Abstract
Evans (1991) has demonstrated that Blanchard’s (1985) finite-horizon model obeys approximate Ricardian equivalence. This paper shows th at this result is determined largely by an unrealistic assumption that labor income grows monotonically over the consumer’s entire lifetime. With more realistic lifetime earnings profiles, the effects of government debt on the real interest rate and the capital stock are considerably larger. In particular, leaving aside the effects of distortionary capital taxation, the extended model with liquidity constraints predicts that real interest rates would decline by about 150–200 basis points if government debt were eliminated completely in all countries of the Organization for Economic Cooperation and Development (OECD).
THE PERSISTENT accumulation of government debt is attracting an increasing amount of attention in policy debates. According to OECD estimates, net public debt as a percentage of nominal GDP for the Group of Seven countries has doubled (to 40 percent) over the past 25 years. Many analyses of the implications of higher public debt assume that there will be no impact on the equilibrium world real interest rate. Although this assumption may be appropriate when a country is relatively small, it may not be appropriate for a large country like the United States or for the combined effects of the debt buildup in OECD countries.
Barro (1974) has shown that the effects of deficit financing depend to a large extent on whether consumers view government debt as net wealth. If consumers are connected to all future generations and can borrow and lend against their future income streams, changes in debt will not crowd out private consumption and investment. In that case, consumers equate the bond-financed reduction in taxes with an increase in (the present value of) future tax burdens. Consequently. Ricardian equivalence holds and the choice between tax finance or deficit finance becomes irrelevant (see Bernheim and Bagwell, 1988, for a critical review of the Ricardian approach). Evans (1991) has demonstrated that Blanchard’s (1985) overlapping agents framework obeys approximate Ricardian equivalence: deficit financing has very small effects on the equilibrium real interest rate and capital stock.
However, by assuming that an agent’s income grows monotonically over lime, Evans effectively treats agents as dynastic households (rather than disconnected individuals) with finite horizons. Not surprisingly, under this interpretation the deviations from Barro (1974) are very small. Alternatively, one could interpret the Blanchard model from a life-cycle perspective, consisting of overlapping generations rather than dynasties. This paper extends the Blanchard model to allow for realistic individual lifetime-income profiles and to incorporate consumers that in the early part of their life cycle cannot borrow against their future income. We show that these life-cycle modifications are sufficient to generate significant crowding-out effects from government debt in the spirit of Diamond (1965).
Specifically, OECD estimates of aggregate net public debt for 18 of the largest industrial countries show an increase of about 20 percentage points in the debt-GDP ratio since the late 1970s. The model developed in this paper suggests that this increase in government debt has caused an increase in the world real interest rate of 76 basis points and a permanent reduction in world real GDP of 2.9 percent.
I. The Model
The following analysis presents an extended version of the Blanchard (1985) overlapping agents model. Liquidity-constrained consumers have been included as well as life-cycle earnings profiles to allow for agedependent income. As will be shown, these features increase the non-Ricardian properties of the model so that fiscal policy and public debt have a significant impact on real economic activity.
Specifically, we assume that certain younger generations (as a fixed proportion λ of the total population) are denied access to capital markets and are constrained by their current resources.1 We also incorporate typical life-cycle profiles for labor income, in which income rises with age and experience before eventually declining with retirement. To introduce this concave earnings profile over an individual’s lifetime, we assume that the labor income y(s, t) accruing to an individual from generation s at time t can be expressed in terms of (age-dependent) weights on aggregate labor income Y(t) and (to allow for aggregation) equal to the sum of two exponential functions:2
The first exponential can be interpreted as the gradually declining endowment of labor (that is. gradual retirement), which is inelastically supplied. The second exponential can be interpreted as the relative productivity and wage gains from experience with increasing age. or more precisely, the lower cost of inexperience.
The main modifications to the basic Blanchard model can be summarized by four equations. In the presence of age-dependent income (and taxes) and liquidity-constrained consumers, aggregate consumption (with log utility)3 is given by
where W is financial wealth, Y–T is disposable income, and H1 and H2 comprise human wealth, defined as the present value of disposable income over the agent’s lifetime:4
In the above equations, p is the probability of death, θ is the rate of time preference, and r is the rate of interest. With generation-specific income, the (excess) sensitivity of consumption to income depends on the relative share of aggregate disposable income held by liquidity-constrained consumers seen by the coefficient βλ1 +(1 – β)λ2.5
An important implication of life-cycle income for fiscal policy is increasing the wedge between public and private discount rates. With eventually declining labor income, private agents have a higher effective discount rate on future disposable income (that is, αs in equations (4) and (5)). Facing a declining income profile over their lifetime, agents further discount the impact of future tax liabilities as the prospective tax base shifts further to future generations with higher taxable income.
