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Ben J. Heijdra is a professor in the Department of Economics at the University of Groningen. This project was initiated when both authors were working at the University of Amsterdam. The authors would like to thank Liam Ebrill for helpful comments on a previous draft.
In the Diamond (1965) model people work in the first period and retire in the second period, which implies that a period is roughly 30–40 years. In this framework, individuals from different generations have different marginal propensities to consume out of wealth because young agents save for retirement. In the Blanchard (1985) model, however, all generations have the same propensity to consume out of wealth. In both frameworks generations are different in the amount of wealth they have accumulated.
Heijdra (1994) also extends the Blanchard model to allow for variable labor supply, but assumes imperfect competition on the goods market and studies the output effects of a rise in public expenditure.
See Judd (1985, 1987) for this type of analysis in a dynamic model featuring infinitely lived individuals and Auerbach and Kotlikoff (1987) for a 55-period numerical analysis in a Diamond (1965) type of overlapping generations framework. Anticipation effects and temporary policy changes are not addressed in the current paper but will be left for further extensions.
Auerbach and Kotlikoff (1987, p. 68) also show, using their dynamic computable general equilibrium model for the U.S. economy, that a rise in consumption taxes increases savings if the intertemporal labor supply response is small. However, they do not provide a further analysis of this result.
The property of a constant probability of death implies that a young person has the same expected lifetime (given by l/β) as a very old person. Accordingly, expected lifetimes increase for smaller values of β.
Leisure is defined as the household’s time endowment (which is normalized to unity) less labor supply, L(v, t).
This means that production is measured after allowing for depreciation of the capital stock.
where σ represents the intratemporal elasticity of labor supply. Labor supply is then given by L(v, t)=[(1-tL(t))W(t)/(1+tc(t))]σ.
The higher effective rate of time preference in the finite horizon case leads to a higher value of the marginal product of capital and correspondingly a lower capital stock than in the case of an infinite-horizon model.
where αH(v) is decreasing in the age, -v, of the generation. Very old generations (with v→-∞) have accumulated over their life a large stock of financial assets which implies a negligible share of human capital in total wealth (αH (v)→0). Young agents (with v→0), however, own no financial wealth so that αH (v)→1) and thus fully consume out of human wealth.
In doing so the need to discuss the GT effect for these two taxes is obviated since it does not affect the qualitative allocation effects. For the consumption tax, the GT effect does, however, play a crucial role. For that case, the intuition is explained with the version of the model for which labor supply is exogenous so that the GT effect dominates the LS effect.
The properties of the adjustment term are as follows: A(λ1, 0)=1-limt→∞A(λ1,t)=0 and dA(λ1,t)/dt≥0.
If households do not receive any transfers from the government, the elasticity of labor supply has no effect on the long-run incidence of the labor tax change. This is in line with incidence analyses embedded in neoclassical growth models with variable labor supply (i.e., Feldstein (1974)). In the next section it is shown that the intertemporal labor supply response does matter for the incidence analysis of consumption taxes.
The change in the consumption tax must also be unanticipated and permanent for the equivalence result to hold.