In this chapter we introduce the government into the exogenous growth models we have analyzed so far. We first introduce and discuss the inter-temporal budget constraint of the government and the conditions for government debt sustainability. Then, we analyze the impact of the level of lump sum taxes, primary government expenditure and government debt in the representative household
model and a model of overlapping generations. Finally, we analyze the short and long term effects of distortionary taxes on labor and capital income, consumption and business profits before interest and depreciation.

The government budget constraint is defined in a similar way as the inter-temporal budget constraint of a household that can borrow and lend freely at the market interest rate. It requires the equality of the present value of current and future tax revenue to the sum of the current stock of government debt and the present value of current and future primary government expenditure. Primary government expenditure is defined as government expenditure excluding interest payments on government debt, and present values are calculated using the market interest rate.

The government budget constraint does not prevent a government with an infinite horizon from having debt, or even from increasing its level of debt. It means, however, that the limit of the present value of debt, as time tends to infinity, cannot be positive. For example, if the real interest rate is positive, a positive but constant real government debt – which means that the government never repays it – satisfies the government budget constraint. Even if government debt increases continuously, the government budget constraint is satisfied to the extent that the real interest rate exceeds the growth rate of real government debt.

When one introduces the government budget constraint in the representative household model, it can be shown that the only aspect of it that matters for the choice of the optimal path of private consumption, is the present value of primary government expenditure. The method of financing primary government expenditure, i.e the breakup between government debt and (non-distortionary) taxes, does not affect the optimal path of consumption of the representative household. This property is known as Ricardian equivalence between taxes and government debt. In other words, the stock of government bonds held by the representative household is not considered as part of its total wealth, and does not affect its consumption path. The representative household realizes that the bonds will be financed by future taxes equal in present value to the stock of existing government debt.

Ricardian equivalence does not apply to overlapping generations models. The stock of government debt affects aggregate savings, as current generations realize that part of the present value of future taxes required in order to finance the stock of government debt, will be paid by future generations. In overlapping generations models, current generations are not concerned with the welfare of future generations. Thus, current generations treat part of the existing stock of government debt that they hold as part of their wealth, since it exceeds the present value of their own future taxes. As a result, debt and tax finance are not equivalent in overlapping generations models, and Ricardian equivalence does not hold.

Therefore, in overlapping generations models, both the stock of real government debt and real primary government expenditure affect private and total savings, and the accumulation of capital. Rises in real government debt or real primary government expenditure reduce savings and capital accumulation, and have negative effects on the steady state capital stock, output, private consumption, real wages and the real interest rate. This is because current generations know that part of the increase in future tax revenues in order to finance a higher level of primary government expenditure and/or interest payments on the increased debt, will be shouldered by future generations. Private savings are thus affected negatively by an increase in real government debt, and total savings, private and government, are affected negatively by an increase in real primary government expenditure. This leads to an adjustment process with a declining capital stock and private consumption, and a lower steady state level of capital, output and consumption per head.

Taxes are rarely non-distortionary, as they affect incentives for savings, investment and labor supply. In the representative household and overlapping generations models that we have considered, labor supply is exogenously given, and does not depend on net of tax real wages. Consequently, tax rates on labor income or (time invariant) consumption taxes do not cause distortions in labour supply and savings, and do not affect either the adjustment path or the balanced growth path. In contrast, capital income taxation and taxes on business earnings before interest and depreciation, have a negative impact on savings and investment. Such taxes affect savings and capital accumulation negatively, and, as a result, have a negative impact on the steady state capital stock, steady state output and income, steady state real wages and steady state private consumption.

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