Financing Government Expenditures: Some Basics

Transcription

1 Financing Government Expenditures: Some Basics Mark Huggett 1 1 Georgetown April 11, 2017

2 Washington Post Editorial October 2009: Why fund war with debt but insist that health-care reform be deficit neutral? The editors of the Post try to offer a rationale for debt finance for wars but balanced-budget finance for health care. 1. Their answer is full of logical non-sequitors and is devoid of an underlying principle. 2. The great economists of the past laid down long ago the theoretical foundations for an answer. 3. Moreover, there is a consensus among economists on the answer. It s available with a Google search. It can be expressed at various levels including the level of the journalist and the lay public.

3 An answer at the journalist s level: Economists have argued for the principle of tax rate smoothing. This is the idea that it is not benefical for tax rates to change radically across time periods in the absense of new information on future government expenditures. In the absense of new information on such expenditures, the principle dictates smooth tax rates over time (i.e. constant) to finance government expenditures.

4 Tax Rate Smoothing Example 1: A Perfectly Forseen War 1. Imagine a temporary increase in expenditure due to a war. The war is forseen at least some time in advance. 2. In the absense of other changes, tax rate smoothing implies that the tax rate on labor income or consumption should be higher but constant over time. 3. To finance this war, the government accumulates assets before the war. At the time of the war, it pays for the war by running down the assets and by borrowing. After the war, the debt stays constant and taxes pay the interest on the debt and for government spending.

5 Tax Rate Smoothing Example 2: A Permanent Increase in Govt Spending 1. Imagine a permanent increase in expenditure due to health care. This is forseen some time in advance. 2. In the absense of other changes, tax rate smoothing suggests that the tax rate on labor income or consumption should be higher but constant over time. 3. To finance the permanent expenditure, the government accumulates assets before the change. At the time of the expenditure increase, it pays for the expenditure with taxes and the interest from the asset accumulation. The debt stays constant after the expenditure increase.

6 Tax Rate Smoothing Example 1-2 Summary In both examples the tax rate is higher in all periods... but the tax rate is constant over time after the news that the spending shock will occur is available. Thus, tax rates are smooth over time. What the theory implies is that debt is determined as a residual based on the principle of tax rate smoothing. If the expenditure is a one-time spike then it is funded by a change in debt. If the expenditure is a permanent increase, then it is not funded by increased debt. The key principle is that tax rates should be smooth over time.

7 Tax Rate Smoothing Some References: 1. Barro, (1979), On the determination of the public debt, Journal of Political Economy 8, Lucas and Stokey (1983), Optimal Fiscal and Monetary Policy in an Economy without Capital, JME, 12, Chari and Kehoe (1997), Handbook of Macroeconomics. Example 1 is in Lucas and Stokey (1983) as example 4. Their results apply the ideas of Ramsey (1927). They view the different goods being taxed in Ramsey s formulation as consumption at different points in time. Their results are based on time separable utility functions.

8 Ramsey (1927), A Contribution to the Theory of Taxation, Economc Journal, 37, The problem I propose to tackle is this: a given revenue is to be raised by proportionate taxes on some or all uses of income, the taxes on different uses being possibly at different rates; how should these rates be adjusted in order that the decrement of utility may be a minimum? I propose to neglect altogether questions of distribution and considerations arising from the differences in the marginal utility of money to different people; and I shall deal only with a purely competitive system with no foreign trade. Theory: One consumer. Government chooses tax rates on goods to maximize the consumers utility, given the revenue constraint. The consumer makes best choices given prices and taxes.

9 A Ramsey Tax Problem: Notation τ = (τ 1,..., τ n ) proportional tax rates p = (p 1,..., p n ) producer price (fixed by linear production fn) q = (q 1,..., q n ) = (p 1 (1 + τ 1 ),..., p n (1 + τ n )) consumer price x i (p, τ) optimal consumer demand for good i given prices l(p, τ) optimal labor supply given prices max τ U(x 1 (p, τ),, x n (p, τ), l(p, τ)) subject to n i=1 τ ix i (p, τ) R

10 A Ramsey Tax Problem: Inverse Elasticity Rule Special Case: No crosss-price effects Define: ɛ i as elasticity of demand for good i wrt price of good i. τ i = constant 1 + τ i ɛ i i = 1,..., n Implication: in a solution to Ramsey s problem, it is optimal to apply a higher rate to goods with a lower price elasticity of demand.

11 A Ramsey Tax Problem: Inverse Elasticity Rule Apply the inverse elasticity rule over time periods assuming no cross-price effects. Additive utility functions are consistent with this. A constant elasticity over time (i.e ɛ 1 =... = ɛ n ) implies constant tax rates or tax rate smoothing. Thus, when a government expenditure shock occurs tax rates in all periods rise equally. Government debt is determined residually.

12 Three Remaining Theoretical Issues: 1. Does it matter if consumption or labor income is taxed? 2. If a specific good is perfectly inelastic, then is it optimal to tax this good only and not other goods? 3. In a dynamic model one might argue that the capital stock in the initial model period is inelastically supplied. If so, then is it optimal to tax only this good and not others?

13 Does it matter (in theory) if consumption or labor income is taxed? P1 max U(c 1, l 1,..., c T, l T ) s.t. T p t(1+τ t)c t t=1 (1+r) t 1 P2 max U(c 1, l 1,..., c T, l T ) s.t. T t=1 p tc t (1+r) t 1 T t=1 w tl t (1+r) t 1 T w tl t(1 τt w) t=1 (1+r) t 1 Theorem: Assume 1 τt w = 1/(1 + τ t ), t and that tax rates are constant. (c 1, l 1,..., c T, l T ) solves P1 if and only if (c 1, l 1,..., c T, l T ) solves P2. Proof: Budget sets are the same. Thus, so are best choices.