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Why does natural resource abundance not always lead to better outcomes? Limited financial development versus political impatience

  • Lavan Mahadeva EMAIL logo
Veröffentlicht/Copyright: 27. März 2014
The B.E. Journal of Macroeconomics
Aus der Zeitschrift The B.E. Journal of Macroeconomics Band 14 Heft 1

Abstract

Is the failure of natural resource abundance to achieve better economic outcomes due to limited financial development or fiscal policy short-termism? I answer this question in a precautionary savings model where both resource revenues and asset returns are uncertain. Calibrating for Colombia, I find that under policy impatience, welfare costs are large, net assets are insufficient and net discretionary expenditures are too sensitive to resource revenues. If financial markets are underdeveloped, we can generate welfare costs of the same magnitude but not also explain why there are insufficient net effective assets, nor the heightened sensitivity to revenues.

Keywords: financial development; optimal management of windfalls; political short-termism; public capital
JEL-Classification: E44; E60; H60; Q32
Corresponding author: Lavan Mahadeva, Oxford Institute for Energy Studies, A Recognized Independent Centre of the University of Oxford, 57 Woodstock Road, Oxford OX2 6FA, UK, e-mail:

Acknowledgments

I gratefully thank an anonymous reviewer for suggesting substantial improvements on an earlier version of this paper. I would also like to Juan Pablo Zárate Perdomo for his helpful comments. All errors remain my responsibility.

Appendix

A Interpretation of the real return on net assets

I have assumed that there is such a thing as the real return on net assets, that part of this return is stochastic and exogenous and that the other part depends on net worth with a negative elasticity. The reader might welcome some more detail and clarification on these points.

Let us assume that the public capital stock At–1 produces a service flow Yt according to a Cobb-Douglas production function:

(21)Yt=ra,t(At−1)ζ(ΛtLt)1−ζ−μ(Wt−1)μ. (21)

where there are constant returns in physical capital, At–1, and labour, Lt. ra,t is an exogenous productivity shock (to be fully specified below). An unusual feature is that previous net worth is an input into production as working capital because the greater the net worth, the easier it is to deal with unanticipated expenditures. For example, under duress, while a government might contemplate raising finance through privatisations, that might only translate into retired liabilities at a poor conversion rate (because of firesaling). For simplicity, I assume that this is an externality.[21]

The marginal product of capital using the production function 21 is

(22)rk,t+1≡ra,t+1ζ(At)ζ−1(Λt+1Lt+1)1−ζ−μ(Wt)μ=ra,t+1ζ(ϑ1,t)ζ−1(Λt+1Lt+1)1−ζ−μ(Wt)μ+ζ−1=ra,t+1ζ(ϑ1,t)ζ−1wtτμ+ζ−1 (22)

where ϑ1,t is the share of time t net wealth held in physical capital.

To finance production the government invests in net risky financial assets paying a gross interest rate (rd,t+1) and an asset with a risk-free gross return (rf), fixed for simplicity. A negative investment in the risky liquid asset is interpreted as debt being greater than the total of assets such as foreign reserves and wealth funds.

ra,t+1 and rd,t+1 follow jointly distributed autocorrelated log-normal process:

(23)lra,t+1=κalra,t+ua,t+1lrd,t+1=(1−κd)lrf+κdlrd,t+ud,s+1 (23)

with lrx,t+1≡ln(rx,t+1) for x=(a, d, f). ua,t+1 and ud,t+1 are normally distributed variables with means of zero, respective variances of daa and ddd and a covariance dad. The excess log returns to net liquid assets and capital are on average equal to the risk-free rate, by arbitrage.