II. Long-Run Effects of Government Debt
This section examines the comparative effects of various calibrations of the model in terms of its long-term predictions. As mentioned in the introduction, Evans (1991) has demonstrated that Ricardian equivalence holds approximately in the Blanchard (1985) model. Therefore, it is worthwhile to start with his calibration and explain why the effects on the real interest rate are so small.
In his base-case calibration of the Blanchard model, Evans assumes zero population growth and a steady-state productivity growth rate (μ) of 3 percent a year. He then investigates the comparative statics of the model for various assumptions about the length of planning horizons (1/p), the intertemporal elasticity of substitution (1/p), and the rate of time preference (θ). As our model is a generalization of this framework, it is straightforward to replicate Evans’s basic results to show that the model obeys approximate Ricardian equivalence.
As mentioned, net public debt currently stands at about 40 percent of GDP. To proceed, we compute a steady-state solution, assuming that this debt ratio stabilizes at this level forever, and compare this with two alternative solutions. The first experiment investigates the long-term benefits of eliminating all government debt in the OECD countries, that is, reducing the debt-GDP ratio by 40 percentage points. The second assumes that the debt ratio continues to drift up by an additional 20 percentage points. This experiment broadly replicates the experience over the last two decades.
Steady-State Effects of Government Debt in Evans’s (1991) Calibration of the Blanchard Model [θ =0.01; p = 0.02; μ = 3; σ = 1; λ = 0; α1 = α2 = 0] Change from an Initial Steady State with a Debt-GDP Ratio of 40 Percent
Steady-State Effects of Government Debt in Evans’s (1991) Calibration of the Blanchard Model [θ =0.01; p = 0.02; μ = 3; σ = 1; λ = 0; α1 = α2 = 0] Change from an Initial Steady State with a Debt-GDP Ratio of 40 Percent
| Debt-GDP ratio | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| 0 | 10 | 20 | 30 | 40 | 50 | 60 | |||
| Output (in percent) | 0.13 | 0.10 | 0.06 | 0.03 | 0.00 | –0.03 | –0.06 | ||
| Consumption (in percent) | 0.01 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 | –0.01 | ||
| Capital stock (in percent) | 0.51 | 0.38 | 0.25 | 0.13 | 0.00 | –0.13 | –0.25 | ||
| Real interest rate (basis points) | –4 | –3 | –2 | –1 | 0 | 1 | 2 | ||
Steady-State Effects of Government Debt in Evans’s (1991) Calibration of the Blanchard Model [θ =0.01; p = 0.02; μ = 3; σ = 1; λ = 0; α1 = α2 = 0] Change from an Initial Steady State with a Debt-GDP Ratio of 40 Percent
| Debt-GDP ratio | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| 0 | 10 | 20 | 30 | 40 | 50 | 60 | |||
| Output (in percent) | 0.13 | 0.10 | 0.06 | 0.03 | 0.00 | –0.03 | –0.06 | ||
| Consumption (in percent) | 0.01 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 | –0.01 | ||
| Capital stock (in percent) | 0.51 | 0.38 | 0.25 | 0.13 | 0.00 | –0.13 | –0.25 | ||
| Real interest rate (basis points) | –4 | –3 | –2 | –1 | 0 | 1 | 2 | ||
Following Evans (1991), we assume that the elasticity of substitution (1/σ) is equal to one (that is. logarithmic utility). Given an initial debt ratio of 40 percent, a planning horizon of 50 years (p = 0.02), and a rate of time preference of 0.01, the steady-Male real interest rate is 4.4 percent.6 Table 1 provides our comparative statics for the two experiments, as well as for several intermediate cases. According to this calibration, eliminating all government debt in the OECD countries would reduce the real interest rate by only 4 basis points and increase output and consumption by 0.13 percent and 0.01 percent, respectively. Although agents have finite horizons, the model’s predictions are very close to the pure Ricardian case in which agents effectively have infinite horizons. Evans further shows that adding liquidity-constrained individuals does not change this basic property of the model. However, as demonstrated below, this result is directly tied to the treatment of labor income and the interest sensitivity of consumption.
