Interest Rates and the Market For New Light Vehicles

Transcription

1 Federal Reserve Bank of New York Saff Repors Ineres Raes and he Marke For New Ligh Vehicles Adam Copeland George Hall Louis Maccini Saff Repor No. 741 Sepember 2015 This paper presens preliminary findings and is being disribued o economiss and oher ineresed readers solely o simulae discussion and elici commens. The views expressed in his paper are hose of he auhors and do no necessarily reflec he posiion of he Federal Reserve Bank of New York or he Federal Reserve Sysem. Any errors or omissions are he responsibiliy of he auhors.

2 Ineres Raes and he Marke for New Ligh Vehicles Adam Copeland, George Hall, and Louis Maccini Federal Reserve Bank of New York Saff Repors, no. 741 Sepember 2015 JEL classificaion: E44, G31 Absrac We sudy he impac of ineres rae changes on boh he demand and supply of new ligh vehicles in an environmen where consumers and manufacurers face heir own ineres raes. An increase in he consumers ineres rae raises heir cos of financing and hus lowers he demand for new vehicles. An increase in he manufacurers ineres rae raises heir cos of holding invenories. Boh channels have equilibrium effecs ha are amplified and propagaed over ime hrough invenories, which serve as a way o boh smooh producion and faciliae greaer sales a a given price. Through he esimaion of a dynamic sochasic marke equilibrium model, we find evidence of boh channels a work and of he imporan role played by invenories. A emporary 100 basis poin increase in boh ineres raes causes vehicle producion o fall 12 percen and sales o fall 3.25 percen a an annual rae in he shor run. Key words: ineres raes, auomobiles, invenories, Bayesian maximum likelihood Copeland: Federal Reserve Bank of New York ( adam.copeland@ny.frb.org). Hall: Brandeis Universiy ( ghall@brandeis.edu). Maccini: Johns Hopkins Universiy ( maccini@jhu.edu). The auhors hank James Kahn, Adrian Pagan, and numerous seminar paricipans for houghful commens. The views expressed in his paper are hose of he auhors and do no necessarily reflec he posiion of he Federal Reserve Bank of New York or he Federal Reserve Sysem.

3 1 Inroducion This paper measures he dynamic response of real prices, sales, producion, and invenories o changes in real ineres raes for a paricular durable goods marke new cars and ligh rucks. This is an imporan issue because he marke for durable goods is a key channel hrough which moneary policy a ecs he real economy. Changes in real ineres raes a ec boh sides of he marke for durable goods. For consumers who purchase durable goods on credi, higher real raes increase he cos of borrowing, inducing a decline in demand. Hence, sales and real prices should fall. Depending on he speed wih which manufacurers reduce producion in response o his shock, invenories may rise or fall in he shor run. We refer o he e ec of higher real ineres raes on consumer purchases of durable goods as he household expendiure channel. For manufacurers of durable goods, higher real ineres raes raise he cos of holding invenories, inducing hem o economize on invenories by cuing real prices o raise sales and by reducing producion. However, if higher invenories faciliae sales by making i easier for consumers o be mached wih he precise produc hey wan, he reducion in invenories will dampen sales. Hence, he overall impac of higher real ineres raes on manufacurers sales is ambiguous. We refer o he e ec of higher real ineres raes on durable goods producers as he firm invenory channel. These counervailing forces sugges ha he responses of sales and invenories o changes in ineres raes may be nonmonoonic, helping explain why previous research has found lile e ec of real ineres raes on hese wo variables in durable goods markes. We analyze how changes in real ineres raes a ec he U.S. marke for new cars and ligh rucks hrough he household expendiure and firm invenory channels. New moor vehicles are he quinessenial durable good comprising a lile over 25 percen of all durable goods expendiures by U.S. households. Furhermore, given he indusrial organizaion of he marke for new vehicles, we expec ineres raes o a ec boh sides of he marke. On he supply side, he vas majoriy of auomobiles are buil o sock, wih he ypical dealer holding hree monhs of sales in invenory. Because ineres raes are an imporan componen of invenory holding coss, heory suggess ha firms will reduce invenory levels in response o increases in ineres raes. 1 On he demand side, higher real ineres raes raise he oal cos of buying a vehicle for many consumers. In addiion, he purchase of any durable good has an ineremporal componen; he more he consumer discouns he fuure, he lower he reurn is o he consumer from buying he good in he presen period. Consequenly, we expec higher ineres raes o dampen consumer demand. Alhough he auomobile marke is well suied for assessing he responses of boh firms 1 For he sample of dealerships repored in appendix 1 of Baines and Courchane (2013), from 2002 o 2011 hese floorplan ineres expenses averaged $288,000 per year per dealership or $166 per vehicle sold. The average gross profi per new vehicle sold was roughly $2,300, so ha hese ineres coss represen roughly 7 percen of gross profis. 1

4 and consumers o ineres rae changes, he mechanisms we idenify should apply o oher durable goods indusries as well. We consruc a dynamic model of he marke for new auomobiles ha embeds hese wo channels. On he demand side, he model consiss of a represenaive household ha incurs shopping coss when deciding on which cars o purchase and chooses beween overall purchases of new auomobiles and oher consumpion goods o maximize is discouned flow of expeced uiliy. The household faces a sochasic ineres rae a which i can borrow and finances new car purchases wih income and loans. On he supply side, he model consiss of a represenaive producer of new auomobiles. This firm is a monopolisic compeior ha maximizes he discouned flow of expeced profis. The firm faces a sochasic ineres rae and holds invenories o faciliae sales. Specifically, higher available supply ha is, beginning-of-period invenories plus curren producion reduces he household s shopping coss. The soluion of our model deermines he equilibrium real prices, sales, and oupu of new cars. There are high-qualiy daa on auomobiles, from oal sales and oupu by producers o household expendiures on auomobiles. Combining hese imeseries wih daa on ineres raes faced by producers and by households, we consruc a panel daase of monhly daa from 1972 o Wih hese daa, we esimae our model by means of a Bayesian maximum likelihood procedure. As evidence of goodness of fi, we demonsrae ha our esimaed model successfully replicaes resuls from recursive vecor auoregressions, which indicae ha an increase in ineres raes paid by households and firms generaes a modes bu significan reducion in boh he raio of oupu o sales and he raio of available supply o sales. We find ha changes in he ineres raes faced by firms and consumers have a significan impac on he auomobile marke a he monhly frequency. A 100 basis-poin increase in boh ineres raes causes auomobile producion o fall nearly 12 percen and sales o fall 3.25 percen a an annual rae. Since producion falls by more han sales, available supply relaive o sales also decreases. If we assume ha 17 million new cars and ligh rucks are produced and sold in he Unied Saes each year, his response ranslaes ino abou 170,000 fewer cars produced and 46,000 fewer cars sold in he firs wo monhs afer he shock. The growh rae of sales remains below is seady sae for abou six monhs; for many monhs hereafer, sales growh slighly exceeds is seady-sae rae and only slowly drops back o he seady sae. Our heory implies ha firm-side and consumer-side responses reinforce each oher in he equilibrium and ha invenories play a key role in amplifying he impac on sales. Neverheless, since boh oupu and sales fall, he impac of higher ineres raes on he raio of available supply o sales is small. We build on a subsanial lieraure on he marke for auomobiles. The vas majoriy of sudies focus on eiher he consumer/demand side or he firm/supply side. On he demand side, much of he work focuses on he role of credi consrains in he auo loan marke. Examples are Chah, Ramey, and Sarr (1995); Alessie, Devereux, and Weber (1997); Ludvigson (1998); and 2

