APPENDICES to Interest Rates and the Market for New Light Vehicles

Transcription

1 APPENDICES o Ineres Raes and e Marke or New Lig Veicles Adam Copeland Federal Reserve Bank o New York George Hall Brandeis Universiy Louis J. Maccini Jons Hopkins Universiy Augus 7, 28 A SUMMARY OF THE MODELS AND THE OPTIMALITY CONDITIONS In is appendix we re-sae e ouseold s and auomaker s problems and derive e irs-order condiions in secions A. and A.2. We lis e equaions deining a symmeric marke equilibrium (secion A.3), provide deails on ow o reormulae e model so a key variable are in raio orm or grow raes (secion A.4), demonsrae ow we eliminae e labor inpu and produciviy erms (secion A.5), and lis e equaions describing e seady sae o e marke equilibrium (secion A.6). In secion A.7, we repor e second-order condiions in e symmeric marke equilibrium and discuss su seady sae. cien condiions or an opimum a e To allow or an easier comparison o e paper, noe a equaions a are numbered (), (2), Te views expressed do no represen e views o e Federal Reserve Bank o New York or e Federal Reserve Sysem. Assisan Vice Presiden, Researc Group, Federal Reserve Bank o New York, 33 Libery Sree, New York, NY 45; pone (22) ; adam.copeland@ny.rb.org Proessor, Deparmen o Economics, Brandeis Universiy, 45 Sou Sree, Walam, MA ; pone: (78) ; gall@brandeis.edu Proessor Emerius, Deparmen o Economics, Jons Hopkins Universiy, 34 N. Carles Sree, Balimore, MD 228; pone: (4) ; maccini@ju.edu

2 ec. are e equaions a are saed in e paper. Te equaions a are numbered (A.), (A.2), ec are e equions saed solely in Appendix A. A. Models o e Houseold Sopping Cos Model Te represenaive ouseold underakes a wo-sage opimizaion process. In e irs sage, e ouseold minimizes e sopping coss o purcasing auomobiles. Te coss o purcasing an auomobile consis o bo purcase coss and sopping coss. Deine P j as e real price o a new auomobile o ype j and S j as e quaniy o new auomobiles o ype j purcased a ime. Ten P j S j is e real cos o purcasing new auomobiles o ype j a ime. Deine ( A j/a ) S j as e oal sopping cos o purcasing new auomobiles o ype j, were ( A j/a ) is e per uni sopping cos o purcasing new auomobiles o ype j, A j N j +Y j is e supply o new auomobiles available or sale in period by producer o ype j, N j is e sock o invenories o new auos o ype j eld by e producer o ype j auos a e end o period, Y j is e curren producion o new auomobiles by producer o ype j, A N + Y is e supply o new auomobiles available or sale in e indusry as a wole, N is e sock o invenories o all new auos in e indusry, Y is curren producion in e indusry as a wole, and were we assume a <. Ten, ( A j/a ) P j S j is e oal real sopping cos o purcasing new auomobiles o ype j valued a P j. Te oal real cos o purcasing new auomobiles o ype j, denoed by SC, is e sum o e purcase coss plus e sopping coss is en SC P j S j + Aj A apple P j S j + Aj A P j S j. () In e irs sage, e represenaive ouseold cooses S j o minimize Z apple + Aj A P j S j dj (2) subjec o were >. Te Lagrangian is applez S S j dj (3) Speciically, P j is e nominal price o new auomobiles o ype j divided by e price o consumpion, excluding car services. 2

3 Z apple L SC + Aj A P j S j dj + sc S applez S j dj #. Te irs-order condiion SC apple j Aj A P j sc Sj S (A.) were sc is e muliplier associaed wi aggregae sales. Solving equaion (A-) yields S j S apple Pj sc + Aj A. (A.2) Assume a sopping coss are ( A j/a )( A j/a ). Ten, e demand uncion or new auomobiles, (A.2) is S j S Pj sc Aj. A (A.3) To solve or sc, ake e deiniion o aggregae sales, equaion (3), and use equaion (A.3) o subsiue or S j o ge applez S Z 4( sc ( sc S j dj S Pj sc ) S 2 ) S 4 Z Aj Z P j A P j Aj A # Aj A # 3 dj5 # 3 dj5 3 dj5. (A.4) Solving equaion (A.4) or sc 2 4 Z P j Aj A sc yields # 3 dj5 Z P j Aj A ( ) dj# P, (A.5) were P is deined as e average real indusry price level. equaion (A.3), e demand uncion can en be wrien as Subsiuing equaion (A.5) ino 3

