Can non-traded goods solve the “comovement problem?”

Journal of Macroeconomics 25 (2003) 169–196 www.elsevier.com/locate/econbase

Can non-traded goods solve the ‘‘comovement problem?’’ K.H. McIntyre Department of Economics and Business Administration, McDaniel College (formerly Western Maryland College), 2 College Hill, Westminster, MD 21157-4390, USA Received 23 November 1999; accepted 21 December 2001

Abstract The inability to replicate positive international comovement of investment spending and employment remains one of the most vexing issues facing the international real business cycle (IRBC) research program. To attack this so-called ‘‘comovement problem,’’ I develop a multisector IRBC model highlighting the role of non-traded goods and international capital mobility. In addition to broadly replicating prior IRBC successes, the model more importantly delivers positive international investment and employment correlations. The model is also able to generate internally the observed result that variables associated with traded goods sectors exhibit higher volatility than those in non-traded sectors. Ó 2003 Elsevier Science Inc. All rights reserved. JEL classification: C68; E32; F41 Keywords: Comovement; Open-economy business cycles; Non-traded goods

1. Introduction and overview Over the past decade, real business cycle theory and modeling strategies have become commonplace in open-economy macroeconomics. Yet while significant progress has been made––open-economy real business cycle models have been quite successful in examining a variety of international phenomena ranging from the dynamics of the current account (Backus et al., 1994) to international savings/investment correlations (Baxter and Crucini, 1993)––this general class of models fails in certain key areas. Most notably, the typical international real business

E-mail address: [email protected] (K.H. McIntyre). 0164-0704/03/$ - see front matter Ó 2003 Elsevier Science Inc. All rights reserved. doi:10.1016/S0164-0704(03)00024-7

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cycle (IRBC) model predicts that capital investment and labor input are negatively correlated across countries when in reality these macro variables exhibit strong positive comovement, a difficulty Baxter (1995) has coined the ‘‘comovement problem.’’ The comovement problem arises in IRBC models primarily as a result of the feature that physical capital is freely mobile (or mostly so) internationally. This coupled with the fact that capital positively affects the marginal product of labor results in international capital flows––triggered by a productivity shock in one location––generating strongly negative investment and labor input correlations between counties. Therein lies the most bedeviling aspect of the comovement problem: it is a by-product of trade in capital goods, one of the IRBC modelÕs most salient features. It has been suggested that one way to alleviate these problems is to extend the one-good, one-sector structure of the standard IRBC model to a multigood, multisector one. Multigood models of this sort were first developed in the mid-1990s by introducing an additional consumption and investment good by assuming national specialization (see Backus et al., 1994; Arvanitis and Mikkola, 1996). This approach was further expanded by Stockman and Tesar (1995), who introducing non-traded goods into an IRBC framework. As it has been estimated that roughly half of the typical G-10 countryÕs output consists of non-traded goods and services, Stockman and TesarÕs inclusion is an important extension to the IRBC program. And introducing a non-traded good allows one to evaluate the ability of this class of models to reproduce the salient features of disaggregated international data. But whereas the Stockman and Tesar model does take the seemingly important step of including non-traded goods, it includes the serious flaw insofar capital trade is not permitted, even though it is a well-established fact that capital trade dominates fluctuations in the current accounts of developed countries (Baxter, 1995). This paper corrects the capital flow problem inherent in the Stockman and Tesar model by introducing the potential for capital flows in a multisector IRBC model featuring both traded and non-traded goods. This introduction involves placing a set of restrictions on intra- and international capital use and trade, restrictions that are both realistic in terms of the stereotypical nature of and non-traded goods and practical in terms of ameliorating the comovement problem. The results obtained from this study are quite encouraging, as the model is able to replicate most of the empirical regularities of international business cycles delivered by previous IRBC models as well as to provide positive cross country employment and investment correlations. In addition, the model is able to generate internally the result that non-traded consumption and investment goods tend to be less volatile than their traded counterparts. The organization of the remainder of the paper is as follows: Section 2 briefly considers some of the stylized international business cycle facts for traded and nontraded goods. Section 3 describes how the introduction of non-traded goods can help mitigate or eliminate the comovement problem. Section 4 presents the model. Section 5 discusses the calibration of the model and solution methods. Sections 6 summarizes results and Section 7 concludes.

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2. Sectoral stylized facts I begin by reviewing business cycle facts for a variety of traded, non-traded, and aggregate macroeconomic variables from annual NIPA and labor statistics for 10 developed countries: the United States, Canada, France, Germany, the United Kingdom, Australia, Belgium, Denmark, Norway, and Sweden. Moments were calculated from data found in the 1996 Organization for Economic Cooperation and Development (OECD) International Sectoral Data Base and OECD Quarterly National Accounts; a more thorough description of the data is located in Appendix A. The data were detrended using the Hodrick–Prescott filter with the smoothing parameter (k) set to 10, the value recommended by Baxter and King (1995) for use with annual data. 2.1. Domestic properties I assume the reader is familiar with the empirical regularities of international business cycles and will consequently be quite brief in this and the proceeding subsection. Tables 1 and 2 contain some of the more important within-country results for aggregate and traded and non-traded macroeconomic variables. Table 1 displays a variety of volatility statistics for NIPA components and employment measures. Observe the typical results for aggregate data: consumption and labor input are less volatile than output but investment is more volatile that output by a factor of two to three. In addition, Table 1 suggests that for all NIPA components and employment measures, traded variables tend to be more volatile than their non-traded counterparts. Perhaps the best way to explain this observation is that traded sectors produce relatively more highly volatile durable and/or capital goods than non-traded ones. Yet when disaggregating into traded and non-traded goods, the usual empirical regularities apply: consumption is slightly less volatile than output, labor is also less volatile than output but is somewhat more volatile than consumption, while investment is about two to three times as volatile as output. Table 2 contains within-country business cycle correlations. Consumption and employment are both strongly correlated with output at both the aggregate and sectoral levels. Investment and output tend to share an even stronger positive correlation regardless of whether aggregate, traded, or non-traded data is being examined. The one minor distinction between sectors is found with the consumption/output correlation, where traded consumption and output are more highly correlated than their non-traded counterparts. Table 2 also includes cross-sector correlations of output, consumption, investment, and labor input. A regular pattern is easily discernible: all four macro of these macroeconomic aggregates are highly correlated across sectors. Consumption and employment generally possess the strongest correlations across sectors, averaging +0.61 and +0.67 respectively. With an average correlation of +0.29, the weakest relationship is found between cross-sector investment expenditures, and this correlation is actually negative for the United Kingdom data. The other statistics of interest in Table 2 concern the correlation between the relative price of non-tradeables and the ratios of non-traded to traded consumption and output. In both cases, these correlations are strongly positive for every country

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Table 1 Standard deviations (% per year) of macro aggregates Output

Consumption

Investment

Employment

Net exports

Terms of trade

US Aggregate Traded Non-traded

1.83 2.62 1.01

1.49 1.87 0.91

3.66 4.32 3.77

1.51 2.02 1.00

1.80

4.48

Canada Aggregate Traded Non-traded

1.91 2.07 1.04

1.46 2.47 0.71

2.81 7.18 1.72

1.39 1.99 0.93

2.01

3.53

France Aggregate Traded Non-traded

1.04 1.47 1.03

0.80 0.97 1.00

2.01 3.21 1.77

0.74 1.12 0.93

2.14

2.38

Germany Aggregate Traded Non-traded

1.63 1.92 1.63

1.22

2.89 3.98 2.73

1.04 1.14 0.99

2.09

2.65

1.23 2.07 1.15

2.78 4.14 3.25

1.07 1.34 1.04

1.59

4.71

1.02

3.85 5.32 4.14

1.27 1.06 1.65

1.79

6.11

United Kingdom Aggregate 1.99 Traded 2.50 Non-traded 2.22 Australia Aggregate Traded Non-traded

1.47 1.70 1.54

Belgium Aggregate Traded Non-traded

1.17 1.54 1.30

3.48 5.35 3.39

0.72 0.82 0.85

2.05

2.87

Denmark Aggregate Traded Non-traded

1.42 1.49 1.86

6.31 7.13 6.53

0.93 1.27 0.92

1.52

2.36

Norway Aggregate Traded Non-traded

1.30 1.92 1.40

3.05 5.33 3.89

0.97 1.06 1.05

0.97

2.35

Sweden Aggregate Traded Non-traded

1.81 2.13 1.41

4.35 6.60 3.34

1.02 1.31 0.92

2.06

2.78

Source: OECD; sample period is 1970–1992. All variables except net exports are in natural logs; variables detrended using the Hodrick–Prescott filter with smoothing parameter ¼ 10.

Table 2 Domestic correlations US

France

Germany

UK

Australia

Belgium

Denmark

Norway

Sweden

0.85 0.92 0.70 )0.47

0.59 0.89 0.80 )0.34

0.71 0.73 0.70 )0.20

0.55 0.70 0.26 )0.33

0.34 0.78 0.80 )0.21

0.48 0.52 )0.04

0.75 0.92 )0.57

0.35 0.23 0.14

0.78 0.58 )0.40

Traded sector Consumption Investment Employment

0.77 0.95 0.76

0.87 0.34 0.70

0.61 0.86 0.76

0.65 0.61

0.51 0.52 0.55

0.47 0.54

0.35 0.49

0.63 0.80

0.28 0.14

0.82 0.57

Non-traded sector Consumption Investment Employment

0.56 0.82 0.92

0.37 0.49 0.79

0.09 0.56 0.31

0.61 0.85

0.45 0.24 0.04

0.66 0.77

0.56 0.71

0.68 0.87

0.50 0.54

0.21 0.67

Cross-sector correlations ðy TR ; y NT Þ ðcTR ; cNT Þ ðiTR ; iNT Þ ðN TR ; N NT Þ

0.73 0.83 0.67 0.92

0.63 0.61 0.26 0.48

0.24 0.28 0.09 0.92

0.60

0.22 0.70 )0.24 0.48

0.60

0.33

0.48

0.44

0.76

0.27 0.81

0.10 0.47

0.68 0.47

0.25 0.67

0.24 0.64

)0.13 )0.54

0.48 0.35

0.58 0.57

0.4

0.63 0.03

0.32

0.58

0.12

0.45

0.42

Prices and quantities ðpNT =pTR ; Y NT =Y TR Þ ðpNT =pTR ; C NT =C TR Þ

0.61 0.80

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Correlation with own-sector output Aggregate Consumption 0.88 Investment 0.97 Employment 0.82 Net exports )0.55

Canada

173

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in the sample except the US, where both are negative. These results, however, should be viewed with caution. Gordon (1990), for example, constructs an alternate measure of non-durable to durable relative prices which Baxter (1996) has shown to behave differently at business cycle frequencies than the relative price series I (and others) have constructed using standard price indices. While not directly applicable here, this notion is nonetheless relevant insofar non-traded goods are often associated with non-durable goods and services. Because these correlations are of minor importance for the purposes of this paper, these matters are not further investigated at this time. 2.2. International properties Table 3 summarizes some international business cycle statistics of note. Once again, a number of generalities arise when examining aggregate data. First, contemporaneous movements in aggregate output tend to be positively correlated across countries or better, positively correlated with US output. Second, US and international aggregate consumption correlations follow the same pattern, only these correlations tend to be weaker than those between outputs. Aggregate investment and employment also exhibit positive international comovement. As with consumption, international investment and employment correlations are not as strong as the corresponding output correlations. Third, US and foreign net exports do not seem to be systematically correlated. Although the same patterns of correlations are common across aggregate, traded, and non-traded data, there is one distinct difference between the international correlations of traded and non-traded variables. Namely, traded sector outputs tend to share a stronger correlation internationally than non-traded outputs do. One can make a similar statement about traded and non-traded consumption aggregates. In contrast, the disaggregated cross-country investment and employment correlations do not exhibit any such relationship––five of nine countries had a higher correlation between their and US non-traded investment and/or labor inputs than the corresponding correlations for traded sector investments and labor.

3. How can non-traded goods help? Before proceeding with a discussion of the model and simulation results, it is of some interest to discuss the mechanism by which the inclusion of non-traded goods may help to solve or mitigate the comovement problem. As previously stated, a common feature of standard IRBC models is capital trade. Unfortunately in these models, the comovement problem arises as a result of this most salient feature. Indeed, because capital is able to freely move internationally in response to productivityenhancing disturbances, investment spending is negatively correlated in model economies. Given that the returns to labor are positively impacted by capital flows, along with possible divergent permanent income effects stemming from asset market structure, negative labor input correlations are also commonly observed. Of course, this is the opposite of what is observed empirically.

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Table 3 Correlation with same US variable Output

Consumption

Investment

Employment

Canada Aggregate Traded Non-traded

0.80 0.79 0.07

0.58 0.75 0.17

0.36 0.24 0.30

0.65 0.75 0.04

France Aggregate Traded Non-traded

0.43 0.46 0.27

0.47 0.46 0.49

0.41 0.59 )0.07

0.37 0.33 0.22

Germany Aggregate Traded Non-traded

0.66 0.61 0.42

0.50

0.39 0.39 0.47

0.51 0.50 0.36

United Kingdom Aggregate Traded Non-traded

0.21 0.80 0.09

0.56 0.49 0.18

0.61 0.49 0.25

0.74 0.72 0.49

Australia Aggregate Traded Non-traded

0.63 0.70 0.48

0.57

0.39 0.31 0.34

0.62 0.55 0.65

Belgium Aggregate Traded Non-traded

0.41 0.38 0.52

0.07 0.02 )0.07

0.62 0.43 0.74

Denmark Aggregate Traded Non-traded

0.73 0.66 0.53

0.40 0.28 0.58

0.62 0.50 0.59

Norway Aggregate Traded Non-traded

0.39 0.20 0.51

)0.32 )0.19 0.12

0.23 0.27 0.19

Sweden Aggregate Traded Non-traded

0.36 0.40 0.10

0.00 )0.01 )0.30

0.23 0.21 0.29

The inclusion of additional sectors provides three avenues by which the comovement problem can be at least partially solved while still permitting capital mobility. First, it is very reasonable to suggest that capital use and degree of mobility should differ across sectors. The distinction between traded and non-traded goods is especially helpful in this respect. By definition, non-traded output cannot be used for consumption and more importantly, investment goods abroad. This curtails the

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volume of capital which can flow out of a country in response to a favorable foreign shock (recall that approximately half of a developed countryÕs output can be classified as ‘‘non-traded’’). This notion is the cornerstone of the modeling strategy employed in this paper, the particulars of which will be detailed in the proceeding section. Second, a common equilibrium condition in multisector models is that factor prices, notably the marginal product of labor, must be equalized across sectors. The model developed in this paper is no exception. This should at least somewhat mitigate any real wage effects caused by productivity shocks and capital flows, hence limiting movements into and out of labor markets in response to asymmetric shocks. A final issue regards intersector labor movements. While individuals can and do reallocate labor hours from one sector to another, it is not apparent that reallocated hours are immediately or completely available to employers. That is, firms may face a delay in the form of training time or a similar friction before new hours come ‘‘fully on-line.’’ Incorporated into my model as a labor adjustment cost process, this will also curtail labor movements in response to business cycle disturbances.

4. The model economy 4.1. Preferences and time The world economy consists of two countries, each of which is populated by a infinitely-lived household that maximizes the expected present discounted value of lifetime utility over consumption, c, and leisure, L: 1 1 X 1 ðct Þ1r Lvt : U ðct ; Lt Þ ¼ E0 Dt ð1Þ 1  r t¼0 Utility is discounted at rate D. Consumption is a CES aggregate of a composite traded good, cTR , and a non-traded good, cNT : h i1=w w NT w ct ¼ ðcTR Þ Þ : ð2Þ þ ðc t t The elasticity of substitution between traded and non-traded goods is 1=ð1 þ wÞ. Following Mendoza (1991), the discount factor is allowed to vary with time to ensure a unique, stationary steady state in an incomplete markets economy. D is defined as:

1 Following the RBC literature, I assume that all of the modelÕs variables, with the exceptions of leisure/ labor and bond holdings, share a common, deterministic growth rate. This growth rate in turn corresponds to trend growth in labor productivity. Specifically, labor productivity, X , is assumed to increase at a constant rate, c, that is, Xtþ1 ¼ cXt . The modelÕs variables are then normalized by X . A variable so normalized is denoted with a lowercase letter, for example, ct ¼ Ct =Xt . See King and Rebelo (1999) for further discussion.

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" Dt ¼ exp 

t1 X

#   v=ð1rÞ b ln 1 þ cs Ls ;

177

ð3Þ

s¼0

where b 6 r ensures a well-behaved utility function (Epstein, 1983). Domestic households also face the following time constraint: 1 6 Lt þ NtTR þ NtNT ;

ð4Þ

where N TR and N NT are hours worked in the traded and non-traded sectors, respectively. Finally, foreign consumers face an analogous problem. 4.2. Technology Each country has two profit maximizing firms, one producing a good that is traded internationally, the other producing a good that is non-traded. Both firms act competitively. With certain restrictions (to be discussed shortly), each good can be used for either consumption or investment purposes. Traded output, y TR , is produced using a Cobb–Douglas technology combining labor services, N S;TR , and capital, k TR , and is subject to a stochastic, asymmetric productivity disturbance, aTR : TR ytTR ¼ aTR t ðkt Þ

1a

a

ðNtS;TR Þ :

ð5Þ

Non-traded goods are produced similarly: NT 1n ytNT ¼ aNT ðNtS;NT Þn : t ðkt Þ

ð6Þ

Observe that capital and labor shares may differ by sector. Firms face a small, convex cost of altering their work force, as in Kouparitsas (1996). Labor servies hence denotes effective time spent in direct sectorial production after elimination of time spent in training or in some other not directly productive activity. Labor services in sector j are related to labor hours as follows:  j Ntþ1 S;j Ntþ1 ¼ f ð7Þ NtS;j ; j ¼ fTR; NTg; NtS;j where f > 0, f0 > 0, f00 < 0. Capital in each sector accumulates as follows:  j i j cktþ1 ¼ ð1  dÞktj þ / tj ktj ; j ¼ fTR; NTg; kt

ð8Þ

where d is the depreciation rate of capital. / is an adjustment cost function, with properties / > 0, /0 > 0, /00 < 0, as in Hayashi (1982). Because capital is, with certain restrictions, freely mobile both internationally and intersectorally, the capital used in any given sector will be an aggregate of both domestic and foreign capital goods, the details of which follow shortly. Again, the foreign country possesses similar technologies.

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The productivity shock vector at ¼ ½aTR aNT aTR aNT follows a VAR(l) prot t t t cess in natural logarithms: ln atþ1 ¼ H ln at þ eat ;

eat iid ð0; RÞ:

ð9Þ

4.3. Capital mobility and prices Capital is not completely mobile across all sectors and countries. Specifically, capital goods utilized by the non-traded sectors may not be used elsewhere, although traded output may be used as a capital good in all four sectors in the world economy. (One should note that this paperÕs use of the term ‘‘non-traded goods’’ is something of a misnomer insofar that foreign capital goods can be and are imported into the non-traded goods sector.) The intuition behind this restriction is the fact that many traditional non-tradeables such as say, many types of services, are intangible; the output produced in these industries cannot be used as a capital input elsewhere. Yet it is also the case that these intangible commodities are often produced using foreign equipment or with foreign financing. The restrictions on intra- and international capital movements are imposed through the economyÕs resource constraints. Extending Backus et al. (1994), domestic traded output can be disaggregated as follows: ytTR ¼ s1t þ s2t þ s3t þ s4t ;

ð10aÞ

where s1 represents the volume of domestic traded goods which stay in the domestic traded goods sector; it is the portion of final domestic traded output which is consumed by domestic agents plus the portion of domestic traded output that is used as an investment good in the domestic traded sector. Similarly, s2 is an investment flow to the domestic non-traded sector, s3 is exports of domestic traded output to the foreign traded sector for both consumption and/or investment purposes, and s4 is domestic investment in the foreign non-traded goods sector. Similarly, domestic nontraded output is ytNT ¼ s5t ;

ð10bÞ

so that all non-traded output remains in that sector. Foreign outputs can be expressed in a similar manner: ytTR ¼ z1t þ z2t þ z3t þ z4t ;

ð10cÞ

ytNT ¼ z5t :

ð10dÞ

Here z1 is the share of foreign traded output which stays in that sector, z2 is ‘‘exports’’ to the foreign non-traded sector, z3 is sent to the domestic traded sector, and z4 is exports to the domestic non-traded goods sector. Perhaps more effectively explained visually, these patterns of allowed intra- and international consumption and capital goods movements are illustrated in Fig. 1. Consumption and investment in each sector is a composite of both domestic and foreign goods. These composites are expressed as a series of Armington (1969) aggregates:

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179

Foreign Traded

Domestic Traded

s3 cTR

iTR

+ = TR G (s1, z3)

s2

cTR* + iTR* = GTR*(s3, z1)

z3

s4

z4

z2

c NT + i NT = G NT(s2, s5, z4)

c NT* + i NT* = G NT*(z2, z5, s4)

Domestic Non-traded

Foreign Non-traded

Fig. 1. Trade patterns in baseline model. l cTR þ iTR ¼ GTR ðs1t ; z3t Þ ¼ ðx1 sl 1t þ x2 z3t Þ t t

1=l

l þ iTR ¼ GTR ðz1t ; s3t Þ ¼ ðx2 sl cTR 3t þ x1 z1t Þ t t

ð11aÞ

;

1=l

ð11bÞ

;

l l þ iNT ¼ GNT ðs2t ; z4t ; s5t Þ ¼ ðx3 sl cNT 2t þ x4 s5t þ x5 z4t Þ t t

1=l

1=l

l l cNT þ iNT ¼ GNT ðz2t ; s4t ; z5t Þ ¼ ðx3 zl 2t þ x4 z5t þ x5 s4t Þ t t

ð11cÞ

; :

ð11dÞ

The elasticity of substitution between own-sector and imported goods is 1=ð1 þ lÞ. The xÕs are weights that capture exogenous home and/or ‘‘sector’’ bias. As the aggregator functions are homogenous of degree one, the following equilibrium relationships can be defined: þ iTR ¼ pts1 s1t þ ptz3 z3t ; cTR t t

ð12aÞ

cTR þ iTR ¼ ptz1 z1t þ pts3 s3t ; t t

ð12bÞ

cNT þ iNT ¼ pts2 s2t þ ptz4 z4t þ pts5 s5t ; t t

ð12cÞ

cNT þ iNT ¼ pts4 s4t þ ptz2 z2t þ ptz5 z5t : t t

ð12dÞ

The prices of each good are in terms of their associated G-composite. Using the resource constraints, domestic outputs can be written as

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  s þ iTR =pt 1 þ ½s2t þ s3t þ s4t  qt z3t ; ytTR ¼ cTR t t

ð13aÞ

  s þ iNT =pt 5  ½ptNT ðs2t þ qt z4t Þ ; ytNT ¼ cNT t t

ð13bÞ

 1 ptz1 þ z2t þ z3t þ z4t  s3t ; qt  

  1 NT z5 NT þ i ¼ cNT  p z s þ ; p 2t 4t t t t t qt

  ytTR ¼ cTR þ iTR t t ytNT



ð13cÞ

ð13dÞ

where q ¼ pz3 =ps1 ¼ pz1 =ps3 , pNT ¼ ps2 =ps5 is the price of domestic tradeables in terms of domestic non-tradeables and pNT ¼ pz2 =pz5 is the price of foreign tradeables in terms of foreign non-tradeables. The terms in brackets represent net exports for each sector. A helpful property of the Armington aggregator is that the terms of trade and other relative prices can be defined using partial derivatives of the G function. Using (10a), for example, one observes that qt ¼

oGTR oz3t



oGTR x2 ¼ os1t x1



z3t s1t

l1 :

4.4. Asset markets Asset markets are incomplete; global financial trade is restricted to include only trade in a non-contingent real bond. Domestic holdings of these bonds evolve according to Btþ1 ¼ nxt þ ð1 þ Rt ÞBt ;

ð14Þ

where nx ¼ ½s3 þ s4  qðz3 þ z4 Þ is priced in terms of the traded good composite. The transversality condition for domestic asset accumulation is lim Dt Wt Btþ1 ¼ 0;

t!1

ð15Þ

where W is the Lagrange multiplier associated with (14). Foreign bond holdings evolve identically. Bonds are in zero net supply worldwide, which implies pBt þ ð1  pÞBt ¼ 0:

ð16Þ

p weights for country size. An upside of this asset market structure is that it will play a role in mitigating with the comovement problem. Indeed, Baxter and Crucini (1995) show that asset market structure has profound implications for the behavior of business cycle models if the shocks driving the model economy are persistent, especially if the shocks are not transmitted across countries. (Section 5 will show that these two criteria are met). In particular, an incomplete asset market structure limits agentsÕ ability to engage in international risk-pooling, thereby reducing the incentive to increase labor input in response to wealth-increasing productivity shocks. Consequently, this eliminates a

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contributor to the negative investment and labor correlations predicted between countries by most IRBC models.

5. Calibration and solution The model is calibrated to replicate the steady-state behavior of the US economy at annual frequencies. Table 4 summarizes these parameter values. The elasticity of substitution between own-sector and imported goods, 1=ð1 þ lÞ comes from Backus et al. (1994) and is initially set to 1.5. Traded and non-traded consumption goods are much less substitutable, with an elasticity of 1=ð1 þ wÞ ¼ 0:30. Following the guidelines set forth in King et al. (1988), the exponent on leisure in the utility function, v, is set to )1.16, and the coefficient of risk aversion, r, is set to 2. The steady-state bond yield is set to 6.5% per annum. Finally, the value of the discount factor parameter, b, is determined by the steady-state condition equating the rate of time preference to the interest rate and is set to 0.147. This value corresponds to a steady-state net foreign asset position of zero in each country. The labor share parameters were set to a ¼ 0:61 and n ¼ 0:56 after estimating (4) and (5) using a constant returns to scale-restricted GMM procedure instrumented with military spending, a dummy denoting the political party of the president, and world oil prices. (These are instruments commonly used to estimate production functions; see Burnside (1996) for more information.) The results obtained are comparable to those found in Stockman and Tesar (1995) and thus provide support for the assertion that traded sectors are slightly more capital intensive. Sector sizes are set equal across countries, consistent with the average traded sector size calculated using the ten country sample. Given that the traded and non-traded sectors are of uniform size, it follows that approximately 52% and 48% of steady-state labor hours are spent in the traded and non-traded sectors, respectively. The derivative properties of the capital adjustment cost functions (6) are set to closely match the empirical volatility of aggregate investment. Finally, at 5.5% per year, the depreciation rate of capital falls within the usual range of values found in the IRBC literature. Exogenous home bias was introduced by borrowing from Arvanitis et al. (1994) and to assign the following values for the weights in the traded good aggregator: x1 ¼ 0:8, x2 ¼ 1  x1 ¼ 0:2. It follows that the other three weights are functions of the home bias parameters and sector size. For example, x3 , the weight on traded goods used in the production of non-traded output, is set as follows: x3 ¼ x4 ¼ (size of traded sector)  (bias towards domestic goods) ¼ (0.5)  (0.8) ¼ 0.4. By default, x5 ¼ 1  x4  x3 ¼ 0:2. The parameters of the technology process are estimated using Solow residuals obtained for the US and an aggregate of the nine other sample countries. Domestic Solow residuals are estimated with the production function residuals and foreign Solow residuals are calculated assuming identical input shares. Following a practice common to the IRBC literature, international symmetry is imposed the estimates of the world exogenous state vector. The AR(1) forcing process for the vector of productivity disturbances ½aTR aNT aTR aNT is estimated as t t t t

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2

0:76 6 0 H¼6 4 0 0

0 0:69 0 0

3 0 0 7 7: 0 5 0:69

0 0 0:76 0

Table 4 Parameter values for model calibration Preferences and steady-state values r¼2 1=ð1 þ lÞ ¼ 1:5 1=ð1 þ wÞ ¼ 0:3 v ¼ 1:16 b ¼ 0:147 R ¼ 0:065 ¼ 6:5%

Intertemporal elasticity of substitution Domestic/foreign elasticity of substitution Traded/non-traded elasticity of substitution Leisure parameter in utility function Elasticity of the discount factor with respect to utility Steady-state bond yield

Technology and aggregation c ¼ 1:016 N TR ¼ 0:1043 N NT ¼ 0:0957 a ¼ 0:56 n ¼ 0:61 d ¼ 0:055 D2 ½/ði=kÞ i=k ¼ 0:0465

Technology trend growth (annualized) Steady-state labor hours, traded sector Steady-state labor hours, non-traded sector LaborÕs share of output, traded sector LaborÕs share of output, non-traded sector Depreciation rate of capital Elasticity of i=k with respect to TobinÕs q

D2 ½fðN S =N Þ N S =N ¼ 19:65

Curvature parameter in labor adjustment cost function Bias towards domestic goods Bias towards foreign goods Bias towards own-country, traded goods (non-traded sector) Bias towards own-country, non-traded goods (non-traded sector) Bias towards non-country, traded goods (non-traded sector)

x1 ¼ 0:80 x2 ¼ ð1  x1 Þ ¼ 0:20 x3 ¼ 0:40 x4 ¼ 0:40 x5 ¼ 0:20 Size s ¼ 0:50 p ¼ 0:50 Forcing processes 2 0:76 0 6 0 0:69 H¼6 4 0 0 0 0 2 1:0048 6 0:6422 V ðRÞ ¼ 6 4 0:6664 0:5633

Size of traded sector Country size 3 0 0 0 0 7 7 0:76 0 5 0 0:69 0:6422 1:0010 0:1408 0:2605

0:6664 0:1408 1:0048 0:6422

3 0:5633 0:2605 7 7 0:6422 5 1:0010

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All spillover terms were insignificant ance–covariance matrix is 2 1:0048 0:6422 0:6664 6 0:6422 1:0010 0:1408 V ðRÞ ¼ 6 4 0:6664 0:1408 1:0048 0:5633 0:2605 0:6422

183

and hence set to zero. The associated vari3 0:5633 0:2605 7 7: 0:6422 5 1:0010

Note that the variances of within-country productivity shocks are of roughly equal size; on average, traded sector shocks are no larger than their non-traded counterparts. Note also that the international covariances associated with non-traded shocks tend to be much weaker then than those of traded shocks, implying a stronger country-specific component to the non-traded productivity process. The equilibrium allocations of consumption, leisure, labor effort and services, investment, and capital are obtained by solving the problem faced by a social planner who maximizes the expected lifetime utility of the two representative households: 1 1 X X pE0 Dt uðct ; Lt Þ þ ð1  pÞE0 Dt uðct ; Lt Þ; t¼0

t¼0

subject to (2)–(6) and their respective foreign analogues, (7), (8), (13), (14) and (16). p weights for country size. As previously stated, I am initially abstracting from differences in country size and/or wealth; this parameter is set to p ¼ 0:50. The terms of trade, the relative price of non-tradeables, and composite-good prices are functions of the modelÕs shadow prices/Lagrange multipliers. The set of efficiency conditions, constraints, and identities describing the economy are log-linearized and cast into a first-order expectational difference system of the form MEt Xtþ1 ¼ HXt þ VðLÞat ; where the vector X contains the modelÕs endogenous variables and a is the vector of productivity disturbances previously discussed. M and H are matrices and V(L) is a matrix polynomial of unspecified order in the lag operator. M and H need not necessarily be invertible. This system was then solved and simulated using the singular systems methods developed by King and Watson (1998).

6. Properties of the theoretical economy 6.1. Benchmark results Tables 5–7 compare the quantitative predictions of the model to the data. In these tables, the entries in the ‘‘Data’’ column are averages with a one standard deviation range in parentheses calculated from the values found in Tables 1–3. The columns marked ‘‘Benchmark’’ contain results obtained from simulating and then HP-filtering the model as outlined in Sections 4 and 5. For reference purposes, I have included analogous results obtained in a ‘‘standard’’ open-economy RBC model, here chosen

184

Data

Benchmark

Sensitivity analysis, domestic/foreign elasticity of substitution

Sensitivity analysis, traded/non-traded elasticity of substitution

Complete markets

Sectorspecific capital

Standard IRBC (Baxter, 1995)

ð1 þ lÞ1 ¼ 1

ð1 þ lÞ1 ¼ 3

ð1 þ wÞ1 ¼ 0

ð1 þ wÞ1 ¼ 0:60

Standard deviation (aggregate) y 1.56 (1.23, 1.99) 1.74 c 1.20 (0.94, 1.46) 1.28 I 3.52 (2.34, 4.70) 4.15 N 1.07 (0.81, 1.33) 0.48 nx 1.77 (1.41, 2.13) 1.24

1.69 1.06 4.18 0.49 1.15

1.81 1.55 4.31 0.48 1.28

1.76 1.20 5.59 0.48 1.03

1.68 1.80 3.48 0.49 1.08

2.14 1.80 5.48 0.49 1.89

1.53 0.89 4.22 0.51 0.29

1.72 0.98 7.01 0.78 0.57

Standard deviation (traded) y TR 1.94 (1.54, 2.34) 1.88 1.85 (1.22, 2.48) 1.54 cTR iTR 5.26 (3.89, 6.62) 5.19 N TR 1.03 (0.80, 1.26) 0.56

1.85 1.29 4.81 0.57

1.94 1.64 5.67 0.57

1.97 1.08 4.83 0.56

1.76 1.88 4.83 0.56

2.25 2.39 9.78 0.53

1.56 0.94 3.46 0.57

Standard deviation (non-traded) 1.44 (1.05, 1.83) 1.67 y NT cNT 0.94 (0.76, 1.12) 1.37 3.45 (2.09, 4.81) 3.99 iNT N NT 1.03 (0.80, 1.26) 0.53

1.60 1.20 4.23 0.53

1.75 1.47 4.07 0.53

1.55 1.50 4.30 0.52

1.68 1.78 3.05 0.53

1.70 0.69 4.63 0.58

1.50 0.94 2.91 0.56

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Table 5 Volatility performance of models

Relative standard deviation (aggregate) c 0.77 0.74 I 2.26 2.39 N 0.69 0.28 nx 1.13 0.71

0.63 2.47 0.29 0.68

0.86 2.38 0.27 0.71

0.68 3.18 0.27 0.59

1.07 2.07 0.29 0.64

0.84 2.56 0.23 0.88

0.58 2.76 0.33 0.19

0.57 4.08 0.45 0.33

Relative standard deviation to own-sector output 0.95 cTR iTR 2.71 N TR 0.68

0.70 2.60 0.31

0.85 2.92 0.29

0.55 2.45 0.28

1.07 2.74 0.32

1.06 4.35 0.24

0.60 2.22 0.37

0.57 4.08 0.45

Relative standard deviation (non-traded)to own-sector output 0.65 0.82 0.75 0.84 cNT 2.40 2.39 2.64 2.33 iNT N NT 0.72 0.32 0.33 0.30