The budget constraint of the state is as in equation (3) but with net worth now explicitly disaggregated into net financial assets and public capital:

(24)Ct+1=((−ϑ1,t−ϑ2,t)rf+ϑ1,t(rk,t+1−δk)+ϑ2,trd,t+1)Wt−Wt+1+X1,t+1−X2,t+1⇒Ct+1=rp,t+1Wt−Wt+1+X1,t+1−X2,t+1 (24)

where ϑ2,t is the share of time t net wealth represented by net financial assets. This will be negative if debt is greater in amount than financial assets. rp,t+1 is the gross return on the government’s portfolio defined as

(25)rp,t+1rf,t+1=1+ϑ1,t(rk,t+1−δkrf−1)+ϑ2,t(rd,t+1rf−1)rp,t+1rf,t+1=1+ϑ1,t(elrk,t+1−δk−lrf−1)−ϑ2,t(elrd,t+1−lrf−1). (25)

Taking logs of the above,

(26)lrp,t+1−lrf=ln(1+ϑ1,t(elrk,t+1−δk−lrf−1)−ϑ2,t(elrd,t+1−lrf−1)). (26)

Define a vector of excess returns as

(27)lrs,t+1≡[lrk,t+1−δk−lrflrd,t+1−lrf]. (27)

Then

(28)Et[lrs,t+1]=[Et[lrk,t+1]−δk−lrfEt[lrd,t+1]−lrf]=[κalra,t+ln(ζ(ϑ1,t)ζ−1(wtτ)μ+ζ−1−δk−lrf)κd(lrd,t−lrf)] (28)

and

(29)vart[lrs,t+1]=[Vart[lrk,t+1]Covt[lrk,t+1, lrd,t+1]Covt[lrk,t+1, lrd,t+1]Vart[lrd,t+1]] (29)
(30)=[daadaddadddd]. (30)

Consider a first-order approximation of lrp,t+1 with respect to lrs,t+1 about 0

(31)lrp,t+1≈(1−ϑ1,t−ϑ2,t)lrf+ϑ1,t(lra,t+1+ln(ζ(ϑ1,t)ζ−1)+(μ+ζ−1)ln(wtτ)−δk)+ϑ2,tlrd,t+1 (31)

such that the gross portfolio return is approximately the product of the exogenous return and an endogenous component, just as in equation (3):[22]

(32)rp,t+1≈rr,t+1wtw¯−δ.whererr,t+1=rf1−ϑ1,t−ϑ2,tra,t+1ϑ1,trd,t+1ϑ2,te−δkϑ1,tζϑ1,t(ϑ1,t)ϑ1,t(ζ−1),δ=ϑ1,t(1−ζ−μ)andw¯=τ. (32)

If debt dominates financial assets (ϑ2,t<0) and there is a rise in rate of return on risky financial claims (unrelated to the productivity shock ra,t) then the exogenous component of the rate of return on net assets (rr,t) will fall. Under these circumstances, a countercyclical policy that raises rates on risky financial claims when windfall revenues are high connotes a negative conditional dependence between the real rate on net assets and revenue. Conversely, procyclicality implies a positive conditional dependence between the real rate on net assets and non-discretionary revenue. This is the interpretation I follow in the rest of the text.

Taking expectations conditional on period t information,

(33)Vart[lrr,t+1]≈ϑ1,t2daa+ϑ2,t2ddd+2ϑ1,tϑ2,tdad. (33)

Equation (33) links limited diversification to risk, just as in standard portfolio theory. Poor diversification in this context is equivalent to a more negative covariance between lending costs and investment returns such that for example a lower rate on investments is more likely to be associated with creditors raising their offered lending rates. According to equation (33), the more negative dad, the larger conditional variance of the log returns on net assets providing that debt dominates liquid financial assets (ϑ1,t).

Turning now to the interpretation of the endogenous component in equation (32), the elasticity of the quantity of net assets on the endogenous component of the return on net assets, δ, is a combination of two opposing forces of diminishing marginal returns to capital and the beneficial effect of having higher net worth on production.