4 were S j S Pj P Aj (5). Tis is e demand uncion saed as equaion (5) o e paper. Uiliy Maximizaion Model In e second-sage, e represenaive ouseold is assumed o coose C, X, S,B, and D o maximize subjec o A X E o U(C,X ) (6) I C + P S +(r + µ) B (7) X ( )X + S < < (8) B ( µ) B + D <µ< (9) D P S apple apple () were C denoes consumpion, excluding car services, X is e sock o exising cars, S is purcases o new cars, I denoes real labor income, B represens e sock o car loans, D is new loans incurred o purcase auomobiles, P is e average real price o new cars, A is e sock o new auomobiles available or sale during period in e indusry as a wole, r is e real ineres rae on new car loans, is e racion o a new car purcase inanced by a new loan, is e rae a cars depreciae, and µ is e racion o exising loans a needs o be paid back every period. Assume a e uiliy uncion is were > and 2 >. Te Lagrangian is en U(C,X ) ln C + 2 ln X, () L H E n + ln C ln X I + C + P + S + (r + + µ) B + 2+ (( )X + S + X + )+ 3+ ( µ) B + P + S + B + i + ln C + 2 ln X + I C P S (r + µ) B + 2 (( )X + S X )+ 3 ( µ) B + P S B io Te irs-order condiions are: 4

5 @L E [ C ] (A.6) E o + [( ) 2+]+ [ 2 X 2 ] (A.7) E o n P P 3 o E o n + [ (r + + µ) + +( µ) 3+] 3 o (A.8) (A.9) Assuming a inormaion is known a ime, en e irs-order condiions and e consrains are: (2) C ( )E X 2+ (3) 2 P P 3 (4) o 3 E n( µ) 3+ (r + + µ) + (5) C + P S +(r + µ) B I (7) X ( )X + S < < (8) B ( µ) B + D <µ< (9) D P S apple apple () Tese are equaions (7) roug () and (2) roug (5) saed in e paper. A.2 Model o e Firm Te represenaive irm, irm j, produces and sells a single durable good, namely, a ype o new auomobile, ype j. Te irm is assumed o be an inegraed dealer-producer. Te irm is also a monopolisic compeior a aces a socasic downward-sloping demand curve or is produc 5

6 and a variable and socasic ineres rae a wic i discouns uure prois. Eac period, e represenaive irm, irm j, maximizes: X PV j E o s s j (6) were s +r 2s (7) j P j P S j W P L j K j (8) subjec o: S j Pj Aj S > > (9) P A apple Aj K j apple o N j apple > apple > (2) S j A j N j + Y j (2) A j A j S j + Y j (22) Y j j L j < < (23) were P j is e real price irm j ses or an auomobile o ype j, S j is sales o auomobiles o ype j by irm j, L j is labor services, N j is e sock o invenories o irm j o inised auomobiles a e end o e period, A j is e sock o goods available or sale during period, Y j is e oupu o auomobiles o ype j, j is labor produciviy, r 2 is e real ineres rae aced by e irm, K j is invenory sorage coss, S, is indusry sales, N is e indusry sock o invenories o inised auomobiles a e end o e period, P is e real indusry price level, and W is e real wage rae. In e auo indusry, newly produced veicles are ypically sipped wiin days o dealers los; ence we assume e socks o goods or sale, A j, is e sum o residual invenories rom e previous period and newly produced veicles. Using e deiniion o A j invenory sorage coss, equaion (2), can be wrien as 6

7 apple Aj Nj + Y apple j K j apple o N j apple o N j. S j S j Now, use equaion (9) o eliminae price as an explici coice variable and rewrie equaion (2) o ge N j A j Y j ; en ne revenues, equaion (8), can be wrien as Sj j S A j A S W P L j apple o Aj S j apple (A j. Y j). (24) Te irm en cooses S j, Y j, A j, and L j o maximize equaion (6) subjec o equaions (22) and (23) and were ne revenue is now deined in equaion (24) and e discoun acor is again given by equaion (7). Te Lagrangian is L F E o (... + Sj+ s s apple o Aj+ S j+ S Sj s s A j+ A + S+ W + P + L j+ apple (A j+. Y j+)+ + (A j S j + Y j+ A j+) S + 2+ j+ L j+ Y j+ # A j A S W P L j apple o Aj S j apple (A j. Y j) + (A j S j + Y j A j )+ 2 ( j L j Y j ) #) Te irs-order condiions are F E j Sj S A j A + apple o apple Aj S j apple Aj. S j Y j E + + ) F apple Aj E o apple o j S j 2 (A.) 7

