Demand-Driven Business Cycles: Explaining Domestic and International Comovements

Transcription

1 Demand-Drven Busness Cycles: Explanng Domestc and Internatonal Comovements Y Wen Department of Economcs Cornell Unversty Ithaca, NY yw57@cornell.edu Aprl 17, 2001 Abstract When capacty utlzaton s allowed to vary, standard equlbrum theory predcts that demand shocks can generate not only closed-economy busness cycles that are prevously thought explanable only by technology shocks, but also nternatonal busness cycles that are more consstent wth the data than what can be generated by technology shocks. JEL class caton: E13, E32, F11, F41. Keywords: Internatonal real busness cycle; Open-economy busness cycle; Demand shocks; Capacty utlzaton.

2 1. Introducton In real lfe, ckle consumers are often blamed for causng output uctuatons around ts long-term trend sustanable by technology growth. Booms and recessons, for example, are usually thought by central bankers and busness men as beng drven by perods of consumer optmsm and pessmsm. In ths paper, I show that random changes n consumer demand can ndeed generate realstc features of the busness cycle { for both closed and open economcs { when the economy's producton capacty can vary n response to changes n aggregate demand n an otherwse standard general equlbrum real busness cycle model. Other people have shown that shocks to consumpton demand can be mportant for explanng the busness cycle when there exst producton externaltes (most notably Baxter and Kng, 1991, Farmer and Guo, 1994, Wen, 1998, and Benhabb and Wen, 2000). I show here that even n the absence of externaltes, demand shocks are capable of explanng many de nng features of the US busness cycle that are often thought explanable only by technology shocks, such as the postve comovement of domestc output, consumpton and nvestment, as well as the relatve volatlty order among these varables. More mportantly, I show that demand shocks can help resolve many nternatonal busness cycle puzzles documented recently n the open-economy lterature, e.g., the hgh cross-country correlatons for output and the low cross-country correlatons for consumpton; and the postve cross-country correlatons for employment and nvestment. These nternatonal comovements are called puzzles or anomales n the lterature because they cannot be explaned by standard open-economy models drven by technology shocks. In standard models, output, nvestment and employment are negatvely correlated across countres, whle consumpton s strongly postvely correlated across countres. 1 The exstng lterature suggests that market mperfectons n one way or another are responsble for these anomales. For example, Kehoe and Perr (2000) argue that ncompleteness n the nternatonal credt markets may be responsble for these anomales. Guo and Sturzenegger (1998) argue that externaltes and ncreasng returns to scale can help resolve these anomales. 1 See Backus, Kehoe and Kydland (1992), Baxter and Crucn (1995), Stockman and Tesar (1995), and Kehoe and Perr (2000). 2

3 I show, however, that these nternatonal comovement anomales are what standard economc theory predcts, once demand shocks are acknowledged as the prmary source of uctuatons and once capacty utlzaton s allowed to vary n response to changes n aggregate demand. Imagne an ncrease n consumpton demand n the home country. The ncrease rases demand for the world output (both domestc and foregn output). Output, employment and capacty utlzaton therefore ncrease both at home and abroad, resultng n ther strong comovements across countres. Snce the urge to consume (demand shocks) s country spec c, consumpton s less correlated across countres than s output. Capacty utlzaton plays a key role n generatng postve comovements n nvestment, as t allevates the crowdng out e ect of consumpton demand on nvestment by ncreasng the elastcty of output response to demand shocks, hence allowng for postve captal accumulaton both at home and abroad to sustan the ncrease n the world demand. The observed nternatonal comovement patterns are thus fully consstent wth a demand-drven busness cycle theory. 2 The propagaton mechansm of the demand-drven channel of the busness cycle can be further strengthened by allowng for habt formaton on consumpton { an essental element for explanng the equty premum puzzle. Habt formaton renders changes n consumpton demand hghly persstent. Consequently, only ::d: demand shocks are requred to generate hghly persstent busness cycles both domestcally and nternatonally. Ths s n sharp contrast to the case of technology shocks, whose mpact cannot be propagated e ectvely over tme n standard models (e.g., see Cogley and Nason, 1995; and Wen, 1995). The rest of the paper s organzed as follows. Secton 2 descrbes the model. Secton 3 explans n smple terms why demand shocks are essental for explanng nternatonal busness cycles. Secton 4 provdes dynamc analyss, and secton 5 concludes. 2. The Model Ths s a smpl ed verson of the two-country RBC model studed by Backus, Kehoe and Kydland (1992), wth the addtonal features of varable capacty utlzaton and (possbly) ratonal habt formaton on consumpton. The theoretcal 2 The mportant role of capacty utlzaton n amplfyng and transmttng the busness cycle has been emphaszed n the RBC lterature by Greenwood et al. (1988), Burnsde and Echenbaum (1996), Wen (1998), Kng and Rebelo (2000), and Benhabb and Wen (2000). 3

