Sources and Propagation of International Cycles: Common. Shocks or Transmission? Universitat Pompeu Fabra. This revision: November, 1996.

Transcription

1 Sources and Propagation of International Cycles: Common Socks or Transmission? Fabio Canova Universitat Pompeu Fabra; Universita' di Modena; and CEPR 3 Jane Marrinan Universitat Pompeu Fabra Tis revision: November, 1996 Abstract Tis paper studies te generation and transmission of international cycles in a multicountry model wit production and consumption interdependencies. Two sources of disturbance are considered and tree cannels of propagation are compared. In te sort run te contemporaneous correlation of disturbances determines te main features of te transmission. In te medium run production interdependencies account for te transmision of tecnology socks and consumption interdependencies account for te transmission of government socks. Tecnology disturbances, wic are mildly correlated across countries, are more successful tan government expenditure disturbances in reproducing actual data. Te model also accounts for te low cross country consumption correlations observed in te data. JEL Classication No.: C68, E32, F11. Key words: Tecnology and Government Disturbances, Production Interdependencies, Consumption Interdependencies, Transmission. 3 Marianne Baxter, Hal Cole, Robert Hodrick, Ron Jones, Argia Sordone, Alan Stockman, Eric Van Wincoop, Mike Woodford and te participants of seminars at te Federal Reserve of Atlanta, University of Rocester, Queen's University, University of Brescia, University of Rome, IGIER, Federal Reserve Bank of Minneapolis and Nortwestern University ave provided elpful comments and suggestions. Part of te work was conducted at te European University Institute. Financial support from EUI and DGICYT grants is gratefully acknowledged. 0

2 1 INTRODUCTION 1 1 Introduction Te term \international business cycle" refers to te presence of common elements in te cyclical beavior of outputs across countries. Several autors, including Gerlac (1988), Baxter and Stockman (1989), Blackburn and Ravn (1992), Backus and Keoe (1992) and Gregory, Head and Raynauld (1995), among oters, ave documented te existenceof commonalties in economic activity across countries using a variety of metods. Economic similarities can be accounted for by te presence of interdependencies in eiter goods or asset markets, wic spill country specic socks across te world, by common exogenous disturbances, or bot. Witin eac category, demand and supply factors can induce international business cycles. Weter cyclical movements in economic activity are primarily attributable to demand or supply disturbances is a long standing question tat as been tackled from many points of view in a closed economy (see e.g. Blancard (1989), King, Plosser, Stock and Watson (1991), Cooley and Oanian (1991), Cristiano and Eicenbaum (1992) or Gali (1992) among oters) but te answers provided ave often been contradictory. In an international context te generation and transmission of business cycles received attention in te past (see e.g. Morgenstern (1959)) but as only been partially analyzed wit te tools of modern dynamic teory (see e.g. Cantor and Mark (1988) or Canova and Dellas (1993)). Knowledge of wat generates and transmits cycles across countries is important for policy purposes. Te issues surrounding te problem of generation are well understood. If, as widely perceived, output uctuations are undesirable and foreign demand socks are largely responsible, tere may be arole for aggregate Keynesian-type policies cusioning te economy from foreign disturbances. On te oter and, as often empasized in te real business cycle literature, if cyclical uctuations in economic activity arete optimal response to unforeseen disturbances of bot domestic and foreign origin, rater tan mitigating uctuations per se, a more appropriate role for te government is to reduce economically relevant uncertainties. Identifying te cannels of international propagation is also crucial. For example, in designing policies to sterilize undesirable disturbances, it is important to know not only weter socks ave domestic or foreign origin but also weter transmission occurs troug goods or nancial markets. In addition free trade agreements, wic ave generated considerable debate

3 1 INTRODUCTION 2 in policy circles in te last few years, will ave a dierent impact on te cyclical properties of output depending on ow disturbances are transmitted. Te empirical evidence regarding tis last set of issues is somewat scant. Canova and Dellas (1993) document tat trade interdependencies in intermediate goods areimportant in explaining te transmission of country specic disturbances in post WWII data. Tey also nd tat after 1973 te presence of common disturbances plays a role in accounting for international output comovements. Cole and Obstfeld (1991), Backus, Keoe and Kydland (1992) and Crucini and Baxter (1995) suggest tat international risk saring occurs primarily troug te goods markets and tat te welfare loss due to incomplete or autarkic nancial markets appears to be small. Tis paper contributes to te debate by constructing a multicountry general equilibrium model were it is possible to distinguis te contribution of dierent types of disturbances as sources of output uctuations and to quantify te importance of trade interdependencies in bot intermediate and nal goods in transmitting socks across countries. Our task will be to examine wic type of disturbances and wic source of transmission best accounts for te empirical evidence. Te model employed, wic is described in section 2, diers from tose of Cantor and Mark (1988), Mendoza (1991a), Backus, Keoe and Kydland (1992), Baxter and Crucini (1993) orstockman and Tesar (1994) in at least tree respects. First, eac country specializes in te production of one good. Second, agents in eac country consume an array of goods and government expenditure yields direct utility for domestic consumers. Tird, foreign capital is usedas an intermediate good in te production of domestic nal goods. Allowing for production interdependencies introduces an important and previously neglected cannel troug wic country specic disturbances can be propagated across countries. One type of disturbance we considertakes te form of exogenous government expenditure socks (as e.g. in Cristiano and Eicenbaum (1992)). Tese socks leave teinstantaneous marginal product of factors of production uncanged but generate dynamic responses across countries because tey modify te ow of consumption services accruing to domestic ouseolds. Consequently, governments inuence trade of nal goods, as consumers substitute foreign for domestic goods in response to te disturbances, aect trade of intermediate goods, as consumers substitute leisure intertemporally, and alter investment patterns and production levels around

4 1 INTRODUCTION 3 te world (see Asauer (1989) for an empirical documentation of a closed economy version of tis eect for te US economy). A second type of disturbance is modelled as an exogenous tecnology disturbance. Tese socks aect te marginal product of factors of production, inuence investment opportunities witin eac country and alter trade of nal goods because of income eects. One crucial dierence between te two sources of disturbances is in te way tey impact on trade ows: government socks rst alter net exports of consumption goods andlater on net exports of investment goods as leisure coices cange. For tecnology socks te order is reversed. Information about te cyclical properties of te actual datais summarized in section 3 wit statistics based on a semi-structural impulse response function. Since te model as a country specic deterministic trend, te cyclical component of actual data is computed after a country specic deterministic trend is separately extracted from te logaritm of te raw data. Section 4 describes ow te two types of disturbances generate international cycles in tree cases - one were socks are contemporaneously uncorrelated across countries and transmission occurs because of production interdependencies, one were socks are contemporaneously uncorrelated and transmission occurs because of consumption interdependencies and one were socks are contemporaneously correlated and no trade in eiter investment or consumption goods occurs. In eac case we discuss te properties of te spillover mecanism. Section 5 asks weter a realistic parameterization ofte model is able to reproduce te main features of te actual impulse response function. In particular, we are interested inknowing under wat condition, if any, te simulated impulse response function displays similar location of turning points and lengt of te implied cycle and weter it can account for te magnitude and te asymmetries of te cumulative impulse response multipliers. Te results indicate tat, wen te model is parametrized so tat te tree countries all resemble te US, knowledge of te source of uctuations is somewat irrelevant indetermining te qualitative features te propagation of output socks across countries. Quantitatively, te sort run features of te transmission arebestaccounted for by contemporaneously correlated socks. For te medium run features of output responses, on te oter and, production interdependencies play a major role wen tecnology socks drive te cycle, wile consumption interdependencies are crucial wen government socks drive te cycle.

5 2 THE MODEL 4 Te inclusion of cross country eterogeneities, in particular, eterogeneity in te distributions of te exogenous processes, is important in generating asymmetries in simulated total multipliers, but it does not signicantly improve te quantitative performance of te model. Also, wit a country specic parameterization, a model wit tecnology disturbances accounts best for features of te propagation of US and German output socks. Finally, we sow tat te model as te potential to account for te relative magnitude of cross country consumption and output correlations we see in te actual data. Section 6 concludes. 2 Te Model We consider a N country model wit N consumption goods, were eac country specializes in te production of one good. We abstract from money, not because we believe tat monetary aspects are unimportant in generating or transmitting business cycles, but because we do not ave simple models of money wic can produce quantitatively interesting real cyclical eects (see e.g. Dantine and Donaldson (1986)). Eac country is populated by alarge number of identical agents and labor is assumed to be immobile across countries. Preferences of te representative agent of country ; = 1;... ; N are given by: P t N t 3 3 j j=1 j 10 t t jt t X1 X1 Y N (10 ) E 0 U(c ;l )=E 0 [( c )l ] (1) t=0 t=0 1 0 j=1 3 3 jt jt t jt jt jt wit c = c + g if = j and c = c if 6= j, were c is te consumption of good j by te representative agent of country. consumption goods: if good j is not enjoyed by residents of country, Agents value te services of up to N j = 0. Government consumption expenditure yields direct utility for te representative agents of teir own country (as in e.g. Baxter and King (1993)). Wen not aect utility, wile for = 0 government consumption expenditure does = 1, government and private domestic consumption are perfect substitutes. One way to rationalize our specication, is to tink of te government as aving a linear tecnology, m = g,troug wic itproduces services for private use. If < 1, it t t is costly for te society to ave te government provide tese consumption services.

6 2 THE MODEL 5 Consumption goods are produced according to: YN P N j 10 j=1 j t t jt t t j=1 Y = A ( K )(X N ) 8 ; j (2) were X = X wit 1 8. X represents a labor-augmenting Hicks-neutral detert t01 t ministic tecnological progress. Production is subject to a tecnological disturbance A requires domestic labor and up to N intermediate capital inputs. If an intermediate input produced in country j is not used in producing nal goods in country, capital goods are accumulated according to: j t and = 0. Intermediate K =(10 )K + (I =K )K 8 ; j (3) jt+1 j jt jt jt jt were ( I jt K jt 0 00 ) represents te cost in country of using intermediate capital inputs produced in country j and satises 0; 0; 0. Mendoza (1991a), Backus, Keoe and Kydland (1992) and Baxter and Crucini (1993) ave sown tat in a one good international model transaction costs elp to avoid unrealistic unidirectional capital ows in response to tecnology socks. Te formulation adopted ere is similar to Baxter and Crucini (1993) and was cosen because it retains simplicity, wile linking trans- 0 I jt 01 action costs to te Tobin's Q. [ ( K jt )] is in fact Tobin's Q, i.e. te price of existing capital in location relative to te price of new capital produced in location j =1;...; N. Note tat because of production interdependencies, unidirectional capital igts need not occur in tis model: capital may ow toward te country experiencing positive output disturbances (so tat I j > 0), but tere may also be a contemporaneous ow in te opposite direction as investments in intermediate goods used by oter countries increase wit domestic wealt. Leisure coices are constrained by: 0 l + N 1 8 (4) t t were te total endowment of time in eac country is normalized to be equal to 1. To insure tat a balanced growt pat wit a stationary distribution of wealt obtains, we assume tat = and = 8 were is te growt rate of population in country. Intuitively tese conditions imply tat, asymptotically, te more impatient country will not accumulate all of te world wealt.

7 2 THE MODEL 6 Governments consume domestic goods, tax national outputs wit a distorting tax and transfer wat remains back to domestic residents. It is assumed tat government expenditure is stocastic, wile tax rates are parametrically given. Altoug te recent literature (see e.g. Dotsey (1990)) models tax rates as stocastic, we adopt a parametric representation in order to isolate te contribution of government expenditure disturbances to te international transmission of business cycles. Te government budget constraint is given by: g = 0T R + Y 8 (5) t t t were are tax rates and T R transfers in country. Te resource constraints are: X X X Y 0 g 0 c 0 k 0 (1 0 )k 8 (6) t t jt jt+1 jt j j j Te economy is subject to a 2N 2 1 vector ofdisturbances z = [A ; g ] and z is assumed t t t t to be a omoskedastic process wit mean t = (A(`)z t01) and variance 6. Tere is empirical evidence (see e.g. Costello (1991)) tat productivity disturbances ave cross country lagged eects wic are asymmetric. However, tese lagged eects may be te result of misspecications since foreign capital used in domestic production is not explicitly considered wen calculating Solow residuals. For tis paper we will specify a univariate law of motion for te disturbances in order to avoid mixing te transmission due to trade in goods wit te one due to te presence of lagged feedbacks across socks, but we allow eac type of disturbance to be contemporaneously correlated across countries. Tere is also some evidence tat tecnology and government expenditure disturbances may be negatively correlated in some countries (see Finn (1991) or Cristiano and Eicenbaum (1992)). Because ere we are interested in examining te dynamics generated by eac of te two socks separately, we will not consider tis possibility and let 6 = blockdiag(6 ; 6). 1 2 Finally, we assume complete nancial markets witin countries and free mobility of nancial capital across countries. To nd a solution we rst detrend tose variables drifting over time, ten solve te problem faced by a pseudo social planner (a ctitious problem were distortionary taxes are eliminated) and modify te optimality conditions to take care of te distortions (as in Baxter and Crucini (1993)). Te weigts! in te planner problem are cosen to be proportional to te initial

8 3 SOME EMPIRICAL EVIDENCE 7 population in eac country. Te modied optimality conditions are ten approximated wit a log-linear expansion around te steady state as in King, Plosser and Rebelo (1988). Reynolds (1992) as used a model wit some of te same features to study te transmission of productivity disturbances. Tere are two major dierences between er framework and te one used ere. First, se does not consider te impact of government expenditure disturbances. Second, se does not allow for transaction costs in te capital accumulation equations. 3 Some Empirical Evidence One way to address te questions we ave posed in te introduction is toidentify at least one source of domestic and international supply socks and one source of domestic and international demand socks in te actual data using restrictions derived from te model and examine teir international propagation. Te restrictions could take te form of sort run (see Canova (1991)), long run (see Amed, et al. (1993)) or sape constraints. However, as is clear from te description of te model, te imposition of constraints of tis type will not provide a clear answer to te questions we care about since several versions of te model are consistent wit te same set of restrictions on domestic and international variables. To fully exploit te general equilibrium nature of our model and its ric set of constraints we take an alternative approac. We identify semi-structural socks from te actual data using arbitrary restrictions and compare te resulting impulse response function wit te one obtained from data simulated from various specications of te model were socks are identied using te same arbitrary restrictions. In oter words, we use te impulse response function as a \window" to measure te quality ofte model approximation to te data. We would like to know wic model specication comes closest in reproducing te data troug tis window. We cose to report impulse responses, as opposed to simple correlations, to link te analysis wit te large body of statistical literature wic caracterizes business cycles using durations and turning point classications (see e.g., Diebold and Rudebus (1992)). In addition, we narrowly focus attention on te interdependencies of te cyclical components of national outputs for two reasons. First, because multicountry VAR models containing many variables are imprecisely estimated wit sort samples and terefore dicult to interpret (see Gregory, Head and Raynauld (1995) for suc anattempt). Second, since te model diers substantially from

9 3 SOME EMPIRICAL EVIDENCE 8 tose previously used, we nd it useful to rst provide an empirical account simply of output interdependencies and study ow te model performs along tis single dimension. In te last section of te paper we look at wat te model as to say for oter interesting international correlations. Since we are interested in studying te performance of te model for major world trading blocks, we examine te transmission features of output socks in te US, Germany and Japan. To caracterize te cyclical transmission of output socks it is necessary to detrend te series and questions arise as to ow to best extract te long run component of te data. Canova (1994) indicates tat alternative detrending metods impose dierent assumptions on te underlying structure of te time series, induce dierent distributional properties for te cyclical components and, consequently, contrasting descriptions of te empirical evidence. Given te low power of te tests designed to inform us about te data's long run properties and te fact tat no consensus view exists wit regard to te appropriate coice of trend removal, we will use an economic-based decomposition. Since in te model all variables in country, except ours, grow at te rate of labor augmenting tecnological cange, we extract a country specic deterministic trend from te log of raw output data. Wile tis coice is arbitrary, in te sense tat lacking precise knowledge about te long run properties of economic variables an alternative (say, a unit root) assumption on te properties of exogenous tecnological progress may be as sensible, it provides useful restrictions on te cyclical properties of actual data and imposes discipline in simulation exercises. Quarterly real GDP data for te tree countries is taken from OECD tapes, covers te sample 1960,1-1994,4 and is converted into indices using 1980,1 values. Te slope coecients of te deterministic time trends are respectively 0.008, and per quarter wit te slope for Japanese output signicantly dierent from te oter two. We estimate a VAR wit 9 lags and a constant on te log of detrended outputs and report responses wen te contemporaneous correlation matrix of te socks is triangularized in te order US, Germany and Japan outputs. Two potential problems sould be mentioned before te evidence can be interpreted: te impulse response function may not be stable over te sample and te properties of te transmission may not be robust to te ordering of te triangularization. Evidence (available on request) sows tat (i) apart from Japanese output in 1974,1, te VAR residuals ave no visible outliers

10 3 SOME EMPIRICAL EVIDENCE 9 and satisfy bot normality and te wite noise assumption over te entire sample, (ii) te qualitative features of impulse responses are approximately stable across subsamples and (iii) te properties of te transmission are independent of te ordering of te triangularization. Figure 1 plots te mean estimate of te impulse response function togeter wit te upper and lower limits of a95% Monte Carlo band. Table 1 reports statistics summarizing te main features of transmission: te size and te location ofte peak response of te tree variables and te magnitude of te cumulative multipliers. Several interesting features emerge. First, US output socks ave signicantly large and positive international impacts wile tis is not te case for Japanese and German output socks. Second, it takes time for a sock to be transmitted across countries and te return to te trend line is very slow in all cases. For example, te peak response of German output lags tree quarters and te peak response of Japanese output lags eigteen quarters a US output sock. Tird, te duration of te cycles diers depending on te origin of te socks. For example, US output socks generate uctuations lasting 4-6 years wile Japanese output socks produce very sort and irregular cycles. Finally, point estimates of te cumulative multipliers are very asymmetric. A 1% surprise increase in te log of detrended US output generates a 10.91% cumulative response in US output after 24 periods, a 9.72% cumulative response in German output and a large 19.33% cumulative response in Japanese output, wile a 1% increase in te log of detrended German output generates negative cumulative responses in all tree countries. Finally, a 1% surprise increase in te log of detrended Japanese output as a large domestic impact (14.99% after 24 quarters) but very modest international repercussions. Two conclusions can be derived from tis evidence. First, tere exists aninternational transmission of disturbances but, except for US output socks, it is not overwelming in terms of magnitude and it is somewat asymmetric. Rougly speaking, USoutput socks drive te international cycle, leading credence to te popular press argument tat te US economy is a \locomotive" for te world economy. German output socks crowd out foreign outputs in te medium run, wile Japanese output socks ave modest international impacts. Second, te cross country propagation of output socks takes time, wit te lag in te peak response varying from 2to18quarters, and cycle durations dier depending on te national origin of te socks.

11 4 THE PROPERTIES OF THE MODEL 10 4 Te Properties of te Model Since te model we consider as not yet been studied in te literature and since its transmission properties are more complex tan te ones obtained in onegood economies (see e.g. Backus, Keoe and Kydland (1992) or Baxter and Crucini (1993)) and in multigood economies were only domestic capital is used in production (see e.g. Sclagenauf (1989)), we start by rst summarizing ow disturbances are transmitted in existing models and ten describe ow dierent cannels of propagation amplify and transmit disturbances in our model. In a one good world wit idiosyncratic but persistent disturbances, a positive tecnological disturbance in one country raises te productivity of domestic factors of production, along wit domestic investment, ours and output and, to alesser extent, domestic consumption because of permanent income considerations. Because of te one good assumption, capital will ow to te most productive location (te magnitude of te ow depends on te cost of moving capital) inducing a current account decit in te country experiencing te sock and a decline in investment, output and labor demand in te oter countries. Also, because capital markets are perfect, risk saring implies tat consumption proles will be perfectly correlated across countries and tat, once te initial inow of capital goods is exausted, te current account of te country experiencing te socks will sow a surplus. A positive idiosyncratic and persistent government sock, wic yields no utility for domestic consumers and leaves marginal product of capital uncanged, crowds out domestic consumption, aects te intertemporal allocation of leisure and terefore future production possibilities (see e.g. Aiyagari, Cristiano and Eicenbaum (1992)) but as limited eects on te capital accumulation in any country (see e.g. Backus, Keoe and Kydland (1995)). Note tat, because of risk saring, foreign consumption willalso be crowded out. Tese features of te domestic and international transmission appear to be robust to several modications of te basic framework. For example, Mendoza (1991b), Backus, Keoe and Kydland (1992), Baxter and Crucini (1995) sow tat dispensing wit complete capital markets sligtly reduces cross country consumption correlations witout aecting oter features of te transmission (in line wit Cole and Obstfeld (1991)). Te same autors also sow tat making agents more risk averse, increasing te costs ofmoving capital, introducing time to sipor