5 Aanasio, Goldberg, and Kyriazidou (2008). 2 This lieraure, however, does no explicily model he supply side of he marke. We cerainly agree ha credi consrains on boh consumers and firms play an imporan role in he auo marke beyond simply he posed ineres rae. 3 However, our model suggess ha ineres-rae changes will a ec sales hrough boh he demand side and he supply side. Hence, a marke analysis is needed o undersand he impac ha ineres raes, credi marke condiions, and moneary policy have on sales in he marke for auomobiles. On he supply side, a number of sudies of auomobile firms have explored he relaionship beween invenories and producion. See, for example, Blanchard (1983); Kahn (1992); Kashyap and Wilcox (1993); Ramey and Vine (2006); and Copeland and Hall (2011). However, his lieraure akes quaniy demanded as given. Furhermore, his lieraure assumes ha real ineres raes are consan and hus does no address he e ecs of ineres raes on auomobile producion and invenories. This gap highlighs a broader puzzle in empirical research on invenories: over a long period of ime, very few sudies have uncovered a significan relaionship beween real ineres raes and invenories. 4 This is an imporan issue for several reasons. One is ha, in heory, moneary policy changes shor-erm real ineres raes and hereby influences invenory invesmen. The oher is ha he financial press is filled wih ad hoc saemens of how ineres raes a ec invenories boh by influencing he cos o firms of holding invenories and by a ecing sales, which, in urn, cause changes in invenory posiions. 5 The lack of empirical evidence on he mechanism by which real ineres raes a ec invenories is herefore roubling. Since our analysis aemps o look a boh he consumer-side and he firm-side decisions simulaneously, his paper builds mos closely on he work of Blanchard and Melino (1986), who also develop a model of he marke for auomobiles. 6 There are wo primary innovaions in our model relaive o heirs. Firs, we allow real ineres raes o be variable and sochasic. We are hus able o explore he e ecs of real ineres raes on sales, producion, prices, and invenories in he marke, which hey canno do. We also disinguish beween he real ineres raes faced by households and hose faced by firms. Second, Blanchard and Melino model he auomobile indusry as a perfecly compeiive one. In conras, we assume ha producers of auomobiles 2 Addiional influenial papers on he demand for auomobiles include Adda and Cooper (2006), Copeland (2014), Eberly (1994), and Schiraldi (2011). 3 In he recen financial crisis, despie a Fed Funds rae near zero, many consumers were unable o obain new car loans, which conribued o a plumme in auo sales and pushed G.M. and Chrysler ino bankrupcy. 4 See Blinder and Maccini (1991) and Ramey and Wes (1999) for surveys of he lieraure. Maccini, Moore, and Schaller (2004, 2015) are excepions in ha hey provide evidence ha invenories respond o long-run movemens or regime shifs in real ineres raes. However, hey rea sales as given and herefore do no ake up he e ec of real ineres raes on invenories operaing hrough sales. 5 A search of indusry publicaions such as Auomoive News and WardsAuo.com illusraes ha dealers are keenly aware of hese expenses in aricles wih headlines such as Ineres rae spike would rim invenories: The indusry could live wih a modes increase. See LaReau (2013). 6 In he lieraure on indusrial organizaion, here are papers ha model boh sides of a durable goods marke, such as Nair (2007), Eseban and Shum (2007), Goeler and Gordon (2009), Copeland, Dunn, and Hall (2011), and Chen, Eseban, and Shum (2013). Relaive o our paper, his lieraure focuses on di eren quesions and employs di eren mehods. 3

6 are monopolisic compeiors, and we develop a shopping-cos model for he household o decide on auomobile purchases, which yields a demand funcion for new auomobiles ha firms face. As in Bils and Kahn (2000), he demand funcion implies ha invenories play a producive role in simulaing demand. In he remainder of his paper, we presen our model of he marke for new auomobiles, discuss he consrucion of our daase, presen esimaes of he model parameers, and illusrae he dynamic responses o ineres rae shocks of key variables in our model. 2 Model of he Marke for New Auomobiles 2.1 Model of he household The represenaive household underakes a wo-sage opimizaion process. In he firs sage, he household minimizes he shopping coss of purchasing auomobiles. Given his oucome, in he second sage he household maximizes uiliy. In he firs sage, he household minimizes he coss of purchasing auomobiles. The coss consis of boh purchase coss and shopping coss. Define P j as he real price of a new auomobile of ype j and S j as he quaniy of new auomobiles of ype j purchased a ime. 7 Then P j S j is he real cos of purchasing new auomobiles of ype j a ime. Define j, where Aj Aj A A S j as he oal real shopping cos of purchasing new auomobiles of ype is he real per uni shopping cos of purchasing new auomobiles of ype j, A j = N j 1 + Y j is he supply of new auomobiles available for sale in period by producer of ype j, N j 1 is he sock of invenories of new auos of ype j held by he producer of ype j auos a he end of period 1, Y j is he curren producion of new auomobiles by producer of ype j, A = N 1 + Y is he supply of new auomobiles available for sale in he indusry as a whole, N 1 is he sock of invenories of all new auos in he indusry, Y is curren producion in he indusry as a whole, and where we assume ha 0 < 0. The basic idea is ha he shopping cos o he household declines he higher is he supply of new cars ha firm j has available for sale relaive o he supply of new auomobiles available for sale in he indusry as a whole. The higher he supply of invenories ha firm j has available for sale, he higher he probabiliy is ha here will be a mach beween he household s decision o buy an auomobile of ype j and firm j. 8 Aj Then, A P j S j is he oal real shopping cos of purchasing new auomobiles of ype j valued a P j. Finally, he oal real cos of purchasing new auomobiles of ype j is he sum of he purchase coss plus he shopping coss, or 7 Specifically, P j is he nominal price of new auomobiles of ype j divided by he price of consumpion, excluding car services. 8 See Jung and Yun (2007) for a similar specificaion of shopping coss ha is used o derive a demand funcion faced by a monopolisic firm. 4