4 world economy conssts of two dentcal countres, each represented by a large number of dentcal consumers and an dentcal producton technology. The countres produce the same good and have the same preferences. The labor nput n each country, however, conssts only of domestc labor, and consumpton s subject to country-spec c habt shocks. Inthehome(h) andforegn(f) countres, the representatve consumer maxmzes the expected utlty functon E 0 1 X t=0 t 8 < : ln ³ 9 c t ½c t 1 (n t a t) 1+ = ; for = h; f; (2.1) 1+ ; where c s consumpton of the produced good, n s labor supply, ½ 2 [0; 1) s a habt persstence parameter, and s a country spec c random shock to the habt consumpton level, whch generates the urge to consume (Baxter and Kng, 1992). Producton of the sngle good takes place n each country accordng to the constant-returns-to-scale technology y t = ³ e tk t ³ n t 1 ; for = h; f; (2.2) where e 2 [0; 1] n the producton functon denotes captal utlzaton rate. To have an nteror soluton for e n the steady state, I follow Greenwood et al. by assumng that the captal stock deprecates faster f t s used more ntensvely: ± t = 1 ³ e µ t µ ; µ > 1; for = h; f; (2.3) where ± t s the rate of deprecaton. Ths mposes a convex cost structure on captal utlzaton. World output from the two processes, y h t + y f t ; s allocated to consumpton and xed nvestment: X h c t + kt+1 (1 X ³ ± t t )k = e t kt ³ n t (1 ) : (2.4) Next exports s nx t = y t h c t + k t+1 (1 ± t)k t : By explotng the equvalence between compettve equlbra and Pareto optma, an equlbrum n ths world economy can be computed as the soluton to a 4

5 plannng problem of the followng form: max X 8 < 1 : E X t t=0 8 < : ln ³ 99 c t ½c t 1 (n t a t) 1+ = = 1+ ;; (2.5) subject to X µ c t + kt ³ e µ t µ kt = X ³ e t k t ³ n t (1 ) ; (2.6) for = h; f: An equal weght s assumed n the objectve functon. 3. Statc Analyss To understand why demand shocks can help resolve the nternatonal comovement puzzles, I llustrate why technology shocks create these puzzles at the rst place. Usng a smpler verson of my model (wthout loss of generalty), assumng xed capacty utlzaton and no habt formaton, and denotng technology shocks as A for country, then the rst order condtons of the plannng problem n the steady state are gven by: 1 c = (3.1) a ³ n ³ =(1 )A k ³ n (3.2) 1= A ³ k 1 ³ n 1 +1 ± (3.3) for = h; f: These rst order condtons mply the followng cross-country ratos: c h =1 (3.4) cf y h y f = kh k f = Ã A h A f! 1+ (1 ) (3.5) n h n f = Ã A h A f! 1 (1 ) : (3.6) 5

6 These cross-country ratos ndcate a perfect cross-country correlaton n consumpton and mperfect cross-country correlatons n other varables such as output, captal and labor (due to country spec c technology shocks). In partcular, under home-country technology shocks, output, captal and labor are negatvely correlated across countres, because of nternatonal factor movement towards the country where the productvty s the hghest. Ths mples that cross-country correlatons for output, employment and nvestment wll reman negatve as long as country spec c technology shocks are ndependent or not su±cently postvely correlated. Thus puzzles arse: In the model, cross-country correlatons are much hgher for consumpton than for output, whle n the data the opposte s true; and n the model, cross-country correlatons of employment and nvestment are negatve, whle n the data they are postve. There s no puzzle, however, once the source of uncertanty s from the demand sde rather than from technology. Under demand shocks, the above cross-country ratos become c h h =1; (3.7) c f f y h y = kh f k = nh =1: (3.8) f nf These cross-country relatonshps mply that output, captal and labor are perfectly correlated across countres whle consumpton s mperfectly correlated across countres due to country spec c demand shocks. Thus, cross-country correlatons are hgher for output than for consumpton n the model, so are n the data; and cross-country correlatons of employment and nvestment are postve, so are n the data. The only ssue left s the wthn-country comovement. For example, the correlaton between domestc consumpton and domestc nvestment can be negatve due to the crowdng out e ect of demand shocks. Capacty utlzaton solves the crowdng out problem, as t creates more elastc aggregate supply n response to changes n aggregate demand. 4. Dynamc Analyss To study the model's dynamc responses to demand shocks, I solve the model's equlbrum decson rules by log-lnearzaton around the steady state. I calbrate 6

