This chapter introduces the government into the exogenous growth models we have analyzed so far.
We first discuss the intertemporal budget constraint of the government and the conditions for government debt sustainability. Then we analyze the impact of the path of lump sum taxes, primary government expenditure, and government debt in the representative household model and an OLG model.
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.As demonstrated in chapter 2, the intertemporal government budget constraint is defined in a way that is similar to the intertemporal 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 plus 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.
As we will see in the present chapter, the intertemporal budget constraint of a government with an infinite horizon does not prevent it from having debt or even from increasing the level of its debt. It means, however, that the limit of the present value of government 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 the government budget constraint was introduced in the two-period representative household model of chapter 2, it was 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 breakdown between government debt and the path of nondistortionary taxes) does not affect the optimal path of consumption of the representative household. This property has become known as Ricardian equivalence between taxes and government debt, and holds in the infinite-horizon Ramsey model as well. 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 the existing government debt, and, as the household internalizes the welfare of future generations, it treats debt and (lump sum) taxes equivalently. In the absence of financial frictions, when households and the government borrow on the same terms, Ricardian equivalence is a key characteristic of representative household models in general.Ricardian equivalence does not apply to OLG models. The stock of government debt affects aggregate savings, as current generations realize that part of the present value of future taxes required to finance the stock of government debt will be paid by future generations. In OLG models, current generations do not internalize the welfare of future ones. Thus, current generations treat part of the existing stock of government debt that they hold as part of their wealth, because it exceeds the present value of their own future taxes. As a result, debt and tax finance are not equivalent in OLG models, and Ricardian equivalence does not hold.
In OLG models, both the stock of real government debt and real primary government expenditure affect private and aggregate savings and the accumulation of capital. Rises in real government debt or real primary government expenditure reduce savings and capital accumulation, and they also have negative effects on the steady state capital stock, output, private consumption, and real wages.
This is because current generations know that part of the increase in future tax revenues needed to finance a higher level of primary government expenditure (or interest payments on the increased debt) will be shouldered by future generations. Aggregate savings are thus affected negatively by an increase in real government debt or an increase in real primary government expenditure. This leads to an adjustment process with declining capital stock and private consumption and a lower steady state level of capital, output, and consumption per head.Taxes are usually distortionary, as they affect incentives for savings, investment, and labor supply. In the representative household and OLG 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 labor supply and savings, and they 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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