8 F E o E + + j Sj S apple o Aj S j apple A j A apple Aj S j S A Aj S j Y j # + ) F E o 2 jl j W P (A.3) 2 were and are e mulipliers associaed wi e available-supply-accumulaion process and e producion uncion, equaions (22) and (23), respecively. Assume a inormaion regarding exogenous variables is known a ime, en e irs-order condiions and e consrains are E + + Sj S A j A apple Aj Aj. + appleo apple S j S j Y j (25) + apple o Aj S j apple 2 (26) E Sj S A j A S A apple o Aj S j apple apple Aj S j Aj S j Y j # + (27) 2 jl j W P (28) A j N j + Y j (2) A j A j S j + Y j (22) Tese are equaions (25) roug (28) and (2) and (22) saed in e paper. A.3 A Symmeric Marke Equilibrium We solve or a symmeric equilibrium. Firms make coices believing eir irs order condiions and consrains are given by equaions (2) roug (28). Bu since all irms are idenical and 8

9 e oal mass o irms in e economy is uniy, in equilibrium S j S, A j A, L j L, Y j Y, and j. Tus eir opimizing beavior makes ese opimaliy condiions become in equilibrium apple A A. + apple o apple S S Y E + + (A.4) E A S apple A apple o + S 2 (A.5) apple apple apple A o S apple A A Y S S + (A.6) 2 L W P (A.7) A A S + Y (A.8) Y L. (A.9) For e ouseold in marke equilibrium, e opimaliy condiions and e consrains are C (2) ( ) E X 2 (3) 2 P + P 3 (4) ( µ) E 3+ E (r + + µ) + 3 (5) C + P S +(r + µ) B I (7) X ( )X + S (8) B ( µ) B + P S. (A.2) 9

10 Te marke equilibrium model us conains ireen equaions in ireen endogenous variables: S, Y, A, L, C, P, X,B,, 2, 3,, and 2. A.4 Raios and Grow Raes Our esimaion approac relies on e daa being saionary. Aloug uni sales o lig veicles and e irms and ouseolds ineres raes are saionary, ere are rends in real prices, real wages, and real disposable income. Consequenly, we reormulae e model so a e relevan variables are in raio orm. Tese raios are saionary and us guard agains any saisical problems wi nonsaionary imeseries. Deine e ollowing raios and grow raes: R CI C I R PSI P S I R PXI P X I R BI B I R AI A I R AS A S R YS Y S LS W L P Y R YL Y L I (+i ) I P (+p ) P S (+s ) S Y (+y ) Y L (+l ) L (+ ) W (+w ) W were i is e grow rae o real income, p is e grow rae o e real price o auomobiles, s is e grow rae o real sales, y is e grow rae o oupu, l is e grow rae o labor, is e grow rae o labor produciviy, and w is e grow rae o real wages. Te deiniion o raios generaes ree addiional equaions a relae raios o grow raes. In paricular, observe a e raios, R PSI, R YS, and LS can be wrien as R PSI P S I ( + p ) P ( + s ) S ( + p )(+s ) ( + i ) I ( + i ) R PSI (A.2) R YS Y S ( + y ) Y ( + s ) S ( + y ) ( + s ) RYS (A.22) LS W L P Y ( +! )(+l ) W L ( + p )(+y ) P Y ( +! )(+l ) ( + p )(+y ) LS. (A.23) We now sow a, using e raios and grow raes and eliminaing labor inpu, e model reduces o a sysem o ieen equaions and ieen endogenous variables. Using e raios and grow raes, e equaions o e model consising o equaions (A.4)-