7 P j S j + Aj A apple P j S j = 1+ Aj A P j S j. (1) Now, in he firs sage, he represenaive household chooses S j o minimize ˆ 1 0 apple 1+ Aj A P j S j dj (2) subjec o appleˆ 1 S = 0 S 1 j dj where >1. Assume ha shopping coss ake he form Aj A = Aj A 1 (3) 1 (4) wih <0. Then, in appendix A we show ha he soluion o his problem yields a demand funcion for new auomobiles of ype j of he form S j = Pj Aj S (5) P A where S is he aggregae purchases of new auomobiles, P is he average real price of new auomobiles, and = > 0. This is he demand funcion faced by he firm ha produces new auomobiles of ype j. We refer o as he own-price elasiciy and o as he available-supply elasiciy of he demand for new auomobiles. In he second sage, he represenaive household is assumed o choose C, X, S,B, and D o maximize X 1 E o U(C,X ) (6) subjec o =0 C + 1 P S + r 1 B 1 + µb 1 = I (7) X =(1 )X 1 + S 0 < <1 (8) B =(1 µ) B 1 + D 0 <µ<1 (9) D = P S 0 apple apple 1 (10) 5

8 where C denoes consumpion, excluding car services, X is he sock of exising cars, S is purchases of new cars, I denoes real labor income, B represens he sock of car loans, D is new loans incurred o purchase auomobiles, P is he average real price of new cars, r 1 is he real ineres rae on new car loans, is he fracion of a new car purchase financed by a new loan, is he rae ha cars depreciae, and µ is he fracion of exising loans ha needs o be paid back every period. Following a number of papers in he lieraure, for example, Blanchard and Melino (1986) and Alessie, Devereux, and Weber (1997), we rea he sock of cars as a coninuous variable and he household as a represenaive one whose purchases add o he sock of cars. The household derives uiliy from he services provided by he auomobiles i possesses, which is proporional o he sock of auomobiles where he proporionaliy facor is normalized o uniy, and from consumpion of goods oher han auomobiles, which we will refer o simply as consumpion. As equaion (8) indicaes, purchases of new auomobiles, S, add o he sock, which in urn also depreciaes a rae. Purchases of new auomobiles are financed in par wih income, 1 P S, and in par wih new loans, D = P S. The budge consrain, equaion (7), incorporaes he paymen of ineres on loans, r 1 B 1, and he amoun of he sock of loans ha is paid back each period, µb 1, where he fracion ha is paid back is assumed o be consan. Assume ha he uiliy funcion is U(C,X ) = 1 ln C + 2 ln X (11) 1 > 0 2 > 0 and use equaion (10) o eliminae D. The firs-order condiions are hen 1 C = h 1 (12) (1 ) E h X = h 2 (13) h 2 1 P h 1 + P h 3 = 0 (14) h (1 µ) E 3+1 E (r µ) h 1+1 = h 3 (15) ogeher wih equaions (7), (8), and (9). The endogenous variables are hen C, X, S,B and he mulipliers are h 1, h 2 and h 3. The household expendiure channel is embodied in hese firs-order condiions. The hree mul- 6

9 ipliers represen he marginal uiliy of consumpion ( h 1 ), he marginal uiliy of he auomobile sock ( h 2 ), and he marginal disuiliy from consumer auomobile deb ( h 3 ). The firs-order condiion, equaion (14), saes ha he cos o he household from purchasing more auos is he sum of 1 P imes he cos of he forgone curren period consumpion and P imes he disuiliy of more deb. Since he household choice beween C and S depends on fuure ineres raes, an increase in he curren ineres rae, r 1, acs jus like a drop in income, reducing he demand for boh goods. An increase in nex period s ineres rae r 1+1 increases fuure disuiliy of auo deb, hus increasing he price of purchasing a new auomobile relaive o nonauo consumpion. 2.2 Model of he firm We consider a represenaive firm, firm j, ha produces and sells a single durable good, namely, a ype of new auomobile, ype j. The firm is an inegraed dealer-producer. 9 The firm is a monopolisic compeior ha faces a sochasic downward-sloping demand curve for is produc and a variable and sochasic ineres rae a which i discouns fuure profis. Each period, he represenaive firm, firm j, maximizes: X 1 PV j = E o s=0 s =0 j (16) where s = 1 1+r 2s (17) subjec o: j = P j P S j W P L j K j (18) S j = Pj P Aj S >1 >0 (19) A apple1 Aj K j = apple o N j 1 apple 1 > 0 (20) S j A j = N j 1 + Y j (21) A j = A j 1 S j 1 + Y j (22) 9 We inegrae he dealership ino he auomaker and consider a unified pricing decision. See Blanchard (1983, page 370) for he argumen for reaing he manufacurer and he dealer as a single eniy. 7