7 the model's parameters as follows: the tme perod t s a quarter, the captal ncome share =0:3; the dscount factor =0:99; the labor supply elastcty parameter = 0 (Hansen's (1988) ndvsble labor), 3 the capacty elastcty parameter µ s chosen so that the steady state captal deprecaton rate ± =0:025; and the steady state habt-demand to consumpton rato c =0:1:4 The country spec c demand shocks are modeled as log normal statonary AR(1) processes: ln t = ½ ln t 1 + " t ; for = h; f; (4.1) where the persstence parameter ½ can be zero or postve, and where the nnovatons ³ " h t ;" f t are ::d: whte noses Comovement n Closed Economy I rst show n gure 1 the mpulse responses of the home country to a domestc consumpton demand shock when there s no trade. 5 The left wndow n gure 1 sthecasewthar(1) shocks and wthout habt formaton (½ h =0:95;½ h =0); The rght wndow n gure 1 s the case wth ::d: shocks and habt formaton (½ h =0;½ h =0:95). Several remarkable features of gure 1 are worth menton. Frst of all, persstent demand shocks can generate postve comovement n output, consumpton, nvestment and hours wthout habt formaton. In partcular, wth respect to output, consumpton s less volatle and nvestment s more volatle. Such a postve comovement and a relatve volatlty order among the three varables are two of the most robust and celebrated stylzed busness cycle facts that are thought n the lterature explanable only by supply (technology) shocks n a standard model. 6 Secondly, when habt formaton s allowed for, the model has a rch endogenous propagaton mechansm that can transform the mpact of ::d: demand shocks nto hghly persstent movement n output, nvestment and employment (see the rght wndow). Ths happens because habt formaton renders shocks to consumpton 3 >0 s requred n the case of technology shocks n order to avod sngularty. 4 The model's predctons are not senstve to ths rato. 5 The mpulse responses of a closed economy can be obtaned from the two-country model by smulatng the model under an equal and perfectly correlated mpulse of consumpton demand n both countres (so that no trade takes place). 6 If both persstent demand shocks and habt formaton are allowed, consumpton can be even smoothed further. 7

8 demand endogenously persstent. Ths s n sharp contrast to the case of technology shocks whose mpact can last only as long as the shocks themselves n standard models (e.g., see Cogley and Nason, 1995; and Wen, 1996). The combnaton of AR(1) demand shocks and habt formaton can generate even more volatle nvestment. Ths s shown n gure 2. The model has other vrtues. Rotemberg and Woodford (1996) hghlght a characterstc of economc uctuatons that s d±cult for standard RBC models to explan. They show that, n US data, forecastable changes n output, hours, nvestment and consumpton are postvely correlated, whereas standard RBC models predct the opposte. Wth capacty utlzaton and habt formaton ncorporated nto an otherwse standard RBC model, the forecastable changes n these four varables become postvely correlated. Fgure 3 shows that output, consumpton, nvestment and employment comove n the same drecton n the transton to the steady state after a decrease n the captal stock. 7 In partcular, hours and capacty utlzaton both ncrease when captal stock les below ts steady state, generatng more output avalable for both nvestment (captal accumulaton) and consumpton (although the magntude of consumpton s relatvely very small compared to output and nvestment). Hence, along the transton paths, these varables comove together. In addton, consumpton s less volatle and nvestment s more volatle than output along the transton path { another stylzed fact emphaszed by Rotemberg and Woodford (1996) as evdence aganst standard RBC models Comovement n Open Economy In open economy settngs, Backus, Kehoe and Kydland (1992), Baxter and Crucn (1995), Stockman and Tesar (1995), and Kehoe and Perr (2000) nd two major dscrepances between standard general equlbrum models and the data. In the open economy models, cross-country correlatons are much hgher for consumpton than for output, whle n the data the opposte s true; and cross-country correlatons of employment and nvestment are negatve, whle n the data they are postve. Snce these two dscrepances are robust to changes n both parame- 7 It s shown by Rotemberg and Woodford (1996) that the forecastable (permanent) movement of a model can be captured by the transtonal dynamcs of the model wth captal startng o ts steady state. Fgure 2 shows the transtonal dynamcs when captal starts one percent below ts steady state. 8

