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The Time-Inconsistency Problem of Labor Taxes and Constitutional Constraints

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Abstract

This paper investigates the time-inconsistency problem of labor taxes in an economy with balanced-budget policies and no capital taxes. With full commitment, we show that Ramsey labor taxes change with the cost of distortionary taxation and with the cost of not being able to tax capital. We numerically show that these make labor taxes increasing over time. With limited commitment, we find that this time-inconsistency problem leads to underprovision of public consumption. For our baseline parameter values, we find that imposing carefully chosen bounds on labor taxes as constitutional constraints can be optimal. While our proposed bounds sustain the Ramsey as the best sustainable equilibrium, our lower bounds alone or, in combination with some upper bounds, induce higher public consumption and higher welfare in the worst sustainable equilibrium.

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Notes

  1. For example, Lucas [17] and, more recently, Mankiw et al. [20].

  2. The finding that optimal labor taxes are increasing over time when capital cannot be taxed is connected to the comments of Atkenson et al. [3]. They observe that a positive tax on capital is comparable to an increasing tax rate on consumption and the latter corresponds to an increasing tax rate on labor income. These policies are comparable but not equivalent. In our economy, we do not count with consumption taxes and not having capital taxes eliminates an instrument that is necessary for decentralization and therefore changes the Ramsey problem.

  3. See [4, 5, 18, 26], etc.

  4. More precisely, in Ramsey problems with full commitment, access to bonds, capital taxes, and with homothetic preferences, optimal labor taxes are typically low (even negative) in the initial period and then positive and roughly constant from then on. In contrast, in our paper, labor taxes are increasing over the transitional phase.

  5. An alternative approach is to consider Markov-perfect equilibria as in [15].

  6. In this model, with only one source of government income, the non-negativity of public consumption requires a non-negative labor tax. Moreover, Laffer curve effects generate a ’natural’ upper bound on labor tax rates.

  7. The first-order conditions in period 0 are different due to the initial wealth.

  8. As usual, an optimal interior solution is assumed to exist.

  9. We refer to [12] for details in the approximation of convex-valued sets and to [10, 11] for applications of the algorithm to similar games (and for recovering the strategies).

  10. We discretize the state space with \(400\) equally spaced points for \(k\in [0.01,1.5]\), \(400\) points for \(m\), and \(100\) points for \(\tau \in [0,0.9]\). We use linear interpolation for values falling outside of the grid. We ran our C++ MPI code using an IBM iDataPlex cluster, with 50 Intel Sandy Bridge 2.6 GHZ processors.

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Authors and Affiliations

  1. School of Economics, The University of Queensland, Colin Clark Building (39), St. Lucia, Brisbane, QLD, 4072, Australia

    Begoña Domínguez

  2. Department of Economics, University of Illinois at Urbana-Champaign, David Kinley Hall, 1407 W. Gregory, Urbana, IL, 61801, USA

    Zhigang Feng

Authors
  1. Begoña Domínguez
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  2. Zhigang Feng
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Corresponding author

Correspondence to Zhigang Feng.

Additional information

We thank the Editors and an anonymous Referee for their valuable comments. All the remaining errors are ours.

Appendix

Appendix

See Figs. 1, 2, 3 and 4.

1.1 Calibration

In order to calibrate the parameters for our quantitative exercise, we consider an initial steady state that corresponds to an economy with similar statistics to those of the USA. In our simulations, one period corresponds to 1 year.

Our calibration follows that of [4], which is consistent with US data. In the initial steady state, the tax rates on capital and labor income are set equal to 27.1 and 23.7 %, respectively. We choose a public consumption to output ratio equal to 19 % and consider no public debt.

We assume the utility function (2) and a Cobb-Douglas production function \(y_{t}=k_{t}^{\alpha }n_{t}^{1-\alpha }.\) We choose a capital share of 0.34 and a depreciation rate of 0.08. The discount factor is set to deliver a capital to output ratio of 2.71 in the initial steady state. In (2), the coefficient of risk aversion \(\sigma \) is set equal to unity and the labor-supply elasticity is set so that \(\chi \)= 0.32. The weight on labor disutility \(\gamma _{n}\) is chosen so that hours worked are 0.23 in the initial steady state. The weight on public consumption \(\gamma _{g}\) is chosen so that social planner’s solution delivers a public consumption to output ratio equal to 19 %.

Table 1 summarizes the parameter values used in our baseline economy.

Table 1 Parameter values for the baseline economy
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Domínguez, B., Feng, Z. The Time-Inconsistency Problem of Labor Taxes and Constitutional Constraints. Dyn Games Appl 6, 225–242 (2016). https://doi.org/10.1007/s13235-015-0149-z

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