IntMacro2018springslidesTopic11May6.pdf

# IntMacro2018springslidesTopic11May6.pdf - Lecture 11...

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Unformatted text preview: Lecture 11 Extensions to the Baseline IS/MP/AS Model: Fiscal Policy and Investment Mark Gertler NYU Intermediate Macro Theory Spring 2018 0 Fiscal Policy We …rst introduce government spending Gt …nanced by lump sum taxes Tt – Resource constraint Yt = Ct + Gt – Government budget constraint Gt = Tt Gt exogenous Assume capital market perfect ! Ricardian Equivalence holds – i.e., only present value of taxes a¤ects consumpton spending - not timing – present value of taxes = present value of government expenditures Adding Fiscal Policy to Aggregate Demand Sector Resource constraint Yt = Ct + Gt Consumption demand Ct = Pt n (Rt+1 ) Pt+1 Fiscal Policy Gt = Gt Ct+1Dt IS Curve with Fiscal Policy Combining equations Pt n (Rt+1 ) Pt+1 Yt Gt = Yt = Pt n (Rt+1 ) Pt+1 (Yt+1 Gt+1)Dt IS Curve (Yt+1 Gt+1)Dt + Gt Gt &quot; ! IS curve shifts &quot; (direct impact on demand) Gt+1 &quot; ! IS curve shifts down (households save in anticipation of higher taxes) Loglinear Model bt Let x log Xt log X ; X steady state value of Xt Start with Yt = Ct + Gt Linear approximation dYt = dCt + dGt dYt dCt dGt Y =C +G Y C G t (=Given dX X b t for small changes) ! loglinear approximation x Y ybt = C cbt + G gbt Loglinear Model (con’t) Y ybt = C cbt + G gbt ! Loglinear resource constraint ybt = C G cbt + gbt Y Y Consumption demand Fiscal policy cbt = (rtn t+1 r ) + cbt+1 + dt gbt = gbt IS Curve with Fiscal Policy b cbt = Y C yt Gg b C t IS curve ybt = c(rtn t+1 G b r ) + ybt+1 + (g t Y gb C t+1 ) + dt Y IS/MP/AS given adpative expectations ( t+1 = t 1 and t= t 1) IS ybt = c(rtn t 1 G (g b rn ) + ybt+1 + Y t MP rtn = r + AS t + y (ybt ybt ) Cd gbt+1) + Y t t = (ybt ybt ) + t 1 LRAS bt ybt = a (since yt = at + x, y = a + x and ybt = yt y ) Flexible Price Benchmark Resource constraint ybt = C G cbt + gbt Y Y IS curve ybt = (rt G b r ) + ybt+1 + (g t Y LRAS gbt &quot; ! cbt # with no e¤ect on ybt bt ybt = a cbt = Y ybt C Gb g C gb C t+1 ) + dt Y Intuitively: economy on production possibility frontier. gbt &quot; ! rt &quot;! cbt #. Sticky Price Case IS ybt = c(rtn t 1 G (g b rn ) + ybt+1 + Y t MP rtn = r + t + y (ybt AS t = (ybt ybt ) + t 1 ybt ) Cd gbt+1) + Y t Holding constant rtn; gbt &quot; ! ybt &quot; dybt = G b dg t Y Intuitively, output demand determined in short turn. Fiscal policy a¤ects demand. Fiscal Muliplier Fiscal multplier dYt dGt – i.e. the e¤ect of a one dollar increase in Gt on Yt (holding rtn constant) We know dyt = where yt Since dyt log Yt and gt dYt Y and dgt G dgt Y log Gt dGt G : dYt G dGt = Y Y G ! …scal multiplier of unity dYt =1 dGt Fiscal Policy with Liquidity-Constrained Consumers 2009 Fiscal stimulus package justi…ed on the basis of a multiplier between 1:5 and 2 – Need a fraction of consumers to face borrowing constraints to get a multiplier this high Let Ctu consumption by &quot;unconstrained&quot; households; Ctc &quot;Constrained&quot; households consumption by Ct = Ctu + Ctc – Unconstrained households obey standard consumption/saving behavior – Constrained households consume equal to their disposable income Ctu = Ytu Ttu Loglinear Consumption with Liquidity-Constrained Consumers Aggregate consumption c cbc ! C cbt = C u cbu + C t t where Cc C cbt = (1 c b )cbu + c t t Consumption by constrained households – Assume Ytc = Yt and Ttc = Tt and given C c = C Ctc = C c cbct = Yt Tt ! Y ybt T bt ! Y T bt cbct = ybt Ct C Loglinear Consumption (Con’t) Aggregate consumption cbt = (1 c )cbu t + cbt Consumption of unconstrained households (assuming dt = 0) cbu t = cbu t = (rtn 1 X t+1 n (rt+i r ) + cbu t+1 t+1+i i=0 Consumption by constrained households cbct = Y ybt Ct T bt C r ) IS Curve with Liquidity-Constrained Households Aggregate demand C G cbt + gbt Y Y c cbt = (1 )cbu t + cbt ybt = cbu t = cct = 1 X n (rt+i ybt = (1 ) [ i=0 r ) i=0 Y yt C T t C Combine to form IS curve (and recalling 1 X t+1+i n (rt+i C) =Y t+1+i r )] + [ybt T Gb b t] + g t Y Y IS Curve con’t IS curve ybt = (1 ) 1 X n [(rt+i t+1+i ) i=0 r ] + [ybt T Gb b t] + g t Y Y bt implies feedback e¤ect: ybt depends on ybt Senstitivity of cbu t to y We can solve out for this e¤ect ybt = 1 X i=0 n [(rt+i t+1+i ) r ]+ 1 1 Gb gt Y 1 T bt Y Multiplier IS curve ybt = 1 X n [(rt+i t+1+i ) r ]+ i=0 1 1 Multiplier = 1 1 &gt; 1 dybt = 1 1 dYt 1 = Y 1 1 dYt = 1 Estimates of :4 ! 1 1 1:7 G b dg t ! Y G dGt ! Y G dGt Gb gt Y 1 T bt Y Tax Multiplier IS Curve ybt = 1 X n [(rt+i t+1+i ) r ]+ i=0 1 1 Gb gt Y 1 T bt Y Tax Multiplier dYt = 1 dTt Note that the absolute value of the tax multiplier is less than the expenditure multiplier. Only constrained households respond directly to the tax cut. One can maximize the e¤ectiveness of the tax cut by targeting it toward constrained households. The 2009 …scal stimulus did this by targeting bene…ts toward lower income households and the unemployed. ...
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