11 (A.2), (7)-(8), (2)-(5), and (A.2)-(A.23) can en be wrien as R CI ( + p + ) ( ) E ( + i + ) R PXI µ E +i + E apple o R CI + R PSI + R AS R AS +i (A.24) 2 (A.25) (A.26) r+ + µ 3+ E + 3 (A.27) +i + r + µ R BI (A.28) ( ) ( + p ) ( + i ) RPXI + R PSI R PXI + apple o apple R AS apple apple R AS ( µ) ( + i ) RBI + R PSI R BI apple apple o R AS R AS R AS (A.29) (A.3) R YS E + + (A.3) apple + 2 (A.32) i R YS + (A.33) 2 LS (A.34) R AS + R YS ( + s ) R AS ( + s ) (A.35) y + l (A.36) ( + p )(+s ) R PSI ( + i ) R PSI (A.37) ( + y ) ( + s ) RYS R YS (A.38) ( +! )(+l ) ( + p )(+y ) LS LS (A.39) were I, 2 I 2/P, and 3 I 3. Tere are us sixeen equaions in sixeen endogenous variables: R CI, R PSI, and 2., R PXI, R BI, R AS, R YS, LS, p, s,y, l,, 2, 3, A.5 Reduced Model: Eliminaing Labor Inpu and Produciviy Grow To eliminae labor inpu, solve equaion (A.36) or l o ge l (y ). (A.4)

12 Subsiue equaion (A.4) ino equaion (A.39) o ge Now, solve equaion (A.4) or LS ( +! ) + y ( + p )(+y ) o ge LS. (A.4) + y LS ( + p )(+y ). (A.42) LS ( +! ) Lagging equaion (A.42), muliplying e resuling equaion by,and subracing a equaion rom equaion (A.42) yields ( )+y y LS ( + p )(+y ) LS ( +! ) Bu, rom equaion (39) in e paper, + LS ( + p )(+y ). (A.43) LS 2 ( +! ) ( )+. (A.44) Subsiuing equaion (A.44) ino equaion (A.43) and rearranging erms yields y ( )( )+ y + ( + p )(+y ) ( +! ) LS LS ( + p )(+y ) ( +! ) LS LS 2 +. (A.45) Having eliminaed l, e model reduces o ieen equaions in ieen endogenous variables. 2

13 A.6 Seady Sae: Marke Equilibrium Te seady sae o e model is were + R CI ( + p) ( ) +i R PXI (A.46) 2 (A.47) (A.48) µ r + µ 3 3 (A.49) +i +i R CI + R PSI r + µ + R BI (A.5) +i ( + p) ( ) +i RPXI + R PSI R PXI (A.5) R AS ( µ) +i RBI + R PSI R BI (A.52) + apple o apple R AS apple R AS R YS apple o R AS apple + (A.53) 2 (A.54) apple o R AS apple apple apple R AS R AS R YS + (A.55) 2 LS (A.56) R AS + R YS ( + s) R AS ( + s) (A.57) + p + s i (A.58) y s (A.59) (p!) ȳ (A.6) /+r 2. Te seady sae now consiss o ieen equaions in ieen endogenous variables: R CI, R PSI, R PXI, R BI, R AS, R YS, LS, p, s, y,, 2, 3, and 2. 3

14 A.7 Second-Order Condiions in Symemeric Marke Equilibrium Te second-order condiion or a maximum is a e bordered Hessian mairx associaed wi e Lagrangian mus be negaive deinie. Deine (C,S ) C + P S +(r + µ) B I (A.6) 2 (X,S ) ( )X + S X (A.62) 3 (B,S ) ( µ) B + P S B (A.63) Ten e relevan bordered Hessian marix is: @ Te second-order condiions or e ouseold in marke equilibrium saed in raio orm are I2 I 2 C 2 I 2 R CI X 2 P 2 P 2 I 2 I 2 2 X 2 2 P 2 I 2 R PXI @S @2 @2 @2 @2 @2 (A.68) (A.69) (A.7) 4

15 @2 L P P S I A I S A R PSI R AS R P P S I A I S A R PSI R AS R AI 3 (A.76) For e irm, assume in marke equilibrium a S j S, A j A, L j L, Y j Y, and j.and using e raios, R AS A /S R YS Y /S LS WL /P Y. Te second-order condiion is a e bordered Hessian mairx associaed wi e Lagrangian mus be negaive deinie. Deine g (Y j,a j ) A j S j + Y j A j (A.77) g 2 (Y j,l j ) j L j Y j (A.78) Ten e relevan bordered Hessian marix is: 2 @g @g @g j A j S j S 2 j Y j Y j A 2 j A j L j L 2 j

