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The authors thank without implication their IMF colleagues, seminar participants at American University, and conference participants at the Annual Meetings of the Society of Economic Dynamics. A special thanks to Jeff Gable for acquiring and constructing the data and to Susanna Mursula for assistance with the simulations.
See Alesina and Perotti (1995) for a discussion on this issue.
Interest in the hypothesis of Ricardian equivalence was revived by Barro (1974). See Barro (1989) for a review. However, it should be noted that Ricardo himself did not believe in Ricardian equivalence and indeed was very concerned that there could be deleterious crowding-out effects associated with high levels of government debt.
Evans (1991) further shows that in the simple Blanchard (1985) model—i.e., without any life-cycle features—the departures from Ricardian Equivalence are quite small. In other words, though debt neutrality does not hold exactly, it is nevertheless a good approximation.
Using a similar framework, Romer (1988) examines the effects of “excessive” deficits, without incorporating life-cycles features to the model. Consequently, the economic effects (e.g., on interest rates) of fiscal deficits are second-order; nevertheless, he argues that the normative consequences may still be first-order on (intergenerational) welfare.
See Blanchard (1995). This well-known assumption of a constant death or hazard rate allows for analytical tractability and implies that all agents have been the same expected length of life remaining. This inherent feature of the model is often equated with the absence of a life-cycle dimension; however as well as we shall see, it is only one part of what constitutes “life-cycle behavior,” and perhaps not the most relevant aspect, depending on the issue at hand.
The case of population (and productivity) growth is addressed in the appendix.
The term p w(s,t) in the dynamic budget constraint reflects the efficient operation of life insurance of annuities market. See Yaari (1965) or Blanchard (1985). The budget constraint would also incorporate the depreciation of capital assets, omitted here for simplicity.
For a given (world) real interest rate, individual human wealth can be written as:
In terms of notation, time arguments have been dropped in the text except where potential ambiguities may arise. The time index is reintroduced in the tables.
Weil (1989) shows clearly that what matters for Ricardian equivalence to break down is not that p=0 but that agents alive today are disconnected from some agents in the future. This would be the case for example if new dynasties were being created in the future as a result of immigration, or if some members of existing dynasties severed their relationships and formed new strands. Buiter (1998) confirms this result, showing that the death rate is neither necessary nor sufficient for Ricardian Equivalence to fail; instead, it is the birth rate that matters.
Blanchard (1985) examines the case of individually declining income profiles. The more realistic case of non-monotonic (concave) earnings profiles is mentioned only in passing (footnote 8).
As discussed in section III, the parameters in (3) are chosen such that the weighting function is assumed to be non-negative and initially increasing; by an adding up constraint, we also require that
Integrating up equation (9) yields the definition of the human wealth component H1:
Because there is no population growth at this point in the analysis the birth rate, b, is assumed to be equal to the probability of death p.
Assuming that F(K,L) is homogenous-of-degree-one in its arguments, we can write the production function as LF(K/L, 1) = f(K)[≡ F(K,1)] at L = 1. Also, the following conditions are assumed to apply to guarantee the existence of an interior steady-state solution: 0 ≤ limk→∞ f′(K) ≤r+δ≤ limk→0 f′(K) ≤ ∞. Strict concavity οf f(K)—an increasing function—guarantees uniqueness.
In this model we abstract from sticky prices and terms-of-trade effects. For a discussion about how these could be included into the model see Macklem (1993).
In the numerical simulations that follow, we assume that a (fixed) equity premium exists in calibrating the baseline levels; this is necessary to obtain both a sensible equilibrium capital-output ratio and real interest rate. Otherwise, the real interest rate would be unrealistically high—see for example Romer (1988).
With a time-varying rate of interest, the present value of (dynastic)labor income which comprises of human wealth is given by:
Differentiating this expression with respect to time yields the dynamic equation for human wealth shown in Table 2.
Hayashi (1985), Zeldes (1989) and Jappelli (1990) each find empirical evidence suggesting liquidity constraints are more likely for younger families with lower wealth and income.
In the dynastic case—where labor income is identical across agents—λ also reflects the degree of excess sensitivity in the aggregate consumption to disposable income; in the life-cycle case, the coefficient of excess sensitivity reflects the amount of labor income (and hence consumption) associated with the proportion λ of the population who face borrowing constraints [see appendix]. Departures from the predictions of the strict permanent income hypothesis have been characterized in terms of excess sensitivity of consumption to anticipated changes or excess smoothness to unanticipated innovations in income. See Campbell and Deaton (1989). These issues can be viewed as aspects of the same phenomenon, generated by liquidity constraints; see Flavin (1993).
A common explanation for the presence of borrowing constraints involves agency problems—e.g., moral hazard and adverse selection—in credit markets stemming from collateral issues or asymmetric information. See Buiter (1994) or Stiglitz and Weiss (1981).
Together, the conditions for non-negative and initially-increasing income profiles imply:
This is the more general adding-up condition that allows for population growth (see appendix). The text describes the special restriction with zero population growth (b=p).
Increasing the number of exponential terms increases the number of inflection points.
The cohort ranges are: 18-24, 25-34, 35-44, 45-54, 55-64, 65+. Earnings, employment, and population data are from the U.S. Bureau of Labor Statistics and Census Bureau.
The presumption here is that productivity growth does not affect the relative income distribution very much, i.e., is not biased toward any particular age group of workers. See appendix for more on productivity growth.