12 4 THE PROPERTIES OF THE MODEL 11 canging te size of te countries canges te magnitude of foreign responses but not teir qualitative features. Finally, Costello (1991) sows tat te same international propagation obtains in a two sector model were eac country produces bot consumption and investment goods but only investment goods are traded. In Sclagenauf's (1989) model investment dynamics do not drive te cycle because te investment good is nontraded (see also Stockman and Tesar (1994)). Instead, idiosyncratic socks are propagated to te world economy because of consumption interdependencies. Wen a positive and persistent disturbance increases domestic output, consumption of bot domestic and foreign goods by domestic residents increases. Te increase in demand and te risk saring arrangement imply tat consumption of foreign goods will go up in all countries, depressing foreigninvestments and future foreign output. Hence, altoug cross country outputcorrelations are negative as in te one good economy, te transmission occurs troug a countercyclical net trade in consumption goods as opposed to a countercyclical net trade in investment goods. Mendoza (1991a) and Cardia (1991) sow tat, wit minor modications, te same mecanism operates in a small open economy faced wit exogenous productivity disturbances. In te model considered ere tere are tree reasons for wy domestic disturbances may result in a temporary displacement of foreign outputs from teir trend: socks may be correlated across countries and independent socks may be transmitted eiter troug production interdependencies or consumption interdependencies. Figure 2 displays ow te transmission mecanism works in eac of tese situations wen te tree countries are symmetric: te rst tree panels sow output responses wen tecnology disturbances are present and te last tree panels output responses wen government disturbances wic yield no utility for agents are present. In all cases time series of lengt T=6000 were generated from te model, a VAR wit 9 lags was t to detrended outputs and impulse responses following an output sock in country 1 1were computed triangularizing te system in te order country 1, 2 and 3. Consider rst a situation were tere are tree completely separate economies wic move togeter because tey are it by correlated disturbances. In tis case, te domestic dynamics are te same as in a closed economy (see e.g. King, Plosser and Rebelo (1988) and Aiyagari, 1 Altoug it is typical to compute \population" impulse responses (see e.g. King, Plosser and Rebelo (1988)), to examine te properties of teoretical economies, ere we instead consider \empirical" impulse responses in order to maintain comparability wit te responses of gure 1.

13 4 THE PROPERTIES OF THE MODEL 12 Eicenbaum and Cristiano (1992)). Two features of te cross country output responses need to be noted. First, te model generates te same type ofsort run output responses regardless of te source of structural disturbances. In particular, in bot cases a positive output sock in country one isassociated wit positive output responses in oter countries and a slow return to te steady state position; apeak response lagging te initial sock 3-6quarters in all countries and an expansion pase wic is approximately te same lengt inte two cases. Second, it is possible todistinguis between te two sources of structural disturbances by examining te sign and te magnitude of long run output responses and, to some extent, te smootness of teir convergence to te steady state. Next, consider te case of uncorrelated socks wic are solely propagated to oter countries troug production interdependencies Te experiment, wic mimics asituation were domestic residents consume only domestic goodsandcountries are connected via trade in intermediate goods, is similar to te one examined by Backus, Keoe and Kydland (1993) except tat ere production requires domestic and foreign capital goods wile Backus, Keoe and Kydland do not distinguis between consumption and capital goods in teir model. A positive and persistent disturbance displacing output in country one from its trend increases investments in capital goods used for domestic production (bot of domestic and foreign origin), consumption and ours in te country experiencing te sock. However, contrary to te one good case, te features of te international transmission depend on te relative size of capital inows (substitution eect) and of capital outows due to te spillover of te sock (wealt eect). In turn, te net eect of tese two opposing forces depends on te weigts of various capital goods in te production functions. If te domestically produced intermediate inputs are more intensively used in domestic production, te substitution eect dominates and cross country output dynamics are similar to tose of te one good economy. If foreign produced intermediate inputs are more intensively used, te wealt eect prevails generating positive, altoug lagged, foreign output responses. Te second and ft panelsof gure 2 present anintermediate case were domestic and foreign intermediate inputs ave equal intensity in eac of te tree production functions. Two features of te responses need to be noted. First, wile initially a positive output sock in country 1 induces a negative response in te output of oter countries, as foreign production

14 4 THE PROPERTIES OF THE MODEL 13 of capital goods used in country 1 increases (and foreign investment in capital goods used in foreign countries decline), in te medium-long run te spillover eect dominates and net exports of investment goods from country one become positive. Second, te sape of te output responses to a one standard error output sock in country one does not depend on te structural sources of disturbances. Tese results agree wit tose of Backus, Keoe and Kydland (1993) wo sowed tat bot government and tecnological disturbances induce negative output comovements and a negative current account balance in te country experiencing te sock. Finally, consider te case of uncorrelated disturbances wic are solely transmitted to te world economy because of consumption interdependencies (so tat domestic production requires only domestic inputs). Depending on te parameters of te utility function, we may ave no transmission if te utility function weigs domestic goods eavily, or a substantial one, if domestic consumers prefer foreign goods. Te tird and sixt panels of gure 2 present impulse responses for te case were all goods ave te same weigt in te utility function. Consistent wit te dynamics described in Stockman and Tesar (1994), tis canneloftransmission generates small positive output responses coupled wit a lot of sort run variability wen tecnology disturbances drive te cycle. Wen government disturbances drive te cycle, te dynamics are more interesting. Aneg- ative government disturbance increases current output available for private use and current consumption of all goods. Because te level of foreign output is given wen te sock occurs, te increased domestic demand for foreign goods is accommodated via a reduction of foreign investments. Since foreign ours increase at impact, foreign output increases temporarily and ten falls as te decline in foreign investment reduces te capital stock. Also, because part of te increase in private consumption fallsonforeign goods, domestic investments increase more tan in te closed economy caseboosting domestic production and leading to te lagged domestic peak response observed in te sixt panel of gure 2. Hence, temporary cuts in government expenditure generate positive domestic multiplier eects as resources are moved from current to future consumption, but negative eects onforeign outputs, as resources are moved from future to current consumption. In te medium run te wealt eect dominates and positive cross country spillovers obtain. Tree main conclusions can be derived from studying te dynamics of te model. First, te