10 Y j = j L j 0 < <1 (23) where P j is he real price firm j ses for an auomobile of ype j, S j is sales of auomobiles of ype j by firm j, L j is labor services, N j is he sock of invenories of firm j of finished auomobiles a he end of he period, A j is he sock of goods available for sale during period, Y j is he oupu of auomobiles of ype j, j is labor produciviy, r 2 is he real ineres rae faced by he firm, K j is invenory sorage coss, S, is indusry sales, N is he indusry sock of invenories of finished auomobiles a he end of he period, P is he real indusry price level, and W is he real wage rae. Observe ha equaion (19) is he demand funcion for new auomobiles of ype j ha emerged from he shopping-cos model of he household. The demand for new cars from he represenaive household hus serves as he demand funcion faced by firm j, which is he firm ha produces auomobiles of ype j. This connecs he model of he household o he model of he firm. Using he definiion of A j invenory sorage coss, equaion (20), can be wrien as K j = apple o Aj S j apple1 Nj 1 + Y apple1 j N j 1 = apple o N j 1. Curren-period sorage coss are hus assumed o rise wih he sock of auomobile invenories carried over from he previous period and wih curren producion and o fall wih curren sales. Now, use equaion (19) o eliminae price as an explici choice variable and rewrie equaion (21) o ge N j 1 = A j Y j ; hen ne revenues, equaion (18), can be wrien as 1 1 Sj j = S A j A S W P L j apple o S j Aj S j apple1 (A j. Y j). (24) The firm hen chooses S j, Y j, A j, and L j o maximize equaion (16) subjec o equaions (22) and (23) and where ne revenue is now defined in equaion (24) and he discoun facor is again given by equaion (17). The firs-order condiions are 1 1 Sj S A j A apple1 Aj Aj. + appleo apple 1 S j S j Y j = E +1 f 1+1 (25) apple1 Aj apple o + S j f 1 = f 2 (26) E +1 f Sj S A j A 1 S A (27) 8

11 apple1 1 Aj Aj Aj apple o apple 1 S j S j S j Y j # +1 = f 1 f 2 jl 1 j = W P (28) 1 where +1 = 1+r 2+1, and f 1 and f 2 are he mulipliers associaed wih he available-supplyaccumulaion process and he producion funcion, equaions (22) and (23), respecively. From f equaion (26), we see ha he muliplier 2 measures he negaive of he marginal cos o he firm of producing an addiional auomobile. Equaion (28) saes ha he firm will se he marginal cos of producing an addiional vehicle o he marginal value of an addiional uni of invenory. model. These opimaliy condiions summarize he endogenous dynamics of he supply side of he The muliplier f 1 measures he marginal value o he firm of an addiional uni of invenory. Thus, equaion (27) equaes he coss and benefis o he firm of selling he marginal vehicle. The righ-hand side of he equaion is he marginal revenue from selling one more vehicle his period. The hree erms on he lef-hand side of he equaion are: (1) he marginal revenue from selling he vehicle nex period; (2) he marginal benefi o he firm of having an addiional uni of invenory (he value from he increase in demand for is vehicles) nex period; and (3) he marginal sorage cos of holding an addiional vehicle one more period The higher is r 2,+1,he smaller he benefi is o holding a vehicle in invenory one more period. This equaion capures he firm invenory channel. A firm ha faces an unexpeced high ineres rae nex period will wish o hold fewer vehicles in invenory. Thus, higher ineres raes should lead o lower prices and more sales in he shor run. Bu a reducion in available supply will feed ino he household s problem, reducing consumer demand. 2.3 Marke equilibrium In marke equilibrium, we assume ha S j = S, A j = A, L j = L, Y j = Y, and j =. Then, he opimaliy condiions and consrains for he firm become 1 apple1 A A. + apple o apple 1 S S Y = E +1 f 1+1 (29) E +1 f A S 1 apple1 A apple o + S f 1 = f 2 (30) apple apple1 1 apple A o S apple A A Y 1 S S +1 = f 1 (31) 2 L 1 9 = W P (32)

12 A = A 1 S 1 + Y (33) Y = L (34) where +1 = 1 1+r 2+1. For he household in marke equilibrium, he opimaliy condiions and he consrains are 1 C = h 1 (35) (1 ) E h X = h 2 (36) h 2 1 P h 1 + P h 3 = 0 (37) (1 µ) E h 3+1 E (r µ) h 1+1 = h 3 (38) C + 1 P S +(r 1 + µ) B 1 = I (39) X =(1 )X 1 + S (40) B =(1 µ) B 1 + P S. (41) The marke equilibrium model hus conains hireen equaions in hireen endogenous variables: S, Y, A, L, C, P, X,B, h 1, h 2, h f 3, 1, and f Raios and growh raes Our esimaion approach relies on he daa being saionary. Alhough uni sales of ligh vehicles and he firms and households ineres raes are saionary, here are rends in real prices, real wages, and real disposable income. Consequenly, we reformulae he model so ha he relevan variables are in raio form. These raios are saionary and hus guard agains any saisical problems wih nonsaionary imeseries. 10 Define he following raios and growh raes: 10 An example of a model wih an invenory-holding firm ha is expressed in raio form is Maccini and Pagan (2013). 10

13 R CI = C I R PSI = P S I R PXI = P X I R BI = B I R AS = A S R YS = Y S LS = W L P Y I =(1+i ) I 1 P =(1+p ) P 1 S =(1+s ) S 1 Y =(1+y ) Y 1 L =(1+l ) L 1 =(1+ ) 1 W =(1+w ) W 1 where i is he growh rae of real income, p is he growh rae of he real price of auomobiles, s is he growh rae of real sales, y is he growh rae of oupu, l is he growh rae of labor, is he growh rae of labor produciviy, and w is he growh rae of real wages. The definiion of raios generaes hree addiional equaions ha relae raios o growh raes. In paricular, observe ha he raios, R PSI, R YS, and LS can be wrien as R PSI = P S I = (1 + p ) P 1 (1 + s ) S 1 = (1 + p )(1+s ) (1 + i ) I 1 (1 + i ) R PSI 1 (42) R YS = Y S = (1 + y ) Y 1 (1 + s ) S 1 = (1 + y ) (1 + s ) RYS 1 (43) LS = W L P Y = (1 +! )(1+l ) W 1 L 1 (1 + p )(1+y ) P 1 Y 1 = (1 +! )(1+l ) (1 + p )(1+y ) LS 1. (44) In appendix B, we show ha, using he raios and growh raes and eliminaing labor inpu, he model reduces o a sysem of fifeen equaions and fifeen endogenous variables. 2.5 Exogenous variables We assume ha each ineres rae, r i, is he sum of is mean, a common facor, f, and an idiosyncraic facor, x i. All hree laen facors are assumed o be auoregressive: r 1 = r 1 + f + x 1 (45) r 2 = r 2 + f + x 2 (46) f = f f 1 + f (47) x 1 = x1 x x 1 (48) 11