But how can this parameter be calibrated? The first influence is equal to one minus the share of capital in nominal public output (1–ζ) multiplied by the share of public capital in net worth ϑ1,t. As the share of government spending on GDP is about 40% and the factor share of public capital in total GDP was estimated by Gupta et al. (2011) to be about 20%, (1–ζ) should be about 0.5=2040. But ϑ1 is an optimal share and is therefore difficult to estimate given political impatience. And neither are there, as far as I know, direct estimates of the importance of net worth to production, μ, although Lipschitz, Messmacher, and Mourmouras (2006)’s estimates of the beneficial impact of reserves on debt financing costs suggest that it could be substantial. In what follows I take the view that that δ is positive, but only just.

B Derivation of solution

Differentiating f1(·) from 9 with respect to ct+1 and rt+1, we have

(34)∂2f1∂ct+12=γ(γ+1)(1−δ)ct+12(β(ct+1τct)−γrt+1)(wtτw˜)−δ, (34)
(35)∂2f1∂rt+12=0, (35)

and

(36)∂2f1∂ct+1drt+1=d2f1drt+1dct+1=−γ(1−δ)ct+1rt+1(β(ct+1τct)−γrt+1)(wtτw˜)−δ. (36)

Substituting 34, 35 and 36 into 9 (and assuming that the expression β(1−δ)(Et[ct+1]τct)−γ×Et[rt+1](wtτw˜)−δ is always non-zero) leads to equation (12) in the main text. Pushing the expectations rule 16 one period forward, taking expectations and substituting in from equation (17), yields expressions for the conditional mean and variance of ct+1 as well as its covariance with the rate of return. These are substituted into 12 prior to solution.

The risky steady state is defined by the values of Gww, Gwr, Gwi, w¯ and c¯ that constitute the joint solution of the second-order approximation of the first-order condition (12), the budget constraint as well as the condition that the total derivatives of Φ^ with respect to the states wt–1, rt, x1,t and x2,t are zero (all evaluated at the steady state). The solutions are a function of the underlying parameters β, τ, δ and γ and the parameters describing the exogenous processes – l¯x1,l¯x2,κ1, κ2, l¯r,κr, D.

C Approximation to the conditional variance of future consumption

We work with the following linearised version of the state system and the budget constraint

(37)ws+1=w¯+Gww(ws−w¯)+Gwr(rs+1−r¯)+Gw1(x1,s+1−x¯1)+Gw2(x2,s+1−x¯2);x1,s+1≈(1−κ1)x¯1+κ1x1,t+x¯1u1,s+1;x2,s+1≈(1−κ2)x¯2+κ2x2,t+x¯2u2,s+1;rs+1≈(1−κr)r¯+κrrs+r¯us+1;c^s+1≈((1−δ)r¯τ(w¯w˜τ)−δ−Gww)ws+((w¯τ)1−δw˜δ−Gwr)rs+1+(1−Gw1)x1,s+1−(1+Gw2)x2,s+1−(w¯τ)1−δw˜δr¯+(Gww+1)w¯+Gwrr¯+Gw1x¯1+Gw2x¯2. (37)

Define zn≡(wn, x1,n, x2,n, rn)T. Then

(38)zn+1=Ω1n+1−tzt+∑k=1n+1−tΩ1n+1−t−kΩ2D12vt+k+Ω3 (38)

for n≥t. Here

Ω1≡(GwwGw1κ1Gw2κ2Gwrκr0κ10000κ20000κr),

Ω2≡(Gw1x¯1Gw2x¯2Gwrr¯x¯1000x¯2000r¯),

D12 is the Cholesky decomposition of the matrix D, defined in equation (7),

Ω3≡((1−Gww)w¯−κrGwrr¯−κ1Gw1x¯1−κ2Gw2x¯2(1−κ1)x¯1(1−κ2)x¯2(1−κr)r¯)

and vt+1 is a vector of three mean zero, unit variance, independent normally distributed shocks and IN is a N×N identity matrix. Using equation (38) we can calculate Et[zs+12−Et[zs+1]2] and Et[zs+1zsT−Et[zs+1]Et[zs]] for all s>t. The terms in these matrices give us the necessary expressions to calculate Vart[c^s], using the linear approximation to the budget constraint in the last row of equation (38). Our approximation to utility follows from inserting the terms Vart[c^s],s>t into the expression 19 in the main text.