Intuitively, the degree of crowding out should depend on the sensitivity of consumption to changes in the real interest rate. If part of government debt is viewed as net wealth—because consumers excessively discount future tax liabilities—consumers will tend to “overconsume in response to an increase in government debt,” requiring an increase in the real interest rate to reestablish a new equilibrium. When the degree of intertemporal substitution is high, small changes in the interest rate would be required for individuals to be willing to reallocate their consumption across time periods. This factor is evident from the small effects on the real interest rate and consumption reported in Table 1 and in Evans (1991).7
In the case in which the elasticity of substitution is low (less than one), there are two opposing effects on consumption. The negative impact on consumption of an increase in the real interest rate, which affects human wealth through the discount factor, is partly offset by an increase in the marginal propensity to consume (see footnote 3). As the elasticity of substitution goes to zero (σ → α), these effects increasingly offset each other, and the model requires larger changes in the real interest rate to establish a new equilibrium. Unfortunately, as Evans points out. there is a lower bound in the simple Blanchard model for the elasticity of substitution (about ½), beyond which an (implausible) negative rate of time preference is required to generate a reasonable baseline real interest rate.
However, considerable empirical evidence suggests that consumption is much less responsive to changes in the real interest rate than the degree of responsiveness implied by logarithmic utility. Although there is significant uncertainty around any point estimate of this elasticity, our reading of the literature suggests that a more reasonable range would be centered around 0.3 instead of one.8 In any event, to understand the implications of this assumption, it would be useful to consider a framework that allows for a broader range of elasticities of substitution across time periods.
A second issue is the treatment of labor income. In most quantitative applications of the Blanchard model, representative agents have identical labor income that grows at the rate of productivity growth. This implies an unrealistic, monotonically increasing income profile over an individual’s lifetime and, as we demonstrate below, has significant implications in terms of debt neutrality for reasons discussed earlier. Figure 1 compares the life-time income profiles (with μ = 1.5 percent)9 under Evans’s assumption and our case of age-dependent income, for ρ1 = 0.06, ρ2 = 0.10. These parameters were chosen to replicate broadly the empirical lifetime profiles reported by Jappelli and Pagano (1989).
Lifetime Income Profiles
Citation: IMF Staff Papers 1997, 003; 10.5089/9781451973464.024.A005
Note: Income is normalized to 1 at age 20. The hump-shaped profile assumes 1.5 percent aggregate productivity growth.Fortunately, the specification of life-cycle income also allows for a broader range of elasticities of substitution without imposing negative rates of time preference in the model.10 Indeed, to generate the same initial control solution of 4.4 percent for the real interest rate, the model requires μ = 0.045 when the elasticity of substitution is 0.3. Table 2 reports the results for the same government debt shocks that were considered earlier. In this case, a reduction in the steady-state government debt-GDP ratio from 40 percent to zero reduces the real interest rate by 122 basis points, raises the capital stock by 14.4 percent, and the level of output by 4.8 percent. These effects work to expand the consumption possibilities frontier of the economy; aggregate consumption in the steady state is 2.6 percent higher. These results differ sharply from the results reported in Table 1, as the model is no longer consistent with the property of approximate Ricardian equivalence.
We also examine the case in which 20 percent of the population is liquidity constrained. Estimates of excess sensitivity based on time-series data typically vary between 0.2 and 0.6—see, for example, Campbell and Mankiw (1989), Jappelli and Pagano (1989), and Patterson and Pesaran (1992). Given our calibration of the earnings profile, the model generates a degree of excess sensitivity equal to about 0.37. in line with many reduced-form estimates of excess sensitivity that are reported in the literature.
