on the determination of the public debt
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On The Determination of the Public Debt. Robert Barro 1979. Overview . Accepts that the Ricardian Invariance Therom is a valid first-order assumption This paper introduces a discussion of second order conditions to examine the effects of ‘excess burden’ of taxation

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  • Accepts that the Ricardian Invariance Therom is a valid first-order assumption
  • This paper introduces a discussion of second order conditions to examine the effects of ‘excess burden’ of taxation
  • Several typical features of public debt analysis are dismissed by the Ricardian Therom
  • Thus, the paper will focus on less common issues dominated by first order effects
  • That there is a positive effect of temporary increases in government spending on debt issue
  • The negative effect of temporary increases in income
  • The growth rate of debt will be independent of the debt-income ratio and would only be slightly effected by the level of government expenditure
summary of results
Summary of Results
  • Used data on US post-WWI public debt issue
  • Finds that the empirics agree with the proposed hypothesis
    • Debt issue since WWI seems to be explained by a small number of variables
  • Model Characteristics
    • Applies only to large nations with exogenous populations
    • Government must finance through either current taxation or public debt issue
  • Variables
    • Gt - Volume of Real government expenditure in period t
    • t - Real tax revenue generated in each period
    • Yt - Aggregate real income
    • bt - real stock of public debt outstanding at the end of t
    • P - Price level and is assumed to be constant
    • r - Real, constant, rate of return on public and private debts
budget constraint
Budget Constraint
  • In each period
  • Budget constraint at date t
determination of burden
Determination of Burden
  • Collection Cost in period t
    • Zt - The real cost incurred in period t.
  • Present value of Collection Costs
optimal tax levels
Optimal Tax Levels
  • Optimization requires that 1… are chosen to minimize the present value of revenue-raising costs
    • This requires that the marginal cost of raising taxes be the same in all periods
    • This implies that /Y is equal in all periods
constant income and government expenditures
Constant Income and Government Expenditures
  • When Y is constant over time the constancy of /Y implies constancy of .
  • If G is constant as well then  is determined immediately from Equation 2
  • Combining with Equation 1 dictates that the budget always be balanced and thus steady state value of debt is determined only by its initial value and not as a function of G, Y, r, etc
constant rate of growth of income and government expenditure
Constant Rate of Growth of Income and Government Expenditure
  • If Yt = Y0(1+p)t than in order for the present value of future income to be finite r > p
  • It is assumed that Gt = G0(1+)t thus if G/Y<1 is true ≤ p < r
  • Thus p =  is the only equality that provides finite, steady state growth of G/Y
introducing taxes
Introducing Taxes
  • The tax-income ratio remains constant, thus taxes grow with income and


  • Combining this with the initial budget constraint leads to a formula for the current budget deficit:
transitory income and government expenditure
Transitory Income and Government Expenditure
  • Assume G1=(1+)G0(1+p) and that Y1=(1+u)Y0(1+p)
  • The equation for the determination of taxes in all periods is as follows
transitory income and government expenditure13
Transitory Income and Government Expenditure
  • The longer a “transitory” period of government spending is expected to last the higher the current taxation will be
  • At the same time the longer a “transitory” period of government income the lower the current taxes
transitory income and government expenditure14
Transitory Income and Government Expenditure
  • Growth of Budget Deficit in transitory periods:
  • The deficit grows dependent upon the departure of the current government spending from normal and the proportional departure of income from normal
changes in prices
Changes in Prices
  • Price changes are treated exogenously
  • Future prices increase to P1 and remain static
  • Equation 1 is now modified to be:
  • The primary effect is that changes in the price level, or inflation rate, do not change the growth rate of the nominal debt
changes in prices ii
Changes in Prices II
  • If prices are assumed to change at a constant rate Pt=P0(1+)t
  • Equation 1’ remains almost the same with the exception that the growth rate of nominal debt increases by 
  • This changes Equation 7 to the following:
  • As a result, when inflation is included nominal debt grows by p+ 
changes in rate of return
Changes in Rate of Return
  • If r is not equal to r0 the analysis remains the same as long as debt is measured at market rather than par values
  • Basic result is that increasing r above the average of previous rates reduces the growth rate of debt in terms of par values
empirical analysis
Empirical Analysis
  • Bt is the stock of nominal debt at the end of the calendar year t
  • B¯t is the average amount of debt outstanding
  • t is the average anticipated rate of inflation
  • Pt is the average price level
  • Gt is real federal government expenditure
  • Yt is aggregate real income (GNP)
  • Y¯t is the level of normal income
variables continued
Variables Continued
  • 0: Equal to p as long as the growth of Y and G are equal
  • 1: Equal to unity
  • 2: Equals the [(1+p)/(1+r)]k term in equation 8
  • 3: Equals the [(1+p)/(1+r)]n term in equation 8
the data
The Data
  • Data comes from US public debt information post 1917
  • B is measured as the outstanding stock of federal debt at the end of each calender year
    • These values are not adjusted for changes in rates of return
  •  is constructed based on the estimated GNP deflator from Barro 1978
    • Uses this for the sample 1922-1976 with a dummy for pre-1941
  • Areas of future research: incorporation of currency issue, applications of optimal taxation to public debt determination, and a treatment of uncertainty about future spending
  • Empirically a fix for the anticipated inflation problem is needed