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handouttaxation - Timing of Taxation 1 Ricardian...

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Timing of Taxation 1 Ricardian Equivalence Based on Barro (1974, JPE) and L-S Ch. 10. Question: Does the timing of (lump sum) taxes matter? 1.1 Environment Unit measure of identical in f nitely lived agents as well as a govt. Prefs: P t =0 β t u ( c t ) Endowments y t . Household borrowing or lending a t at price Q t where a 0 =0 Exogenous sequence of government expenditure g t f nanced by lump sum taxes/transfers τ t or one period government debt D t at price q t where D 0 . 1.2 Equilibrium Household problem max c t ,a t +1 ,D t +1 0 X t =0 β t u ( c t ) (1) s.t. c t + Q t a t +1 + q t D t +1 = y t τ t + D t + a t , t. Starting in period t, can rewrite sequence of budget constraints as Q t a t +1 + c t + q t D t +1 y t + τ t D t = a t Q t +1 a t +2 + c t +1 + q t +1 D t +2 y t +1 + τ t +1 D t +1 = a t +1 .... Substituting a t +1 from the second line into the f rst yields Q t Q t +1 a t +2 + Q t q t +1 D t +2 + Q t [ c t +1 ( y t +1 τ t +1 )] + c t ( y t τ t ) +( q t Q t ) D t +1 = a t + D t 1

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Since arbitrage requires the price of government and private debt be equal- ized q t = Q t , t , we can re-write this as X j =0 Ã j Y i =1 Q t + i 1 ! [ c t + j y t + j + τ t + j ]= a t + D t , (2) where we have imposed the transversality condition lim j →∞ j Y i =1 Q t + i 1 a t + j +1 =0 as well as the normalization Ã 0 Y i =1 Q t + i 1 ! =1 . The sequence of govt. budget constraints are given by g t + D t = q t D t +1 + τ t , t (3) given initial debt D 0 . Using a transversality condition, (3) implies an intertemporal govt. budget constraint D t = X j =0 Ã j Y i =1 q t + i 1 ! ( τ t + j g t + j ) (4) where again Ã 0 Y i =1 q t + i 1 !
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handouttaxation - Timing of Taxation 1 Ricardian...

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