Steady-State Effects of Government Debt with Life-Cycle Income [θ =0.05; p = 0.02; μ = 1.5; σ = 3.33; λ = 0; α1 = 0.06; α2 = 0.1] Change from an Initial Steady State with a Debt-GDP Ratio of 40 Percent
Steady-State Effects of Government Debt with Life-Cycle Income [θ =0.05; p = 0.02; μ = 1.5; σ = 3.33; λ = 0; α1 = 0.06; α2 = 0.1] Change from an Initial Steady State with a Debt-GDP Ratio of 40 Percent
| Debt-GDP ratio | |||||||
|---|---|---|---|---|---|---|---|
| 0 | 10 | 20 | 30 | 40 | 50 | 60 | |
| Output (in percent) | 4.83 | 3.57 | 2.35 | 1.16 | 0.00 | –1.13 | –2.25 |
| Consumption (in percent) | 2.59 | 1.94 | 1.30 | 0.65 | 0.00 | –0.65 | –1.30 |
| Capital stock (in percent) | 14.43 | 10,55 | 6.87 | 3.35 | 0.00 | –3.21 | –6.28 |
| Real interest rate (basis points) | –122 | –92 | –62 | –31 | 0 | 31 | 63 |
Steady-State Effects of Government Debt with Life-Cycle Income [θ =0.05; p = 0.02; μ = 1.5; σ = 3.33; λ = 0; α1 = 0.06; α2 = 0.1] Change from an Initial Steady State with a Debt-GDP Ratio of 40 Percent
| Debt-GDP ratio | |||||||
|---|---|---|---|---|---|---|---|
| 0 | 10 | 20 | 30 | 40 | 50 | 60 | |
| Output (in percent) | 4.83 | 3.57 | 2.35 | 1.16 | 0.00 | –1.13 | –2.25 |
| Consumption (in percent) | 2.59 | 1.94 | 1.30 | 0.65 | 0.00 | –0.65 | –1.30 |
| Capital stock (in percent) | 14.43 | 10,55 | 6.87 | 3.35 | 0.00 | –3.21 | –6.28 |
| Real interest rate (basis points) | –122 | –92 | –62 | –31 | 0 | 31 | 63 |
Steady-State Effects of Government Debt with Life-Cycle Income and Liquidity Constraints [θ = 0.08; p = 0.02; μ = 1.5; σ = 3.33; λ = 0.2; α1 = 0.06; α2 = 0.1] Change from an Initial Steady State with a Debt-GDP Ratio of 40 Percent
Steady-State Effects of Government Debt with Life-Cycle Income and Liquidity Constraints [θ = 0.08; p = 0.02; μ = 1.5; σ = 3.33; λ = 0.2; α1 = 0.06; α2 = 0.1] Change from an Initial Steady State with a Debt-GDP Ratio of 40 Percent
| Debt-GDP ratio | |||||||
|---|---|---|---|---|---|---|---|
| 0 | 10 | 20 | 30 | 40 | 50 | 60 | |
| Output (in percent) | 5.90 | 4.40 | 2.92 | 1.45 | 0.00 | –1.43 | –2.85 |
| Consumption (in percent) | 3.12 | 2.37 | 1.60 | 0.81 | 0.00 | –0.82 | –1.66 |
| Capital stock (in percent) | 17.78 | 13.09 | 8.56 | 4.20 | 0.00 | –4.04 | –7.93 |
| Real interest rate (basis points) | –147 | –112 | –76 | –39 | 0 | 39 | 81 |
Steady-State Effects of Government Debt with Life-Cycle Income and Liquidity Constraints [θ = 0.08; p = 0.02; μ = 1.5; σ = 3.33; λ = 0.2; α1 = 0.06; α2 = 0.1] Change from an Initial Steady State with a Debt-GDP Ratio of 40 Percent
| Debt-GDP ratio | |||||||
|---|---|---|---|---|---|---|---|
| 0 | 10 | 20 | 30 | 40 | 50 | 60 | |
| Output (in percent) | 5.90 | 4.40 | 2.92 | 1.45 | 0.00 | –1.43 | –2.85 |
| Consumption (in percent) | 3.12 | 2.37 | 1.60 | 0.81 | 0.00 | –0.82 | –1.66 |
| Capital stock (in percent) | 17.78 | 13.09 | 8.56 | 4.20 | 0.00 | –4.04 | –7.93 |
| Real interest rate (basis points) | –147 | –112 | –76 | –39 | 0 | 39 | 81 |
Again we reconstruct the baseline solution by computing the rate of time preference that is consistent with a real interest rate of 4.4 percent. Table 3 reports the effects for the debt shocks considered earlier. Unlike in Evans (1991), adding liquidity-constrained consumers to the model has significant effects on the comparative statics. Here, real interest rates are predicted to fall by 147 basis points if government debt were eliminated in all OECD countries. Overall, however, the marginal effects of liquidity constraints on the model are small when compared to the effects of adding life-cycle income.
Other avenues may further increase the effects of government debt. For example. Weil (1989) and Buiter (1988) have shown that Ricardian equivalence breaks down in the Blanchard model because of a positive birth rate.11 Although a stationary population may be appropriate lor analysis of the very long term, it is interesting to ask how the comparative statics of the model would change with positive population growth. Hence, we repeated the experiment reported in Table 3. but assumed steady-state population growth of 1 percent a year. In this case, a decline in the debt-GDP ratio of 40 percentage points reduced the interest rate by 163 basis points, compared with the 147 basis points reported in Table 3.
REFERENCES
Barro, Robert J., 1974, “Are Government Bonds Net Wealth?” Journal of Political Economy, Vol. 82 (November/December), pp. 1095–117.
Bernheim, B. Douglas, and Kyle Bagwell, 1988, “Is Everything Neutral?” Journal of Political Economy, Vol. 96 (April), pp. 308–38.
Blanchard, Olivier J., 1985, “Debt, Deficits, and Finite Horizons,” Journal of Political Economy, Vol. 93 (April), pp. 223–47.