16 Ten e second-order condiions or e irm in marke equilibrium saed in raio orm 2 apple apple S S + apple o apple A S apple apple A. S + apple o apple ( + apple ) R AS Y S apple R AS ( + apple ) (A.79) R 2 2 apple S A apple o apple A A S apple S S S A A apple R AS R AS S apple apple +apple + Y apple o apple A S apple o apple apple apple +apple + R AS ( apple ) (A.8) A Y S ( apple ) S apple +apple + R YS A R AS i ( apple 2 ( ) 2 L 2 ( ) Y 2 ( L L ) LS R YL L (A.82) were we ave used e resul a 2 WL /P Y LS rom e apple o apple A S S A S S A apple R AS S A S + apple o apple A apple S + apple o apple A S apple o apple R AS apple+ A A. apple S + apple o apple A S + apple o apple R AS apple+ apple+ S apple A S apple A S apple + apple apple S A R AS Y ## + Y A Y S S A R YS ## + ## + R AS (A.83) (A.84) i A apple apple o apple S apple apple o R AS apple S (A.85) (A.86) 6

17 @Y L 2 j L j Y R YL j j Te second-order condiions or e ouseold in seady sae are @A j 2 Ī 2 RCI P 2 I 2 RPXI @S @2 @2 @2 @2 @2 @2 L @S R PSI R AS R AI (A.95) (A.96) (A.97) (A.) 7

18 3 R PSI R AS R @X For e irm, e second-order condiions in seady sae are: 2 S apple + apple o apple R AS apple R AS R YS i ( + apple ) 2 2 S R AS R AS apple o apple R AS apple apple+apple + R YS R AS ( apple ) # 2 ( ) LSR YL L (A.6) apple o apple R S R AS + apple o apple R AS apple + apple apple R AS R YS R AS + apple apple o R AS A L (A.9) (A.) (A.) 8

19 @A j R YL @A j (A.4) Because o e presence o e rending variables, S, P,B,I, and C, e bordered Hessians are no saionary even wi e model in raio orm. Tus we evaluaed e bordered Hessians using e esimaed parameers, e relevan seady-sae raios, and values or e rending variables a are consisen wi e seady sae. In ese cases, e bordered Hessian marices were negaive deinie, saisying a su cen condiion or an inerior maximum. B DATA DETAILS In appendix B we provide more inormaion on e consrucion o e daa, ollowed by analysis o some o e key variables. B. Daa Consrucion To consruc e imeseries o domesic sales, domesic oupu, domesic invenories, and average price or lig rucks, some work is required. Te BEA publises domesic lig rucks sales rom 972 onward, bu no domesic producion nor domesic invenories. From 985 onward, Ward s Auomoive provides deailed daa on lig ruck invenories or e Unied Saes. Aloug is measure includes some oreign lig ruck invenories, we use is measure as an approximaion o domesic invenories. Te key assumpion beind our approximaion is a canges in Ward s invenories relec mainly canges in domesic invenories, a reasonable conjecure given a lig rucks are dominaed by U.S. manuacurers. Because Ward s daa reaces back only o 985, we use a di eren ecnique o approximae domesic invenories rom 972 o 985. We assume a e days supply igures or lig rucks and auomobiles are equal over is period. Days supply is a measure o e number o days veicles can be sold a e curren rae ou o e curren sock o invenories. Tis saisic is oen used in e indusry as a gauge o weer auomakers are olding oo many or oo ew veicles in invenory. Hence, we are assuming a auomakers coose o arge e same days supply igures or auomobiles and lig rucks. Indeed, rom 985 onward, days supply or auomobiles and lig rucks as a correlaion o.69. An advanage o is approac is a auomoive days supply will pick up macroeconomic socks and allow us o incorporae em ino 9