14 x 2 = x2 x x 2. (49) We allow he growh raes in labor produciviy, wages, and income o depend on heir own one-period lag as well as a sochasic disurbance: = (1 )+ 1 + (50) w = w(1 w )+ w w 1 + w (51) i = ī(1 i )+ i i 1 + i. (52) There are six muually uncorrelaed economic shocks in he model:, x 1, x 2, f, w, and i. All six shocks are normally disribued wih a mean of zero and consan variance. 3 Daa The daa in his paper are drawn from a number of sources, alhough he majoriy come from he Bureau of Economic Analysis (BEA) and Ward s Auomoive Yearbook (various years). To esimae he model, we need daa on ligh moor vehicles describing he growh raes of sales, producion, and prices. We also need informaion on household income, wages, and ineres raes faced by households and by auomakers. Alhough mos of he daa exend farher back in ime, our sample sars in February 1972 because of he availabiliy of daa on ineres raes faced by households and ends in December Ineres raes We consruc wo ineres-rae measures, of which one is he rae faced by auomakers and he oher is ha faced by households. For boh, we define he real ineres as he di erence beween he nominal ineres rae and inflaion expecaions. We assume he rae faced by auomakers is he BAA-bond yield, he ineres rae earned on invesmen-grade bonds. 11 For households, we ake he ineres rae repored on 48-monh new car loans issued by commercial banks. 12 We consruc a measure of inflaion expecaions using a regression approach. Inflaion is calculaed as he year-over-year change in he personal consumpion expendiure price index a he monhly frequency. We hen esimae a regression where inflaion is he dependen variable and he 11 We used Moody s seasoned BAA-corporae bond yield published by he Board of Governors in is H.14 Seleced Ineres Raes able. 12 These daa are published by he Federal Reserve Board in is G.19 Consumer Credi able and sar in February

15 Figure 1: Evoluion of Ineres Raes over he Sample Period, independen variables are las monh s inflaion, conemporaneous values of nominal personal consumpion expendiures, indusrial producion, and he riple-a bond yield. 13 inflaion expecaions in period using he regression coe including 1. We esimae ciens esimaed on daa up unil and Using hese ingrediens, we consruc our wo measures of real ineres raes, which are ploed in figure 1. Ineresingly, he ineres rae faced by households is no always above he rae faced by auomakers. Indeed, from he lae 1990s onward, households could someimes finance he purchase of heir vehicles a raes equal o or below hose faced by auomakers. This is likely due in par o he compeiion banks face from auomakers financing eniies ha o er consumers exremely low financing packages o simulae sales Boh personal consumpion expendiures and he personal consumpion expendiures price index are published by he BEA. The indusrial producion index and Moody s AAA corporae bond yield are published by he Board of Governors in is G.17 Indusrial Producion and Capaciy Uilizaion and H.15 Seleced Ineres Raes able, respecively. 14 Leading up o he financial crisis, for example, U.S. manufacurers adverised heir financing incenives under he zero percen financing slogan. 13

16 3.2 Sales, producion, invenories, and price We collec daa on unis sold, produced, and invenoried separaely for auomobiles and ligh rucks. For auomobiles, he BEA publishes a comprehensive se of monhly saisics racking unis produced and sold in he Unied Saes. A large number of moor vehicles are assembled in Canada and Mexico bu sold in he Unied Saes. Therefore we follow he BEA nomenclaure and define a domesic vehicle as one produced in he Unied Saes, Canada, or Mexico bu inended for he U.S. marke. 15 domesic invenories from he sales and producion flows. Our sales daa also reflec his domesic label. We hen infer The BEA daa for ligh rucks are less comprehensive and someimes also have a shorer hisory. As deailed in appendix C, we use Ward s Auomoive daa o exrapolae hese daa back o We hen sum he auomoive and ligh ruck sales, oupu, and invenories daa because our model does no disinguish beween hese wo ypes of passenger vehicles. We define average price o be equal o he oal expendiures on vehicles divided by vehicles sold. The BEA publishes his figure for domesic auomobiles, bu, once again, some work is needed o consruc average prices for ligh rucks (see appendix C for deails). Guided by he model, we deflae boh auomobile and ligh ruck nominal prices by a nondurables consumer price index. 16 The resuling series is now a relaive price, measuring how he price of a vehicle compares o he ypical nondurable consumpion bundle over ime. 17 Finally, we ake he salesweighed average of real prices for auomobiles and ligh rucks o arrive a he average real price for ligh moor vehicles. Because our model explains monhly growh raes, we compue he percen change in sales, oupu, and real price. In looking a hese daa, we see he well-known sylized facs ha he growh raes of sales and oupu have a high correlaion of 0.64 and are quie volaile over our sample period, wih sales being less volaile han oupu (e.g., see Bresnahan and Ramey (1994)). This volailiy is illusraed in figure 2. Comparing sales and oupu growh wih real price growh 15 A small number of cars and rucks are assembled in he Unied Saes and expored. These vehicles are no considered par of domesic producion. Blanchard and Melino (1986) also noe ha auomobile producion is raher arbirarily disribued across counries. Raher han deermine which vehicles buil in Canada and Mexico are sen o he U.S. marke, hey look a Norh America as a whole. 16 We use he seasonally adjused U.S. ciy average nondurables price index published by he Bureau of Labor Saisics. 17 In conras o our approach, Blanchard and Melino (1986) use he consumer price index (CPI) componen for new cars divided by he personal consumpion expendiures (PCE) deflaor o consruc heir relaive price measure. We do no use his relaive price measure, however, because he CPI componen for new cars is a qualiyadjused price, while our measures of unis sold, produced, and invenoried are no qualiy adjused. Because here is subsanial qualiy adjusmen for new cars and ligh rucks, here is a large mismach beween he qualiyadjused prices and regular unis sold. Using he Frisch produc rule, we can consruc a qualiy-adjused quaniy index for new auomobile sales. By he end of he period, qualiy-adjused unis sales are wice he level of regular uni sales. Finally, he use of qualiy-adjused prices is no appropriae for our model. Auomakers spend significan resources invesing in qualiy-improving echnology. We ake hese qualiy improvemens as given, and consider he firm s pricing and producion decisions. As such, vehicle prices in our model should reflec he increase in qualiy over ime. 14