Blundell, Richard, 1988, “Consumer Behavior: Theory and Empirical Evidence—A Survey,” Economic Journal, Vol. 98 (March), pp. 16–65.
Buiter, Willem H., 1988, “Death, Birth, Productivity Growth and Debt Neutrality.” Economic Journal, Vol. 98 (June), pp. 279–93.
Campbell, John Y., and N. Gregory Mankiw, 1989, “Consumption, Income, and Interest Rates: Reinterpreting the Time Series Evidence,” in NBER Macroeconomics Annual 1989, ed. by Olivier Blanchard and Stanley Fischer (Cambridge, Massachusetts: MIT Press).
Diamond, Peter A., 1965, “National Debt in a Neoclassical Growth Model,” American Economic Review, Vol. 55 (December), pp. 1126–50.
Evans, Paul. 1991, “Is Ricardian Equivalence a Good Approximation?” Economic Inquiry, Vol. 29 (October), pp. 626–44.
Gagnon. Joseph E., and Mark D. Unferth, 1995, “Is There a World Real Interest Rate?” Journal of International Money and Finance, Vol. 14 (December), pp. 845–55.
Hall, Robert E., 1978, “Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence,” Journal of Political Economy, Vol. 86 (December), pp. 971–87.
Jappelli, Tullio, 1990, “Who is Credit Constrained in the U.S. Economy?” Quarterly Journal of Economics, Vol. 105 (February), pp. 219–34.
Jappelli, Tullio, and Marco Pagano, 1989, “Consumption and Capital Market Imperfections: An International Comparison.” American Economic Review, Vol. 79 (December), pp. 1088–105.
Patterson, Kerry D., and Bahram Pesaran, 1992, “Intertemporal Elasticity of Substitution in Consumption in the United States and the United Kingdom.” Review of Economics and Statistics, Vol. 74 (November), pp. 573–84.
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Hamid Faruqee and Douglas Laxton are Economists in the Research Department; Steven Symansky is Deputy Division Chief in the Fiscal Affairs Department. Mr. Faruqee holds a Ph.D. from Princeton and Mr. Laxton completed his masters at the University of Western Ontario. Mr, Symansky holds a Ph.D. from the University of Michigan. The authors thank Leonardo Bartolini, Tamim Bayoumi, Richard Black. Ralph Bryant, Peter Clark, Bob Ford, Guy Meredith, and David Rose for providing comments on an earlier version of this paper.
Jappelli (1990) finds that liquidity constraints are much more binding for younger generations.
The parameters in equation (l) are chosen such that the weighting function is assumed to be nonnegative and initially increasing. By an adding-up constraint, we also require that
Under the class of CRRA utility, the marginal propensity to consume (mpc) out of wealth depends on the interest rate. Specifically, the inverse of the mpc Δ evolves according to: = Δ[(1—1/σ)r(t) + p + θ/σ]Δ – 1, where σ–1 is the intertemporal elasticity of substitution. With log utility, σ = 1 and Δ = 0, as in equation (2).
Integrating up equation (4), for example (and imposing a transversality condition) yields the definition of
We define wherei(t) is an index measuring the oldest generation that is still liquidity constrained. As the population is normalized to unity, and there is no population growth, the proportion of individuals that are liquidity constrained is given by .
Using pooled data, Gagnon and Unferth (1995) report an average real interest rate of 4.2 percent for the sample period 1978–93.
The experiment considered by Evans consisted of a change in the steady-state deficit-to-consumption ratio of 3 percentage points. Without inflation, his experiment translates into a change in the debt-consumption ratio of 100 percentage points, about live times larger than has been observed over the last two decades in the OECD countries as a group.
Blundell (1988) argues in a survey paper that the elasticity of consumption is likely to be less than 0.5; Hall (1978) argues that it may be even lower than 0.2. Econometric work based on the U.S. and the U.K. time-series data by Patterson and Pesaran (1992) suggests that it is somewhere between 0.1 and 0.3.
Here, we depart from Evans’s assumption of 3 percent productivity growth. Over the last two decades, real GDP per worker in the United States has increased, on average, by less than 1 percent a year.
As increases, the steady-state interest rate increases; see Blanchard (1985). Thus, a lower rate of time preference is required to fit a given long-run interest rate. Conversely, life-cycle income acts to lower the steady-state real interest rate via saving for retirement motives.
The intuition for this result is straightforward. In a world in which current generations are disconnected from future generations, a higher rate of population growth will mean that current generations can expect to pass on a larger share of the tax burden to future generations, whose current marginal propensity to save is zero.
