In this appendix the schedules underlying the phase diagram (see Figure 1)—that is, the capital stock equilibrium (CSE) and consumption flow equilibrium (CFE) locus—are derived.
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Ben Heijdra is a Professor at the University of Groningen and Jenny Ligthart is an Economist in the Tax Policy Division of the Fiscal Affairs Department at the IMF. The authors would like to thank Peter Broer, Liam P. Ebrill, and Robert P. Flood for comments on an earlier draft.
Diamond (1965) assumes that individuals live for two discrete time periods, according to a life cycle in which they work and save during the first period and consume out of their savings in the second period.
Rather than working with a linearized version of the model, the main schedules are depicted in nonlinear form.
Issues of tax smoothing are thus abstracted from.
At each instant a cross section of the existing population dies and is replaced by a n ew generation. Since average consumption exceeds consumption by newly born agents (that are born without any financial wealth), the generational turnover effect drags down aggregate consumption growth.
The mathematical proofs are presented in the Appendix.
Being the set of points from which the dynamic system converges to the steady state.
Note that in a representative agent (or Barro-Ramsey) model, aggregate and individual consumption coincide so that the CFE curve represents the locus of points where the rate of interest equals the rate of pure time preference.
Tax incidence is defined as the after-tax wage (including transfers) for labor and the after-tax rate of interest for capital.
By substituting equation (1) in (2) and applying the Laplace transform method (see Judd, 1985, 1987a) to the loglinearized model as set out in Heijdra and Ligthart (2000), analytical expressions for the welfare profiles of existing generations (with a generation index v≤0) and future generations (with v = t ≥ 0) can be derived. These equations are employed in deriving the numerical results.
Human wealth is defined as the present discounted value of maximum after-tax wage income.
Gross wages fall as a result of the introduction of the capital tax. However, receipts of ageindependent lump-sum transfer income—that is, the recycled revenues from the capital tax—attenuate the fall in gross wage income somewhat.
The consumption tax decreases both the long-run capital stock and the long-run level of employment, but the fall in the latter is bigger so that the capital-labor ratio rises.
These values are computed for a 1 percent rise in the respective tax rate. Alternatively, one could look at the degree of political support for tax increases that raise an equivalent amount of revenue, in which case tax base effects would matter.
Note that the government can, if it wants to, issue bonds to compensate old generations for the welfare loss so as to make the introduction of consumption or capital taxes less painful. Future generations are taxed when the public debt is redeemed.
See OECD (1995) for an overview of the policy discussion on coordinated labor-consumption tax reforms.
A full analysis of this reform—using numerical simulations—is beyond the scope of the present paper. Instead, an intuitive account of the effects is provided.
Note that the labor income tax will vary over time reflecting changes in the labor and consumption tax bases during transition.
As is well known, taxes on consumption are implicit taxes on labor that produce both labor and commodity market distortions.
Specifically, distortions are larger, the higher the initial tax rates and the larger the elasticities of labor supply and intertemporal substitution.