15 5 CAN THE MODEL REPRODUCE ACTUAL IMPULSE RESPONSES? 14 transmission of tecnology and government disturbances looks very similar in two out of te tree cases so tat it is not always possible to distinguis wic source of disturbance buets te system. Second, wile socks wic are contemporaneously correlated induce sort run positive cross country output responses wic die out in te medium-long run, socks wic are contemporaneously uncorrelated and transmitted via trade in goods induce an immediate negative response in foreign outputs and a positive spillover in te medium-long run. Tird, te lagged output responses observed in te data could be generated by a model were only contemporaneous spillovers are allowed. 5 Can te Model Reproduce Actual Impulse Responses? Te next question we ask is weter te model can reproduce te most interesting features of te impulse responses of te actual data wit a realistic parameterization. To start wit we consider a situation were te world is composed of tree identical countries. Tis step is useful for two reasons: to clarify wic of te tree cannels we ave discussed is dominant in transmitting te two types of disturbances across te world and to make te analysis comparable wit previous work by e.g. Cantor and Mark (1988), Backus, Keoe and Kydland (1992) or Stockman and Tesar (1994) wic primarily consider te case of identical countries. 5.1 Te Parameterization of te Model Te parameters of te model are ; ; ; ; ; ; A (`); ; ; 6,, te social planner j j j weigts!,te elasticity of te investment-capital ratio to canges in Tobin's Q plus te steady state values of Tobin's Q and steady state ratios (c/y; g/y; i/y). Te selected values are in table 2. As in all calibration exercises, we desire tat a model trying to explain te cyclical properties of te data ts long run observations. Tis parameter selection procedure is equivalent to te metod of moments approac suggested by Cristiano and Eicenbaum (1992) wen only rst moments of te data are used to form ortogonalityconditions. Oncetisisdone, te parameters wic are specic to business cycle frequencies are selected on te basis of existing studies or, absent suc literature, tey are xed a-priori and a sensitivity analysis is performed to assess te robustness of te results. According to tis logic we coose ; ; ;, te steady state ratios j j

16 5 CAN THE MODEL REPRODUCE ACTUAL IMPULSE RESPONSES? 15 and te steady state value of Tobin's Q so tat te steady states of te endogenous variables matc long run averages in te data. Wedirectly estimate A (`) and 6 from te data, wile ; ; ; ; are xed a-priori or selected witin a reasonable range of existing estimates. j Long run averages are computed using data from several sources. Various issues of Eurostat External Trade Analytic Tables and te United Nations International Trade Statistics Yearbook report data on te value of imports and exports toward a particular country and on its composition by category of goods. Te Yearbooks of Labor Statistics provide data on ours worked per week (Establisment Surveys). Te Statistical Abstract of te US, te Japan Statistical Yearbook and te Montly Reports of te Bundesbank provide time series for te sares of labor compensation in GDP. Tese tree sources are used to construct te and paramj j eters. IMF Government Finance Statistics Yearbooks provide data on te tax revenues for te tree countries wic is used to select. Te OECD Economic Outlook, Historical Statistics provides data on te average growt rate of GDP in te tree countries for te sample , wic is used to pin down. Various issues of te Statistical Abstract of te US, Japan Statistical Yearbook and te Montly Reports of te Bundesbank provide te composition of GDP by categories of absorption. Steady state ratios are computed averaging te composition of GDP by categories over te sample Te steady state Tobin's Q is set equal to 1 so tat te model wit adjustment costs as te same steady state as a model witout adjustment costs. Te time series properties of government expenditure are estimated using an AR(1) model on OECD data for te period 1960,1-1994,4 wile te time series properties of te tecnology socks are estimated using a univariate AR(1) model on te Solow residuals of te tree countries. It is wort noting tat government expenditure may contain a component wic is endogenously responding to te developments in te economy. In tis situation it is typical to use military expenditure to proxy for its exogenous component (see e.g. Rotemberg and Woodford (1992)). Here we do not follow tis approac because military expenditure is only a small fraction of total government expenditure (and of GDP) in Japan and Germany, so tat te resulting properties for g t may ave very little to do wit its truly exogenous component. Many estimates of te coecient of relative risk aversion exist for te US but evidence for te oter two nations is scant. To provide a range for selecting we estimate tis parameter

17 5 CAN THE MODEL REPRODUCE ACTUAL IMPULSE RESPONSES? 16 over ve dierent samples using te tree procedures suggested by Brown and Gibbons (1985) and comparable wealt and consumption aggregates. Te ranges of estimates are [1.09, 2.06] for te US, [1.48, 1.97] for Germany, [0.67, 2.23] for Japan. Te values presented refer to exactly identied GMM estimates and are from Canova and De Nicolo' (1995). Many of te values for USparameters presented in table 2 are standard. For te oter two countries te values are similar to tose previously employed in te literature (see e.g. Cardia (1991), Reynolds (1992), Stockman and Tesar (1994), Parente and Prescott (1994)). Te values of tax rates are sligtly lower tan tose used by e.g. Baxter and Crucini (1993) but tis may be due to te presence of measurement errors in tax revenues. Te table contains estimates of parameters wic ave not been previously used (te sare of foreign capital in production) wile te estimates of te sare of foreign consumption in total consumption are partially new. To construct te sare of total intermediate foreign goods in total output we add imports of industrial supplies, fuels and macinery equipment in eac country and divide te total by current GDP. To decompose te total sare by country of origin we calculate te sare of intermediate goods coming from eac of te two oter countries, normalize te sum to one and divide te sare of total intermediate goods using te relative weigts obtained. Tis normalization is necessary because te percentage of intermediate imports from countries oter tan te two considered is, in general, large. Te sare of foreign goods in total consumption is obtained by summing up te value of imports of food, beverages and nondurable goods and dividing by te value of consumption of nondurable goods and services in eac economy. Te sare of foreign consumption goods by country of origin is computed using te same procedure used to obtain eac country's sare of intermediate imports. Te previously used value for te sare of foreign nondurable goods and services coming from abroad is iger tan te one employed ere (Sclagenauf (1989) as e.g ). However, previous measures are biased upward since tey include items like imports of transport equipment wic are neiter nondurable nor nal goods. One sould also note tat our estimates may bedownward biased because no direct measure of te ow ofservices from foreign produced durable goods is available. Tis may beimportant for te US, were consumption of Japanese and German durables is substantial. As in Cristiano and Eicenbaum (1992) and Backus, Keoe and Kydland (1993), we con-

18 5 CAN THE MODEL REPRODUCE ACTUAL IMPULSE RESPONSES? 17 sider primarily te case of =0 but also examine weter results cange wen zero to one. Similarly, j moves from are cosen so tat te investment-capital ratio is sensitive to canges in Tobin's Q but we experiment wit two oter specications were te investment-capital ratio is less responsive. In principle, one could estimate tis elasticity parameter from moment conditions involving te variability of investment. Because te model contains multiple capital goods and because no disaggregated investment data exist, no fruitful estimation seems possible. Finally, we assume tat! 's are proportional to te population of te tree countries in Baxter and Crucini (1993) ave sown tat country size as some eect on te time series properties of saving and investment witin countries. Terefore, we also examine weter te properties of transmission are altered wen tese weigts cange. 5.2 Some Simulation Results Figure 3 presents output responses following a one standard error output sock in country 1 wen te underlying economy is driven by tecnology disturbances (panel 1) or by government disturbances (panel 2) for te case of tree identical countries. Te lower panel of table 1 reports summary statistics. Te gure presents point estimates of te responses were, to reduce te importance of small sample biases, te lengt of te simulated time series is T=6000. To facilitate te comparison wit te actual data, te same 95% condence bands presented in gure 1 wen US GDP is socked are superimposed in eac panel. US parameters are selected 1 for tis baseline case and! =.For tecnology disturbances te standard error is , te 3 serial correlation 0.95 and te cross country contemporaneous correlation For government expenditure disturbances te standard error is , te serial correlation 0.98 and te cross country contemporaneous correlation Wen te economy is driven by tecnology disturbances te eect due to te contemporaneous correlation of socks is strong in te sort run wile production interdependencies are important in determining te magnitude and te sape of te responses in te medium{long run. Not surprisingly, given te small sare of foreign goods in utility, consumption interdependencies play a negligible transmission role. Wen government expenditure disturbances make economies uctuate, te presence of a common component in te disturbances is responsible for te initial dynamics but transmission via trade in nal goods is dominant in te medium run.

19 5 CAN THE MODEL REPRODUCE ACTUAL IMPULSE RESPONSES? 18 For bot types of disturbances we observe a delayed peak response in country 2 and sizable cyclical responses in countries 2 and 3, as is te case wit te actual data. Furtermore, te magnitude of te peak responses is broadly consistent wit tose in te data and, for most orizons, simulated responses are inside te 95% band of te actual ones. In addition, te model driven by government disturbances generates a lagged peak response in country one, a feature wic appears to be important for actual US output socks. One remarkable feature of gure 3 is tat te two specications generate output responses wic are qualitatively very similar. For example, te model can qualitatively reproduce te \US locomotive" in bot cases: positive output socks in country 1 are associated wit instantaneous positive foreign responses, a lagged peak response in country 2 and signicant multiplier eects in two of te tree countries. Bot specications fail in oter dimensions. For example, te model is unable to capture cycle lengts and turning points under bot specications: cycles in simulated data are somewat too sort and te timing of turning points is o by a few quarters. Also, te model does not reproduce te large and positive Japanese output responses following US output socks present in te data and it underestimates te magnitude of total multipliers in all tree cases. 5.3 Sensitivity Analysis Before moving to more complicatedversions of te model, we run 8 experiments to knowweter te features of te impulse responses we ave just described are robust to modications of tose parameters wic are cosen a-priori or measured wit substantial error. Experiment 1 considers a situation were private and public consumption are imperfectly substitutable in te utilityofdomestic agents, i.e., =0:5. Experiment2examines te situation were consumers are very risk averse, i.e. = 10. Experiment 3 covers te case of a lower discount factor, i.e. =0:96. In experiment 4 no distortionary taxes are levied on output, i.e. = 0:0 8. Experiment 5 considers an economy wit serially uncorrelated disturbances, i.e. g = a = 0:0. Experiment 6 presents a case were te elasticity ofte investment-capital ratio 01 to Tobin's Q is lower, i.e. (; j) = 00:005; 8; j. Experiment 7 covers a situation were te cost of using domestically produced capital goods is lower tan te cost of using capital produced in anoter location, i.e. (; j) = 00:01; (; ) = 00:0001. Finally, in experiment 8we study a situation were two of te tree countries trade teir own capital goods more easily, i.e.

20 5 CAN THE MODEL REPRODUCE ACTUAL IMPULSE RESPONSES? (; j) = 00:0001 if, j=1, 2 or =j=3 and (; j) = 00:01 oterwise. Summary statistics for te rst experiment are in table 1andfor te oter 7 experiments are in table 3. Wen government expenditure is a better substitute for private consumption, socks are less persistent and output responses display smaller swings, but te qualitative features of te international transmission are unaltered. Intuitively an increase in government expenditure as two eects on consumption in tis case. Te rst one is troug te resource constraint, as wen = 0:0. Te second occurs because an increase in government expenditure increases current utility of domestic agents, reduces te incentive to substitute leisure intertemporally and, terefore, te magnitude of future output increases. Hence, ceteris paribus, output socks generate uctuations of reduced magnitude and ave smaller international repercussions. Te magnitude of te cange in agents' leisure prole depends on te persistence of government disturbances: for igly persistent disturbances and values of up to 0.7, te importance of tis second cannel is rater small. Increasing or decreasing as similar eects on te transmission of socks. Wen is ig, positive tecnology or negative government disturbances lower total investment, result in less persistent domestic responses and a weaker and less persistent cross country spillover because agents are less willing to substitute intertemporally. Similarly, wit a lower agents wis to consume more today relative to te future. Consequently, wit positive tecnology disturbances more impatient agents will invest less and, wit negative government socks tey will intertemporally substitute more current for future leisure, reducing te prole of future output growt. In bot instances, iger current consumption desires induce weaker persistence, smaller own multiplier and a reduced international transmission of disturbances. Te magnitude of te canges is, owever, small and none of te qualitative features of te transmission is aected. Variations in tax rates from 0 to 50% ave nosignicant eects on te persistence of output responses and on teir cross country transmission wen te economy is driven by tecnology disturbances. Wen government spending disturbances drive te cycle and tere are no distorting taxes, agents enjoy more good times on domestic goods so tat te spillover eect is reduced. Also in tis case qualitative dierences in te propagation of te socks are small. Wen disturbances are serially uncorrelated, output responses die out quickly, spillovers

21 5 CAN THE MODEL REPRODUCE ACTUAL IMPULSE RESPONSES? 20 are small, apart from te initial contemporaneous eect, multiplier eects are insignicant and te location and magnitude of turning points cange. Wen g = 0; 8t, = 1:0, t = = 0 8j 6= and = 1:0, tis economy issimilar to te one examined by Long j j and Plosser (1983) in a domestic framework and Cantor and Mark (1988) in an international setup. Tey assert tat wit iid tecnology socks, te model can generate output comovements across sectors or countries. Tis experiment demonstrates tat even wen output disturbances are uncorrelated over time, comovements in te cyclical component of output do exist (te contemporaneous correlation of outputs is around 0.70). But tis is a ig frequency not a business cycle penomena. Variations in substantially cange te propagation features of output socks. Wen te elasticity of te investment-capital ratio to canges in Tobin's Q is smaller, positive output socks result in less investment bot domestically and abroad, independently of te source of disturbance, and tis reduces te persistence of te socks and teir international impact. Tis is intuitive: if te cost of installing new capital is iger, agents prefer to consume more now and less in te future to avoid tedeadweigt loss. Tis result is independent of te exact value 01 of : for values up to te one used by Baxter and Crucini, similar. = 00:075, output dynamics are Wen iger costs must be paid to install new foreign capital domestically, te transmission features are altered wen tecnology socks drive te cycle as output swings in country 1 are magnied in te medium run. Wen government disturbances drive te cycle, minor dierences wit te baseline case emerge. Tis is not surprising since production interdependencies play a minor role in te transmission of government disturbances. Finally, wen two of te countries (say, countries 1 and 2) enjoy some proximity wic allows tem to incur lower costs in importing eac oter's capital goods, we observe a substantial asymmetry in output responses wen tecnology disturbances drive te cycle. Te responses of country 3 are fairly close to zero at all orizons. Tis is to be expected since investment dynamics are responsible for te international cycle wen tecnology disturbances drive te cycle. Wit government expenditure disturbances, responses do not cange muc since, in tis case, te gross ow ofcapital across borders is of a smaller order of magnitude. In sum, te qualitative properties of te domestic and international transmission of te two