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Published Online: 2014-3-27
Published in Print: 2014-1-1

©2014 by De Gruyter

Artikel in diesem Heft

  1. Frontmatter
  2. Advances
  3. Optimal portfolios with wealth-varying risk aversion in the neoclassical growth model
  4. Inventories and the stockout constraint in general equilibrium
  5. Optimal second best taxation of addictive goods in dynamic general equilibrium: a revenue raising perspective
  6. Inflation effects on capital accumulation in a model with residential and non-residential assets
  7. Optimal capital-income taxation in a model with credit frictions
  8. Contributions
  9. Interest rate fluctuations and equilibrium in the housing market
  10. News shocks and learning-by-doing
  11. Capacity utilization and the effects of energy price increases in Japan
  12. Small-scale New Keynesian model features that can reproduce lead, lag and persistence patterns
  13. Optimal policy and Taylor rule cross-checking under parameter uncertainty
  14. The impact of American and British involvement in Afghanistan and Iraq on health spending, military spending and economic growth
  15. Why does natural resource abundance not always lead to better outcomes? Limited financial development versus political impatience
  16. The skill bias of technological change and the evolution of the skill premium in the US since 1970
  17. Aggregate impacts of recent US natural gas trends
  18. Organizational learning and optimal fiscal and monetary policy
  19. Industrial specialization, financial integration and international consumption risk sharing
  20. Leverage, investment, and optimal monetary policy
  21. Public debt in an OLG model with imperfect competition: long-run effects of austerity programs and changes in the growth rate
  22. Temporal aggregation and estimated monetary policy rules
  23. International transmission of productivity shocks with nonzero net foreign debt
  24. Did the euro change the effect of fundamentals on growth and uncertainty?
  25. Topics
  26. Real factor prices and factor-augmenting technical change
  27. Monetary policy and TIPS yields before the crisis
https://doi.org/10.1515/bejm-2012-0038
Schlagwörter für diesen Artikel
financial development; optimal management of windfalls; political short-termism; public capital

Artikel in diesem Heft

  1. Frontmatter
  2. Advances
  3. Optimal portfolios with wealth-varying risk aversion in the neoclassical growth model
  4. Inventories and the stockout constraint in general equilibrium
  5. Optimal second best taxation of addictive goods in dynamic general equilibrium: a revenue raising perspective
  6. Inflation effects on capital accumulation in a model with residential and non-residential assets
  7. Optimal capital-income taxation in a model with credit frictions
  8. Contributions
  9. Interest rate fluctuations and equilibrium in the housing market
  10. News shocks and learning-by-doing
  11. Capacity utilization and the effects of energy price increases in Japan
  12. Small-scale New Keynesian model features that can reproduce lead, lag and persistence patterns
  13. Optimal policy and Taylor rule cross-checking under parameter uncertainty
  14. The impact of American and British involvement in Afghanistan and Iraq on health spending, military spending and economic growth
  15. Why does natural resource abundance not always lead to better outcomes? Limited financial development versus political impatience
  16. The skill bias of technological change and the evolution of the skill premium in the US since 1970
  17. Aggregate impacts of recent US natural gas trends
  18. Organizational learning and optimal fiscal and monetary policy
  19. Industrial specialization, financial integration and international consumption risk sharing
  20. Leverage, investment, and optimal monetary policy
  21. Public debt in an OLG model with imperfect competition: long-run effects of austerity programs and changes in the growth rate
  22. Temporal aggregation and estimated monetary policy rules
  23. International transmission of productivity shocks with nonzero net foreign debt
  24. Did the euro change the effect of fundamentals on growth and uncertainty?
  25. Topics
  26. Real factor prices and factor-augmenting technical change
  27. Monetary policy and TIPS yields before the crisis
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