Imposed parameters reported in the table are obtained through grid search. Over the sample period, the average “birth rate”—defined as the relative sized of the newest cohort—of the U.S. Adult population was around 2½ percent.
Dynamic and steady-state versions of the model are simulated numerically in TROLL to solve for the equilibrium real interest rate and the capital stock in the closed economy and net foreign asset position for the small open economy, assuming no public debt as an initial condition. This numerical work has been made considerably easier by the development of state-of-the-art newton-based methods that are considerably more robust and efficient than first-order iterative techniques. See Juillard et al. (1988) for a discussion of the algorithm and a comparison with other techniques.
We assume no population or productivity growth here. The parameters used to derive the steady-state profiles shown include: θ = 0.05, σ = 1.0, b = p = 0.021. In the life-cycle income case, the α’s are taken from Table 3, column (3). An assumption that the probability of death is the same across the dynastic and life-cycle cases is used so that we can isolate the implications of life-cycle income. Allowing p to differ significantly across the two models would further strengthen the economic differences between the two models.
Because in the dynastic case agents do not choose to borrow—i.e., no intergenerational lending, borrowing constraints placed on some agents (considered later) is not really relevant here. Hence, current-income consumers must represent naive or rule-of-thumb consumers a la Campbell and Mankiw, rather than liquidity-constrained agents.
Note that individual wealth, which is rising, also includes life insurance or annuity income. This transfer, from agents dying each period to surviving agents, does not add to aggregate financial wealth, which is constant even though individual wealth profiles are rising.
The demand for loans—i.e., intergenerational lending—with lifecycle income allows the possibility for binding borrowing constraints, if they appear early in the life cycle. Jappelli and Pagano (1994) introduce a similar implication in a 3-period OLG model, where liquidity constraints appear in the first period, but income is earned only in the middle period.
The “saving for retirement” motive (absent in the dynastic case) tends to lead to greater wealth accumulation; in the closed economy case, this leads to a lower steady-state real interest rate r (or other things equal). For example, whereas
Because life insurance or annuity dividends are paid only in fixed proportions to the level of financial wealth (i.e., zero profit condition), agents must build up their financial estates— which are turned over to the insurance company at the time of death—in order to receive higher annuity income while alive.
The role of “buffer-stock” or precautionary saving is another well-known channel through which individuals seek to maintain a target level of wealth. However, this type of saving behavior is spurred by income (rather than lifetime) uncertainty and should be more prevalent in the earlier stages of the life-cycle. When labor income is earned. See Carroll and Samwick (1997) for a recent and the references cited therein.
The closed economy model is calibrated so that the baseline real interest rate is always the same across different parameterizations, by fixing the rate of time preference—given other taste parameters—at the level required to obtain an initial long-run real interest rate of 4 percent.
The relation between long-run changes in interest rates and the capital stock is as follows: with Cobb-Douglas production and capital share around a third, a 10 basis-point change in the real interest rate translates to around 1½ percentage point change in capital-output ratio. In turn the relationship between the steady-state change in private consumption and the capital stock (given public consumption) is given by
These results for the dynastic case essentially replicate the findings in Evans (1991), who shows that changes in p do not alter the finding of approximate Ricardian equivalence in this class of models.
With long-run productivity growth, dynastic agents have income profiles that increase monotonically over time, representing an increasing tax base and, thus, greater sensitivity to the future tax implications of public debt.
Interest rates affect saving and consumption through 3 channels: discount rate effects, income effects, and substitution effects. With a low substitution elasticity, the substitution effect is attenuated, allowing the (positive) income effect to more greatly offset the (negative) discount rate—i.e., human wealth revaluation—effect resulting from higher interest rates.
Because the substitution elasticity effects consumption (of permanent-income consumers) directly through the marginal propensity to consume and indirectly through influencing the amount of interest rate adjustments, changes in σ can have non-linear implications for the effects of government debt as shown in figure 5.
This result could easily be overturned with imperfect capital mobility—e.g., imperfect asset substitutability, if (say) the domestic interest rate was determined by the world rate plus a risk premium, sensitive to the degree of fiscal indebtedness.
Simulations (not shown) confirm that the impact of different substitution elasticities is negligible in a small open economy in both the dynastic and life-cycle cases.
As a stability condition in the dynastic case, we require that
The relationship between the long-run change in private consumption and net foreign assets is:
This is the zero profit condition for the perfectly-competitive insurance industry. Insurance firms pay pw(s, t) to surviving member of cohort s and inherit estates worth w (s, t) from the proportion p of that cohort who die at time t. See Yaari (1965).
Leaving aside the depreciation of capital assets.
Under the general class of CRRA utility the marginal propensity to consume (mpc) out of wealth depends on the interest rate: c(s,t) = Δ−1 [w(s, t) + h(s,t)], where the inverse of the mpc Δ evolves according to:
In deriving consumption, a transversality (no-Ponzi game) condition on wealth is imposed, preventing agents from accumulating debt indefinitely at a rate higher than the effective rate of interest: limz→∞w(s,z)e-(r+p) = 0.
A common explanation for the presence of borrowing constraints involves agency problems (moral harzard and adverse selection) in credit markets stemming from collateral issues or asymmetric information. See Buiter (1994) or Stiglitz and Weiss (1991)
By adding up, we have
More generally, with time-varying birth and death rates (demographic shocks), the population level would reflect the past accumulation of these shocks to population growth
Lowercase variables with a time and generation index refer to individual measures whereas lowercase variables with only a time argument reflect per capita measures (in units of labor efficiency).
We now have: