wickens_errata
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Corrections to Macroeconomic TheoryMike WickensJanuary2010p18Equation(2.11)should belims!1s U0(c t+s)k t+s+1=0(2.11) p24Equation(2.18):should have a minus after the equals sign to bec t+1= U0U00 1 1[F0(k t+1)+1 ] (2.18)p26Equation(2.23)should beU00(c ) U0(c )(c t+1 c )+ F00(k )(k t+1 k )'U00(c )U0(c )(c t c )(2.23)and equation(2.24)should bek t+1 k ' f c t [F(k ) k ]g+[F0(k )+1 )](k t k )= (c t c )+(1+ )(k t k )(2.24) This gives the matrix equationc t+1 c k t+1 k ="1+U0F00(1+ )U00 U0F00U0011+# c t c k tkp27The roots should bef 1; 2g'f det AtrA ;trAdet AtrA g=f1+2+ +U0F00(1+ )U00;2+ +U0F00(1+ )U001+2+ +U0F00(1+ )U00gp33penultimate equation should have=0added to be@L t @i t+s = t+s(1+i tk t)+ t+s=0;s 0and NOT@L t @i t+s = t+s(1+2i tk t)+ t+s=0;s 01p55Fourth equation should have=0added to be@L= s U0(c t+s) t+s=0s 0@c t+sand NOT@L= s U0(c t+s) t+s s 0@c t+sp58First new para line2should be U0(c t)dc t and NOT U0(c t)dc tp64Second line.should read"It has two features:its slope(which upwards if r> )..."p67line4.The sentence should read"We note,however,that unlike non-durables and services,durables are not a‡ow variable but a stock;..."p69Third and fourth equations should have=0added to be@L= s U c;t+s t+s=0s 0@c t+s@L= s U D;t+s+ t+s p D t+s(1 ) t+s 1p D t+s=0s>0 @D t+sand NOT@L= s U c;t+s t+s s 0@c t+s@L= s U D;t+s+ t+s p D t+s(1 ) t+s 1p D t+s s>0 @D t+sp71.Fourth and…fth equations should have=0added tobe@L= s U c;t+s t+s=0s 0@c t+s@L= s U l;t+s+ t+s w t+s=0s 0@n t+sand NOT@L= s U c;t+s t+s s 0@c t+s@L= s U l;t+s+ t+s w t+s s 0@n t+sst para add at the end to read"....wealth are(omitting transfers)"st line replace"increase"with"decrease"2p135.5lines from the end should be r t=f0(k t) and NOT r t+1=f0(k t) p141.a whole section needs changing1.Two lines after equation(6.48)should be r t=f0(k t) and NOT r t+1=f0(k t)2.The next three equations and followed para should be"....written as(1+r t+1)(1+n)k t+1=1+r t+12+(1 )k t+n r t+12+thencek t+1=1(2+ )(1+n)k t 12+ 1+ 1+r t+1+11+n t= k t t twhere t=12+ h1+ 1+r t+1+11+n i>0.This equation is represented in…gure6.2.Consequently,an increase in the unfunded state pension shifts the curve downwards.This results in a lower equilibrium capital stock and lower savings. Therefore,only the current old generation bene…ts,not future old generations, in particular,not the current young generation."p155footnote remove the minus sign in the…rst equation for ES after the equals sign.p169.Equation(7.46)should be P T t and not P T.p169next equation replacef t y t = (1+ )(1+ )1+R n f t+n y t+n 11+R n X i=0(1+ )(1+ )1+R i E tP T P t+i(x t+i Q T t+i x m t+iy t+i)byf t y t = (1+ )(1+ )1+R n f t+n y t+n 11+R n X i=0(1+ )(1+ )1+R i P T t+i P t+i(x t+i Q T t+i x m t+iy t+i) p169Replace equation(7.47)bylimn!1 (1+ )(1+ )1+R n f t+n y t+n=0(7.47)3p169Replace next equation byf t yt 11+R1X i=0 (1+ )(1+ )1+R i P T t+i P t+i(x t+i Q T t+i x m t+iy t+i)p169Replace last equation byP T t+i P t+i (x t+i Q T t+i x m t+iy t+i)p211Replace equation9.10and the following sentence withn t(i)=1 u c;t W t(i) "P t 1" 1(9.10) If" ( )1,an increase in W t(i)will reduce(raise)labour supply n t(i).p212.As a result of this correction,equation(9.13)and the equation above should readn t(i)= i A it( 1)W t P t(i) 11 i=1 u c;t W t "P t 1" 1HenceP t(i) P t =i A it( 1)W tP t"1u c;t W t "P t 1" 1#1 i(9.13)p212Second sentence after equation(9.13)should now read"Equation(9.13)implies that an increase in the economy-wide real-wage rate would raise the relative price of…rm i if" 1;but the response is unclear if" 1."p212Second sentence of the last paragraph and equation(9.14)should read: "In this case equation(??)becomes an implicit equation for the real wage, namely,1=A t( 1)W tP t"1u c;t W t "P t 1" 1#1 (9.14)p214Replace the eight and ninth equations on the page(i.e.at the end of the section9.3.3.2)byn t(i)=A 1i [1P tW t] y ty t(i)=A i[ 1P tW t] y t4p220The penultimate equation should bet= (1 )1X0 s E t[p t+s p t 1] and equation(9.23)should bet= (1 )1(p t p t 1)+ 1 E t t+1(9.23)p221replace the in‡ation equation in mid page byt= (1 )(p t p t 1)+ E t t+1+1 t 1p237Replace equation10.16byE(r)=r f (1+r f)Cov(m;1+r)(10.16) p237Replace equation10.17by= (1+r f)Cov(m;1+r)(10.17) p256second equation should bec A;t+1 c A;t =c B;t+1c B;tp378Replace fourth equation byy=y n+ v+"1+ 2p378Replace seventh equation by=12[ v+"1+ 2 k)]2+12(v"1+ 2+ k)2p378Replace next equation byE(Q)=12" 2 2v+ 11+ 2 2 2"+k2#+12 2v+ 1+ 2 2 2"+( )2k2!5p383Starting at the sixth equation insert the following:E(U CB)= 12[( )21++(1+ ) 2v]=(1+ )E(U P)>E(U CB)where U P is the public’s welfare."p383Replace"As the public’s welfare is independent of the value of it obtains no bene…t from having a central bank more antipathetic to in‡ation than itself: In contrast,the welfare cost of the central bank is a¤ected by the size of ."by"For the central bank the optimal value of is obtained from"p383End of the penultimate para add the following:"....having a large .But for the public@E(U P)@= 1+ 2>0;implying that the more conservative the central bank,the better o¤is the public."p384.Replace the…rst equation byE(U P)j C=E(U P)j D+12 1+2>E(U P)j Dp402After equation14.10replace"Noting that E t z t+s=e t for s 0,"by"Noting that E t z t+s=z t for s 0,and z t=e t;" p402Replace equation14.11byx t=11x t 1+G0e t+G1e t 1(14.11) 6which is a vector autoregressive/moving average model(VARMA)in the change in x t."p402Next para should read."Equation(14.11)describes the dynamic behaviour of changes in ln c t and ln k t following a technology shock e t.The precise path followed by the economy depends on the(deep)structural parameters of the model.The equation implies that the system returns to its steady state growth path following a temporary technology shock,but not to its original steady state as the temporary shock e t has a permanent e¤ect on technology z t and hence on ln c t and ln k t."p433The penultimate sentence should read"...that can be solved for y(t)."p450In equation(15.57)and the following three equations should read , and should read .p455Equation(15.66)should bey t=Q yx x t 1s=0Q yy s yy P E t z t+s(15.66)7。