20 our domesic lig ruck invenory measure. Wi lig ruck domesic sales and our esimae o days supply, we can back ou domesic lig ruck invenories rom 972 o 985. Finally, we use e ime series o domesic sales and invenories o back ou domesic lig ruck producion. 2 We consruc e average price or lig rucks using quarerly daa on personal consumpion expendiures and privae invesmen. 3 Beore 987, only invesmen in rucks is publised. We approximae e level o lig ruck invesmen rom 972 o 986 by assuming a lig ruck invesmen as e same grow rae as oal ruck invesmen over is ime period. We en divide e sum o e personal consumpion expendiures and privae invesmen by uni sales o arrive a an average price. Tis average price is or all lig rucks, bu we assume i is a good approximaion o domesic lig rucks based on e small marke sare o oreign lig rucks. Because we compued average prices or lig rucks a e quarerly requency, we use linear inerpolaion o consruc a monly series. B.2 Addiional Analysis o Sales, Producion, Invenories, and Price In looking a e daa on e grow raes o sales, producion, invenories, and real price, we see e well-known sylized acs a e grow raes o sales and oupu ave a ig correlaion o.64 and are quie volaile over our sample period, wi sales being less volaile an oupu (e.g., see Bresnaan and Ramey 994). Tis volailiy is illusraed in igure B.. Comparing sales and oupu grow wi real price grow in igure B.2 igligs e inding a e percenage canges in real prices are subsanially smaller an sales and oupu. Over e sample period, real prices are somewa posiively correlaed wi sales and oupu, wi correlaion coe o.26 and.35, respecively. ciens Given is paper s ocus on ineres raes, we consider ow prices, sales, and oupu lucuae wi ineres raes in e daa. Over our sample period, we ind a e percenage canges in irms real ineres rae and in real prices are posiively correlaed (e correlaion coe is.52), a paern illusraed in igure B.2. Given e ig correlaion beween irms and e ouseolds ineres raes, i is no a surprise o ind e same posiive correlaion beween e percenage canges in ouseolds real ineres rae and in real prices. Finally we also ind a e percenage canges in irms ineres rae are posiively correlaed wi e percenage canges in sales and oupu, wi correlaion coe ciens o.22 and.6, respecively. cien In addiion o e grow raes o sales, oupu, and real prices, e model makes predicions abou e raios o oupu o sales and o available supply o sales. Available supply is equal o 2 We cecked our inerred measure o domesic lig ruck producion agains U.S. lig ruck assemblies. As expeced, e correlaion beween ese wo series is a ig.976. Furermore, domesic producion is ypically iger an U.S. assemblies; e average di erence beween monly domesic lig ruck producion and U.S. assemblies is more an 44, unis. 3 Because governmen invesmen in lig rucks is small and, or mos o e ime periods we examine, no publised separaely rom medium and eavy ruck invesmen, we do no include i in our average price calculaions. 2

21 8 6 4 monly rae Sales grow Oupu grow Figure B.: Grow Raes o Sales and Oupu, Real price grow (le axis) Firm real ineres rae (rig axis) 5 monly rae - 5 percen, annualized rae Figure B.2: Firm s Real Ineres Raes and Real Prices,

22 . 5.5 Raio o available supply o sales (le axis) Raio o veicle expendiures o income (rig axis) Figure B.3: Raios o Available Supply o Sales and Lig Moor Veicle Expendiure o Income, e sock o invenories a e beginning o e mon plus a mon s oupu, and e raio o available supply o sales is commonly used in e indusry as a gauge o ow well producion and sales are aligned. Over e sample period, we ind a bo raios are rougly consan, aloug quie volaile. B.3 Addiional Analysis o Personal Disposable Income and Consumpion Turning o e raio o lig moor veicle expendiure over income, we ind a i lucuaes around.5 or mos o our sample bu sars a gradual decline o.3 saring around 2 (see e doed line in igure B.3). No surprisingly, e raio o non-moor veicle expendiure o income is rougly e mirror image o e raio o lig veicle expendiure o income. In our model, available supply, measured as e beginning-o-period sock o invenories plus curren producion, plays a large role in bo e irm s and e ouseold s problem. In equilibrium, canges in available supply ave a number o direc and indirec impacs on prices and sales. To gain a roug sense o ow available supply, sales, prices, and income lucuae ogeer, we consider e comovemen beween e raios o available supply o sales and o lig veicle expendiures and income. As illusraed in igure B.3, ese wo raios are negaively correlaed, wi a correlaion coe cien o -.6; aloug par o e correlaion may be mecanical as auomobile sales appears in e denominaor o one raio and e numeraor o e oer. Te negaive correlaion suggess a a main orce in e model is a manuacurers use invenories o smoo producion, as available supply ends o grow relaive o sales wen ouseolds reduce e amoun o income ey spend on moor veicles. 22

23 C ADDITIONAL FIGURES Te igure C. illusraes e di erences in e persisence o innovaions o e ineres raes. All innovaions are cosen o creae a basis poin increase in e ouseold or irm s ineres rae relaive o seady-sae in mon. Te evoluion o e raes aer e sock illusrae e di erence degrees o persisence or ree cases: an idiosyncraic sock o e ouseold s rae, an idiosyncraic sock o e irm s rae, a sock o e common componen o ineres raes Dierence rom seady-sae Houseold IR aer idiosyncraic sock Firm IR aer idiosyncraic sock Firm IR aer common componen sock Mons Figure C.: Persisence o Ineres Rae Socks 23

24 Reerences Bresnaan, Timoy and Valerie Ramey Oupu Flucuaions a e Plan Level. Quarerly Journal o Economics 9(3),