9 ter values and the model structure, Backus, Kehoe and Kydland (1992) call them anomales. One way to deal wth these anomales was suggested by Stockman and Tesar (1995), who consder an economy wth nontraded goods and both technology and demand shocks. The ntroducton of nontradable consumpton goods reduces the cross-country correlaton of aggregate consumpton because agents do not have ncentves to trade clams on the output of the nontraded goods sector. Alternatvely, t has been shown that ncomplete asset or commodty markets may help resolve these anomales. For example Baxter and Crucn examne an economy n whch agents trade a sngle rsk-free bond, Kehoe and Perr (2000) examne an economy n whch nternatonal loans are mperfectly enforceable, and Guo and Sturzenegger (1998) examne an economy n whch there are no markets for clams contngent on `sunspot' states. As I ponted out earler, the observed nternatonal comovement pattern s what standard economc theory predcts. It s a classcal \Keynesan" story of aggregate demand. Consder an ncrease n consumpton demand n the home country. Such ncrease rases demand for both domestc and foregn output. Output, employment and capacty utlzaton therefore all ncrease both at home and abroad n response to the hgher world demand. In the mean tme, snce varable capacty utlzaton reduces the crowdng-out e ect of consumpton on nvestment, nvestment n both home and foregn countres also go up so that both countres can mantan necessary amount of captal stocks to sustan the persstent ncreases n world demand. 8 Consequently, we see nternatonal comovement n output, nvestment and employment. Snce the urge to consume (demand shocks) are country spec c, consumpton s less correlated across countres than s output. Fgure 4 shows the mpulse responses of the home country ( rst column) and the foregn country (second column) to an ::d: demand shock n the home country. It s seen there that output, nvestment and employment are hghly persstent n both countres and are perfectly synchronzed across countres, whle consumpton s mperfectly correlated across countres. When both countres are subject to demand shocks, smulatons are requred to characterze the dynamcs of the model. Table 1 reports means and standard devatons of sample moments computed from 500 smulatons of the world economy, 8 The ncreases n world demand are persstent ether due to persstent demand shocks or due to habt formaton on consumpton demand. 9

10 each wth a length of 100 perods. Three versons of the models are smulated, one correspondng to ::d shocks wth habt formaton, another correspondng to AR(1) shocks wthout habt formaton, and another correspondng to AR(1) shocks wth habt formaton. Snce I am nterested only n qualtatve results regardng nternatonal comovements, n all cases the cross correlatons of the country spec c demand nnovatons, cor(" h ;" f ); are set to zero and calbraton s not used. The table shows that n an open economy settng, the relatve volatlty of consumpton to output exceeds one wth large standard errors, mplyng that t can be ether less than one or greater than one dependng on a partcular realzaton of the shocks. Investment, on the other hand, s always more volatle than output (although t s less than the data suggests). The rato of net export to output s always negatvely correlated wth output, whch s a robust emprcal regularty documented by the open-economy lterature (e.g., see Backus, Kehoe and Kydland, 1992, and Kehoe and Perr, 2000). Standard models drven by technology shocks predct ths rato to be procyclcal, rather than counter cyclcal. The nternatonal comovements are also consstent qualtatvely wth the data, n that output, nvestment and employment are strongly correlated across countres and that consumpton s less correlated across countres than s output. The perfect cross-country correlatons of output, employment and nvestment can be reduced f nonseparable perod utlty functons are used. When consumpton and lesure are nonseparable, consumpton demand shocks also a ect labor supply, hence reducng cross-country correlatons for output, employment and nvestment. However, output wll reman more strongly correlated across countres than consumpton. On the other hand, the cross-country correlatons for consumpton can be ncreased further f the cross-country correlatons of the nnovatons, cor(" h ;" f ), are allowed to be postve. 9 9 A rough calbraton by Guo and Sturzenegger (1998) shows that ths correlaton s about 0:45: 10