17 in figure 2 highlighs he finding ha he percenage changes in real prices are subsanially smaller han sales and oupu. Over he sample period, real prices are somewha posiively correlaed wih sales and oupu, wih correlaion coe ciens of 0.22 and 0.25, respecively. Given his paper s focus on ineres raes, we consider how prices, sales, and oupu flucuae wih ineres raes in he daa. Over our sample period, we find ha he percenage changes in firms real ineres rae and in real prices are posiively correlaed (he correlaion coe cien is 0.52), a paern illusraed in figure 3. Given he high correlaion beween firms and he households ineres raes, i is no a surprise o find he same posiive correlaion beween he percenage changes in households real ineres rae and in real prices. Finally we also find ha he percenage changes in firms ineres rae are posiively correlaed wih he percenage changes in sales and oupu, wih correlaion coe ciens of 0.22 and 0.16, respecively. In addiion o he growh raes of sales, oupu, and real prices, he model makes predicions abou he raios of oupu o sales and of available supply o sales. Available supply is equal o he sock of invenories a he beginning of he monh plus ha monh s oupu, and he raio of available supply o sales is commonly used in he indusry as a gauge of how well producion and sales are aligned. Over he sample period, we find ha boh raios are roughly consan, alhough quie volaile. 3.3 Personal disposable income and consumpion To measure households income, we use personal disposable income as published by he BEA. As wih all our nominal variables, we deflae his income measure wih he nondurables consumer price index. We use income o consruc wo raios ha are imporan variables in our heoreical model. The firs is equal o expendiures on ligh moor vehicles over income, where expendiures are equal o he average vehicle price muliplied by sales. The second raio is nonmoor vehicle expendiures over income. For he numeraor of his las raio, we use he personal consumpion expendiure daa published by he BEA minus our measure of ligh vehicle expendiure. The raio of ligh moor vehicle expendiure over income flucuaes around 0.05 for mos of our sample bu sars a gradual decline o 0.03 saring around 2000 (see he doed line in figure 4). No surprisingly, he raio of nonmoor vehicle expendiure o income is roughly he mirror image of he raio of ligh vehicle expendiure o income. In our model, available supply, measured as he beginning-of-period sock of invenories plus curren producion, plays a large role in boh he firm s and he household s problem. In equilibrium, changes in available supply have a number of direc and indirec impacs on prices and sales. To gain a rough sense of how available supply, sales, prices, and income flucuae ogeher, we consider he comovemen beween he raios of available supply o sales and of ligh vehicle expendiures and income. As illusraed in figure 4, hese wo raios are negaively correlaed, wih a correlaion coe cien of This suggess ha a main force in he model is ha manu- 15

18 Figure 2: Growh Raes of Sales and Oupu, Figure 3: Firm s Real Ineres Raes and Real Prices,

19 Figure 4: Raios of Available Supply o Sales and Ligh Moor Vehicle Expendiure o Income, facurers use invenories o smooh producion, as available supply ends o grow relaive o sales when households reduce he amoun of income hey spend on moor vehicles. 4 Empirical Resuls In his secion, we discuss he mehods we used o solve and esimae he model. We also repor he esimaion resuls. We hen illusrae he mechanics and implicaions of he model hrough hree ses of impulse-response funcions. 4.1 Solving and esimaing he model We ake he model o he daa in wo seps. In he firs sep, we esimae he parameers of he sochasic processes of ineres raes, income, and wages independenly from he res of he model. Given hese esimaed sochasic processes, in he second sep we calibrae some parameers and esimae he remainder by aking he model o he daa. We begin by esimaing he laws of moion for ineres raes (equaions 45-49), wages (equaion 51), and income (equaion 52). To esimae he six parameers in he ineres-rae processes, 17

20 we wrie he five equaions in sae-space noaion: x +1 = Ax + Cw +1 (53) y = Gx (54) where x =[f x 1 x 2 ] 0, y =[r 1 r 1 r 2 r 2 ] 0, w +1 =[ f +1 x 1 +1 x 2 +1 ] and A = f x x , C = , and G = #. Parameer values are esimaed by maximizing he likelihood compued using he ime-varying Kalman filer, where he daa are he monhly household and firm real ineres raes described in secion 3.1. The poin esimaes and sandard errors are repored in able 1. All he parameers are ighly esimaed. The poin esimaes highligh he considerable persisence in real ineres raes wih all hree auoregressive coe ciens above Thus, curren high (low) ineres raes imply high (low) ineres raes for many periods in he fuure. The esimaed processes do a good job of maching he second momens of he wo ineres raes. The sandard deviaion of r 1 and r 2 in he daa are and , respecively; for our esimaed specificaion, hey are and The auocorrelaions of r 1 and r 2 in he daa are and 0.988, respecively; for our esimaed specificaion, hey are and On average, consumers pay 71 basis poins more han firms for credi a an annual rae, alhough, as we illusrae in figure 1, oward he end of our sample, consumers have, more ofen han no, paid less. In he daa, consumers have paid less for credi han auomakers 19.2 percen of he ime. In our esimaed process, his occurs 19.6 percen of he ime. In he daa, he conemporaneous correlaion beween he wo ineres raes is 0.945; in our esimaed process, his correlaion is We use BEA daa on real disposable income o esimae he process describing he growh rae of income in our model (equaion 52). Using leas squares, we esimae he growh rae of income o be a fairly persisen process (see able 1). We were no able o find a imeseries of wages for workers in he moor vehicle indusry. Alhough he Bureau of Labor Saisics (BLS) repors wage daa, hese figures do no accoun for benefis, which we believe o be a significan fracion of oal compensaion for moor vehicle workers. The BLS does publish compensaion for workers in he durable goods secor. Using leas squares, we esimae he sochasic process of real wages in he model using hese daa. We find ha real wages grow a an average monhly rae of and are fairly persisen; he coe cien on lagged real wages is Our second sep relies on our solving he model. Because i no possible o obain an analyical soluion o he marke equilibrium model, we use DYNARE o approximae, solve, and esimae 18

