Fiscal Policy in the Ramsey Model October 2007 () Fiscal policy - PowerPoint PPT Presentation

Fiscal Policy in the Ramsey Model October 2007 () Fiscal policy October 2007 1 / 8

A Balanced–Budget Increase in Government Consumption Total tax revenue (lump-sum) equals to expenditure on “public consumption“: T t = G t . , ! these are measured per unit of e¤ective labour Aggregate resource constraint becomes ˙ k t = f ( k t ) � c t � G t � ( n + g + δ ) k t . ! ( ˙ , k = 0 ) locus: c t = f ( k t ) � G t � ( n + g + δ ) k t . , ! intertemporal budget constraint: Z ∞ Z ∞ ˆ ˆ D t c t = k 0 + D t ( w t � G t ) . 0 0 No modi…cation to ( ˙ c = 0 ) locus — why? () Fiscal policy October 2007 2 / 8

c . c=0 E 0 . E 1 k=0 k Figure: Permanent Increase in Government Spending () Fiscal policy October 2007 3 / 8

Private consumption is completely crowded out , ! consumption falls due to a pure wealth e¤ect , ! output and r remains unchanged Could replace lump-sum tax here with a wage tax T t = τ t w t = G , ! implication is the same — why? () Fiscal policy October 2007 4 / 8

Debt versus Tax Financing Evolution of government debt: ˙ B = r t B t + G t A t L t � T t A t L t , ! in intensive form ˙ b t = ( r t � n � g ) b t + G t � T t . Sustainability of public debt ˆ D T b T = 0 lim T ! ∞ Government’s intertemporal budget constraint: Z ∞ ˆ D t ( T t � G t ) = b 0 . 0 () Fiscal policy October 2007 5 / 8

Household’s budget constraint can be expressed as Z ∞ Z ∞ ˆ ˆ D t c t = k 0 + b 0 + D t ( w t � T t ) 0 0 Z ∞ ˆ = k 0 + D t ( w t � G t ) 0 , ! Ricardian equivalence: provided the government satis…es its budget constraint, whether or not spending is …nanced by debt or non-distortionary taxation is irrelevant , ! inde…nite planning horizon and interest rate equivalence are crucial for this result () Fiscal policy October 2007 6 / 8

Distortionary Taxation of Capital Assume revenue is remitted back to households in lump–sum fashion ) no impact on resource constraint After tax interest rate: r t = ( 1 � τ ) f 0 ( k t ) � δ ˜ ) Euler equation: = ( 1 � τ ) f 0 ( k t ) � δ � ρ � θ g c t ˙ c t θ ( ˙ c = 0 ) locus: f 0 ( k t ) = ρ + δ + θ g 1 � τ () Fiscal policy October 2007 7 / 8

. c=0 c E . E 1 k=0 0 k Figure: A Tax on Capital Income () Fiscal policy October 2007 8 / 8