11 Table 1. Open-Economy Busness Cycle Statstcs (std. errors n parentheses) ::d: wth habt AR(1) wthout habt AR(1) wth habt Relatve volatlty to GDP ¾ c =¾ y 1.35 (0.37) 1.23 (0.35) 1.20 (0.37) ¾ =¾ y 1.46 (0.07) 1.46 (0.07) 2.44 (0.38) Domestc Comovement ½(c; y) 0.63 (0.21) 0.68 (0.19) 0.62 (0.24) ½(; y) 0.98 (0.01) 0.98 (0.01) 0.81 (0.03) ½(n; y) 0.99 (0.0) 1.0 (0.0) 0.99 (0.0) ½(nx=y; y) (0.15) (0.13) (0.13) Internatonal Comovement ½(y h ;y f ) 1.0 (0.0) 1.0 (0.0) 1.0 (0.0) ½(c h ;c f ) -0.1 (0.34) 0.01 (0.34) 0.05 (0.43) ½( h ; f ) 1.0 (0.0) 1.0 (0.0) 1.0 (0.0) ½(n h ;n f ) 1.0 (0.0) 1.0 (0.0) 1.0 (0.0) 5. Concluson I have shown that many de nng features of the busness cycle can be explaned by demand shocks alone. In partcular, demand shocks predct that: 1) Domestc output, consumpton, nvestment and hours comove together. 2). The forecastable movements n output, consumpton, nvestment and hours comove together. 3) Output, nvestment and hours are postvely correlated wth ther respectve counter parts across countres, wth stronger cross-country correlaton for output than s for consumpton. 4) Net export to output rato s negatvely correlated wth output. These domestc and nternatonal comovement patterns are well documented n the busness cycle lterature. The key element for the success of my model s capacty utlzaton. Varable capacty utlzaton mtgates the crowdng out e ect, renderng demand shocks fully expansonary both domestcally and nternatonally. Habt formaton, on the other hand, strengthens the demand channel of busness cycle propagaton by makng ::d: shocks to consumpton demand endogenously persstent. 11

12 References [1] Backus, D., P. Kehoe and F. Kydland, 1992, Internatonal real busness cycles, Journal of Poltcal Economy 100, [2] Baxter, M and M. Crucn, 1995, Busness cycles and the asset structure of foregn trade, Internatonal Economc Revew 36, [3] Burnsde, C. and M. Echenbaum, 1996, Factor hoardng and the propagaton of busness cycle shocks, Amercan Economc Revew 86 (December), [4] Cogley, T. and J. Nason, 1995, Output dynamcs n real-busness-cycle models, Amercan Economc Revew 85, [5] Farmer, R. and J. T. Guo, 1994, Real busness Cycles and the anmal sprts hypothess, Journal of Economc Theory 63, [6] Greenwood, J., Z. Hercowtz and G. Hu man, 1988, Investment, capacty utlzaton, and the real busness cycle, Amercan Economc Revew 78, [7] Guo, Jang-Tng and F. Sturzenegger, 1998, Crazy explanaton of nternatonal busness cycles, Internatonal Economc Revew 39, No 1, [8] Hansen, G., 1985, Indvsble labor and the busness cycle, Journal of Monetary Economcs 16, [9] Kehoe, P. and F. Perr, 2000, Internatonal busness cycle wth endogenous ncomplete markets, NBER Workng Paper [10] Kng, R. and S. Rebelo, 2000, Resusctatng Real Busness Cycles, NBER Workng Papers [11] Rotemberg, J. and M. Woodford (1996), Real-busness-cycle models and the forecastable movements n output, hours, and consumpton, Amercan Economc Revew 86 (March), [12] Stockman, A. and L. Tesar, 1995, Tastes and technology n a two country model of the busness cycle: Explanng nternatonal comovements, Amercan Economc Revew 85,

13 [13] Wen, Y., 1995, Where's the beef? The trval dynamcs of real busness cycle models, Manuscrpt, The Unversty of Iowa. [14] Wen, Y., 1998, Capacty utlzaton under ncreasng returns to scale, Journal of Economc Theory 81,

14 Fg. 1. Impulse Responses n Closed Economy. 14

15 Fg.2. Impulse Responses n Closed Economy. 15

16 Fg. 3. Forecastable Movements n Output, Consumpton, Investment and Employment. 16

17 Fg. 4. Internatonal Comovements { Impulse Responses to a Home Country..d. Shock. Frst Column = Home Country; Second Column = Foregn Country. Order of Varables from Top = Output, Consumpton, Investment, Hours and Net Export. 17