21 Table 1: Parameer Esimaes and Sandard Errors for he Laws of Moion for Real Ineres Raes, Real Income, and Real Wages. Parameer Poin Sandard esimae error Law of moion for real ineres raes household rae persisence r sandard deviaion firm rae persisence r sandard deviaion common shock o boh raes persisence f impac coe cien Law of moion for real income consan Ī persisence I sandard deviaion I Law of moion for real wages consan W persisence w sandard deviaion w Noe: The sandard deviaion of he innovaion o f, f, is normalized o he model. 18 The basic sraegy implemened hrough DYNARE is o linearize he model hrough a firs-order Taylor approximaion around is nonsochasic seady sae o obain a sysem of linear di erence equaions. 19 We hen calibrae several parameers such ha he model, in seady sae, maches several key momens in he daa. Finally, we use a Bayesian maximum likelihood procedure o esimae he poserior disribuions of he remaining parameers. We use our model o mach he ime series of he raios of ligh vehicle expendiures o income, available supply o sales, oupu o sales, and consumpion o income, as well as he growh raes of real prices, sales, and oupu. We calibrae six parameers so ha he model, in is iniial seady sae, closely maches he mean values of our seven daa series. We se he reurn on labor ( ), o 0.6, implying ha reurns o labor are 60 percen, inline wih he macroeconomics lieraure. We hen chose he monhly scrappage rae for vehicles ( ) o be , which is equal o a 5 percen annual scrappage rae. This rae implies ha he median car has a 50 percen chance of 18 For more informaion on DYNARE, go o hp:// 19 See appendix B for a saemen of he model as well as he nonsochasic seady sae. 19

22 Table 2: Calibraed Parameers Parameer Value Reurn on labor 0.6 Vehicle scrappage rae Fracion of vehicle loan paid o µ 0.02 Household discoun rae Fracion of new vehicle purchases financed wih a loan 0.35 Law of moion for real wages, consan erm W surviving 15 years, consisen wih esimaes in he lieraure for 1990 model-year vehicles. 20 We se he percenage of he sock of vehicle loans paid o each monh (µ) o be 0.02, which roughly implies ha he average loan lass 4 years. This choice is consisen wih he household ineres rae, which is he rae on a 48-monh new car loan. Nex, we se households monhly discoun rae ( ) o To calibrae he fracion of new vehicle purchases financed wih an auo loan ( ), we use equaion (41), which demonsraes ha in seady sae he mean value of he sock of ligh vehicle loans muliplied by µ is equal o he mean value of ligh vehicle expendiures muliplied by. We have already se µ o 0.02 and can use he BEA daa o compue he mean value of ligh vehicle expendiures over our sample. We also compue he mean value of he sock of vehicle loans using daa published in he Board of Governor s G.19 consumer credi repor. Using hese numbers, we back ou ha is equal Finally, we find ha he esimaed average monhly real wage rae of implies ha in seady sae he growh rae of real prices is below ha of sales. In he daa, however, real prices grow faser han sales. To close he gap beween he model and he daa, we increased he monhly growh rae of real wages ( W ) o A summary of he calibraed parameers is presened in able 2. This leaves us wih 7 parameers o esimae in addiion o he sandard deviaions of he measuremen error erms. We ake a Bayesian approach o esimaing he model s likelihood and hence specify prior disribuions for all he parameers (see able 3 for a lis of he prior disribuions). Based on he lieraure, he average own-price demand elasiciy for ligh moor vehicles is around 3. Berry, Levinsohn, and Pakes (1995), for example, repor own-price elasiciies ha range, in absolue value, from 3 o 6, and Goldberg (1995) repors an average (unweighed) elasiciy of Hence, we characerize he prior for as a normal disribuion wih a mean of 3 and a sandard deviaion of 1.0. There is lile empirical work ha measures he elasiciy of sales wih respec o available supply, and we herefore se is prior disribuion o be normal, wih a mean of 3 and a sandard deviaion of Secion 5.5 of Bandivadekar e al. (2008) provide a review of he lieraure focused on esimaing scrappage raes of ligh vehicles. Noe ha 1990 is abou he midpoin of our sample. 20

23 The growh rae of produciviy is characerized by hree parameers. The consan erm is se o (or 0.2 percen annual growh rae) and is no esimaed. The prior disribuion of he persisence erm is assumed o be a Bea disribuion cenered a 0.75, and we chose an inverse gamma prior for he sandard deviaion of he error erm wih a mean of For he wo erms characerizing he coss of holding invenory (apple 0,apple 1 ), we chose priors wih normal disribuions wih means of 0.1 and 0.8, respecively. Finally, we normalize he uiliy weigh on consumpion ( 1 ) o 1 and chose a prior disribuion for he uiliy weigh on moor vehicle consumpion ( 2 ) o be inverse gamma, wih a mean of 0.1 and sandard deviaion of 0.1. Wih hese chosen values, he seady sae of our model closely maches he mean values of he variables in he daa ha we are rying o mach. Summarizing, we have hree ses of parameers, ( 1, 2, 3 ), where 1 is he se of parameers esimaed in he firs sep described a he beginning of his secion; 2 is he se of calibraed parameers (lised in able 2); and 3 is he se of parameers esimaed by Bayesian maximum likelihood. Formally, leing {X } T =1 denoe he daa, he poserior disribuion is given by P ( 3 ; {X } T =1, 1, 2 ) / p( 3 )L({X } T =1 ; 1, 2, 3 ), (55) where p denoes he prior disribuions of he parameers in 3 and L denoes he likelihood. The poserior disribuions of he parameers are esimaed using he suie of programs available in DYNARE. We chose a Markov chain Mone Carlo (MCMC) approach, which used a Meropolis- Hasings algorihm. Two independen Markov chains were used wih average accepance raes of 23 and 22 percen, respecively, and he MCMC diagnosics demonsraed ha he draws from he poserior disribuions of all parameers converged. In able 3, we repor momens of boh he prior and he poserior disribuions of he parameers in 3. The esimaed poserior disribuions on he wo elasiciy parameers yield sensible resuls. The parameer, which is he own-price elasiciy of he demand for a new vehicle, has a mean of 2.66 in absolue value and lies in he credible inerval of (1.56, 3.84). This is consisen wih he lieraure reviewed earlier. The parameer, which is he available supply elasiciy of he demand for a new vehicle, is esimaed have a mean of 3.09 and so is slighly greaer han he own-price elasiciy. 21 The esimaes of apple 0 and apple 1 imply ha invenory holding coss are increasing and convex (see equaions (20) and (21)). Alhough i is di cul o inerpre hese wo parameer values, heir impac on manufacurers behavior can be seen in he nex secion, which analyzes how households and firms reac o various ineres-rae shocks. Finally, we esimae ha produciviy 21 Copeland, Dunn, and Hall (2011) esimae a similar elasiciy (how changes in an invenory-based variey measure increase sales) o be roughly 0.5. Their discree-choice saic model idenifies his elasiciy from he variaion in he cross-secion, whereas in he curren paper he available supply elasiciy is pinned down by he seady sae, specifically, by he mean values of he raios of available supply o sales and oupu o sales. 21

