexpected part. The rest of the shock, beyond t = 9, is still expected. We leave for further work the generalization of this procedure to look at sequences of unexpected shocks, though because of the perfect foresight assumption, we cannot allow agents to react to uncertainty per se.
There is nothing, however, that prevents the possibility of explosive debt dynamics if the unexpected shock hits the economy at any point in the rising path of debt.
A more interesting but much more challenging approach will be to endogenize default in the model and make the risk premium depend on the model-consistent risk of default.
The model was used to evaluate the authorities’ public investment scaling-up strategies in Togo in the context of the debt sustainability analysis. Moreover it was used to carry out counterfactual simulations using the projections of the macroeconomic framework underlying the standard Excel-based DSA. These simulations provided a useful check on the plausibility and internal consistency of the projections made in the DSA. See Andrle et al. (2012). The model has been also applied to Burkina Faso and is being applied to Afghanistan, Cape Verde, Cote d’Ivoire, Ethiopia, Ghana, and Senegal.
To see this, it may help to note that, for a case in which s =
There is empirical support for declining marginal product of public capital and for the specific Cobb-Douglas version. Isham and Kaufman (1999) show that the ex post rate of return on World Bank-financed projects (which may correspond more closely to
This approach to calibration can be rationalized with the observation that different measures of policy are positively correlated: a country that cannot efficiently build an electrical grid probably is not good at keeping it running well. Thus, countries with low investment efficiency likely also have low marginal product of installed capital, for a given capital stock (i.e., a relatively low value of ψ).This offsets the negative effect of higher efficiency on the