This paper introduces habit-forming preferences in a Barro-type endogenous growth model with productive public services. Government expenditure, which may be subject to congestion, is financed by distortionary income taxation. Different from the standard time-separable model, the presence of habits makes the economy feature transitional dynamics, which are solved in closed form. Setting the income tax so as to equate the elasticity of public services in production is shown to maximize both long-run growth and welfare as in the standard model. This second-best solution coincides with the first-best outcome only in the presence of proportional congestion.

Following the seminal work of Barro [

Barro [

This paper adds to this literature by extending the Barro [

This paper develops an endogenous growth model with habit persistence in utility and productive government expenditure in production, which is financed by distortionary income taxation. As Barro and Sala-i-Martin [

The main results of this paper are twofold. First, we show that, unlike the standard time-separable Barro [

The rest of the paper is organized as follows. Section

We study a closed economy populated by a large but fixed number

The intertemporal utility derived by the agent depends both on its current consumption,

Following G

In the internal-habits model, the reference consumption stock depends only on individual's own past consumption, so that

At each moment of time, the representative agent is endowed with a fixed and constant stock of labor,

Following Turnovsky [

Combining (

The government levies a tax on income at a constant rate

Output can be used for consumption or investment. Thus, the agent's budget constraint is

At time

To derive the optimization conditions, let us set up the Lagrangian of the agent's maximization problem,

Equation (

An equilibrium for this economy is as a set of paths

We will focus on the equilibrium dynamics of aggregate variables,

Along a balanced growth path (BGP),

The following proposition, which is proved in Appendix

The decentralized economy has a unique feasible equilibrium with positive long-run growth which is described by

The equilibrium paths of aggregate consumption, capital, and habits stock are then given by

One important consequence of Proposition

If

The explicit expressions derived in Proposition

Among the different competitive equilibria indexed by the value of the income tax rate,

Using that

This result is similar to that obtained by Barro [

We now turn to the first-best solution that a benevolent social planner would implement. The planner takes into account that private and aggregate outputs are related by

Thus, given the initial conditions on capital,

subject to the resource's constraint

The Lagrangian of the planner's problem is

Let

Let

The following proposition, which is proved in Appendix

The socially-planned economy has a unique feasible optimal solution with positive long-run growth which is described by

The efficient paths of aggregate consumption, capital, and habits stock can be easily computed as

As in the Barro [

If

In the second-best solution, the income tax rate is set according to (

The dynamics of consumption in the first-best and second-best solutions can be easily compared by using the closed-form expressions derived in Propositions

This section illustrates the implications for the dynamics of the economy of introducing habits in the Barro [

The baseline parameterization is shown in Table

Parameter and steady-state values.

We perform an exercise similar to that in Carroll et al. [

Transition dynamics after a 10% reduction in capital.

Time paths of

Growth rates of

Figure

Growth rate of consumption after a 10% reduction in capital.

Effect of

Effect of

Figure

Growth rates of capital and consumption after a 10% reduction in capital: First-best versus second-best solution.

This paper develops an endogenous growth model with habit-persistent preferences and productive public services. Government expenditure, which may be subject to congestion, is financed by an income tax. Unlike the standard time-separable Barro [

In this paper, we have considered that it is the current flow of public investment which is productive. Another strand of the literature assumes instead that the accumulated stock, rather than the current flow, is the source of contribution to productive capacity. One interesting extension would be to analyze a model with public capital or with a mix of productive capital and public expenditure. Another valuable extension would be to consider a more general parameterization of technology, such as CES production. These topics will be the subject of future research.

Since

Given that (

Now, evaluating (

Using (

Now, (

Firstly, the long-run growth rate (

Equation (

Substituting

The stationary value

The proof is similar to that in Proposition

Equation (

As in Proposition

The stationary value

This appendix shows that

Financial support from the Spanish Ministry of Science and Innovation through Grant ECO2008-04180 is gratefully acknowledged.