24 Table 3: Prior and Poserior Disribuions of Esimaed Parameers Parameer Prior Poserior mean sd dev disribuion mean credible inerval Available supply elasiciy normal 3.09 (1.90, 4.38) Own-price elasiciy normal 2.66 (1.56, 3.84) Linear invenory cos apple normal 0.11 (0.06, 0.15) Nonlinear invenory cos apple normal 0.57 (0.27, 0.85) Uiliy weigh on moor vehicle inverse gamma 0.10 (0.09, 0.10) expendiures Persisence in produciviy growh bea 0.59 (0.52, 0.65) Sandard deviaion of produciviy growh inverse gamma (0.003, 0.004) Sandard deviaions on measuremen errors Prior Poserior mean sd dev disribuion mean credible inerval inverse gamma 0.01 (0.01, 0.01) Raio of new vehicle expendiure o income Raio of consumpion o income inverse gamma 0.01 (0.01, 0.01) Raio of available supply o sales inverse gamma 0.51 (0.49, 0.54) Raio of oupu o sales inverse gamma 0.14 (0.14, 0.15) Growh rae of real sales inverse gamma 0.01 (0.01, 0.01) Growh rae of real oupu inverse gamma 0.01 (0.01, 0.01) 22

25 Table 4: Daa and Model Momens Time-series Daa Model mean mean of he mean sd of he mean Raio of new vehicle expendiures o income Raio of consumpion o income Raio of available supply o sales Raio of oupu o sales Growh rae of real prices (annual rae, percen) Growh rae of sales (annual rae, percen) Growh rae of oupu (annual rae, percen) sd mean of he sd sd of he sd Raio of new vehicle expendiures o income Raio of consumpion o income Raio of available supply o sales Raio of oupu o sales Growh rae of real prices (annual rae) Growh rae of sales (annual rae) Growh rae of oupu (annual rae) Noe: sd is sandard deviaion. Model is he simulaed daa generaed by he model. The firs and second momens of he variables in he simulaed daa are compued from 1,000 simulaed daases. is a somewha persisen process and ha he sandard deviaion of produciviy growh is less han Goodness of fi Before using he model o analyze how ineres raes influence households and firms decision making, we demonsrae ha he esimaed model fis he daa well using wo di eren approaches. We firs consider how well daa generaed by he model maches he firs wo momens of variables in our acual daa. To do his, we simulae he model so as o generae 1,000 panel daases of he same size as our acual daa. These simulaed daases mimic our acual daa, in ha hey capure he comovemens of he growh raes of sales, real prices, and oupu as well as he raios of new vehicle expendiures o income, consumpion o income, available supply o sales, and oupu o sales. Using he acual daa, we compue he mean and sandard deviaion of each variable. Using he simulaed daa ses, we firs compue he mean and sandard deviaion of each variable for each daa se. We hen look a he disribuion of each of hese momens and repor heir mean and sandard deviaion in able 4. As illusraed in he able, he model does well in maching he firs and second momens of he raios. The model slighly overpredics he mean growh raes of real prices, sales, and oupu and generaes a more volaile ime series of he growh rae of real prices, as evidenced by he 23

26 much larger sandard deviaion in he simulaed daa ( versus 4.399). However, he model capures reasonably well he sandard deviaions of he growh raes of sales and oupu (see he las wo rows of able 4). Our second goodness-of-fi measure compares impulse-response funcions generaed by a recursive vecor auoregression (RVAR). In he empirical lieraure, researchers have used srucural VARs o esimae he response of real variables o innovaions in ineres raes. A challenge wih his ype of analysis is properly idenifying he causal impac of changes o ineres raes on real variables such as oupu or sales. One approach is o make an idenifying assumpion based on iming, whereby he conemporaneous real variables can respond o an ineres-rae innovaion only wih a lag (e.g., see Bernanke and Blinder (1992)). This approach allows for he esimaion of RVARs, which seek o measure he impac of an innovaion o ineres raes on real variables (see Ludvigson (1998) for an example of such an approach applied o he moor vehicle indusry). In he spiri of hese papers, we esimae a 6 variable RVAR wih 4 lags where he order of he variables is index of indusrial producion, consumer price index, producion price index, raio of available supply o sales, raio of oupu o sales, and firms ineres rae. 22 The hree indexes capure macroeconomic rends, and he wo raios are he variables of ineres. We hen calculae he impulse responses of he wo raios o a one-sandard-deviaion posiive innovaion o firms ineres rae (see panel A of figure 5) To deermine how well he model maches hese esimaed impulse-response funcions, we esimae a RVAR on he simulaed daa. Mimicking he RVAR ha we esimaed on he daa, his is a 3 variable RVAR wih 4 lags, where he variables and heir order are raio of available supply o sales, raio of oupu o sales, and firms ineres rae. 23 The order of hese variables maches he RVAR esimaed on he daa, and we do no include he macroeconomic variables because our model does no generae business cycle rends. For each of he 1,000 simulaed daa ses, we esimae his RVAR and calculae he impulse response of he wo raios o an innovaion o firms ineres rae, as well as he deviaion of firms ineres rae from he seady-sae value. We hen average across he 1,000 impulse responses o arrive a an average esimaed impulse response (see panel B of figure 5). The equilibrium responses of he raios of available supply o sales and oupu o sales have he same dynamics across he wo RVARs, srong evidence ha our model is capuring well he impac of changes in ineres raes faced by vehicle manufacurers. The RVARs from he simulaed daa, however, do predic smaller responses of hese wo raios o he ineres-rae innovaion, roughly an order of magniude less. Almos idenical resuls arise from a one-sandard-deviaion 22 The consumer price index is for all urban consumers, and he producer price index is for all commodiies; boh series are published by he Bureau of Labor Saisics. We smoohed boh he raios using a moving average, which for a given dae, used daa from 6o Following how we reaed he daa, we smoohed he daa on raios using a moving average, which for a given dae, used daa from 6o