0.97 2.77 0.34

1.06 1.82 0.32

0.41 2.72 0.34

0.63 1.94 0.37

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0.82 2.76 0.30

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186

Table 6 Model correlations Data

0.65 0.74 0.63 )0.29

(0.45, 0.86) 0.77 (0.54, 0.93) 0.52 (0.40, 0.87) 0.34 ()0.52, )0.07) )0.53

Sensitivity analysis, domestic/foreign elasticity of substitution

Sensitivity analysis, traded/non-traded elasticity of substitution

Complete markets

Sectorspecific capital

Standard IRBC (Baxter, 1995)

ð1 þ lÞ1 ¼0

ð1 þ lÞ1 ¼3

ð1 þ wÞ1 ¼0

ð1 þ wÞ1 ¼ 0:60

0.63 0.63 0.36 )0.53

0.74 0.50 0.31 )0.64

0.41 0.61 0.29 )0.38

0.86 0.24 0.40 )0.57

0.75 0.82 0.14 )0.92

0.52 0.99 0.65 )0.86

0.87 0.92 0.88 0.51

Traded sector ðy TR ; cTR Þ ðy TR ; iTR Þ ðy TR ; N TR Þ

0.69 (0.53, 0.85) 0.59 (0.35, 0.82) 0.59 (0.40, 0.78)

0.72 0.12 0.57

0.70 0.23 0.57

0.74 0.15 0.55

0.82 0.37 0.49

0.76 )0.13 0.61

0.24 0.64 0.41

0.63 0.53 0.50

Non-traded sector ðy NT ; cNT Þ ðy NT ; iNT Þ ðy NT ; N NT Þ

0.37 (0.17, 0.57) 0.53 (0.34, 0.72) 0.65 (0.37, 0.93)

0.52 0.93 0.14

0.51 0.97 0.19

0.51 0.90 0.10

0.53 0.97 0.12

0.75 0.77 0.19

0.47 0.21 0.38

0.98 0.99 0.32

Cross-sector ðy TR ; y NT Þ ðcTR ; cNT Þ ðiTR ; iNT Þ ðN TR ; N NT Þ

0.50 0.61 0.29 0.67

0.65 0.75 0.12 0.55

0.66 0.34 0.14 0.55

0.66 0.73 0.24 0.53

0.73 )0.43 0.40 0.51

0.69 0.93 0.18 0.56

0.12 0.13 )0.90 0.53

0.57 0.99 )0.44 0.63

)0.37 0.43

)0.30 0.36

)0.64 0.67

)0.38 0.95

)0.34 0.38

0.92 0.12

0.26 0.59

0.87

0.35

0.67

0.71

0.44

0.69

0.70

(0.31, (0.37, (0.00, (0.48,

0.70) 0.84) 0.58) 0.85)

Price/quantity correlations )0.08 ()0.37, 0.55) ðpNT =pTR ; cNT =cTR Þ ðpNT =pTR ; y NT =y TR Þ 0.38 (0.15, 0.61) Miscellaneous ðnx; qÞ

0.07 ()0.14, 0.30)

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Aggregate ðy; cÞ ðy; iÞ ðy; N Þ ðy; nxÞ

Benchmark

Table 7 Model International correlations

Aggregate ðy; y  Þ ðc; c Þ ði; i Þ ðN ; N  Þ

0.54 0.51 0.25 0.51

(0.49, (0.32, (0.00, (0.32,

Traded sector ðy TR ; y TR Þ ðcTR ; cTR Þ ðiTR ; iTR Þ ðN TR ; N TR Þ

0.56 0.57 0.24 0.47

Non-traded sector ðy NT ; y NT Þ ðcNT ; cNT Þ ðiNT ; iNT Þ ðN NT ; N NT Þ

0.33 0.28 0.18 0.40

Benchmark

0.58) 0.71) 0.54) 0.70)

Sensitivity analysis, domestic/foreign elasticity of substitution

Sensitivity analysis, traded/non-traded elasticity of substitution

ð1 þ lÞ1 ¼0

ð1 þ wÞ1 ¼0

ð1 þ lÞ1 ¼3

Complete markets

Sectorspecific capital

ð1 þ wÞ1 ¼ 0:60

Standard IRBC (Baxter, 1995)

0.51 0.75 0.52 0.39

0.40 0.55 0.16 0.33

0.65 0.93 0.72 0.43

0.30 0.38 0.56 0.34

0.61 0.96 0.64 0.39

0.49 0.98 0.67 )0.43

0.82 0.68 0.85 0.55

0.43 0.93 0.77 )0.15

(0.35, 0.76) (0.40, 0.72) ()0.01, 0.49) (0.29, 0.66)

0.69 0.73 0.40 )0.57

0.61 0.45 0.34 )0.65

0.75 0.86 0.65 )0.47

0.56 0.61 0.38 )0.59

0.78 0.82 0.46 )0.59

0.70 0.94 0.93 )0.14

0.23 0.77 )0.28 )0.10

0.44 0.94 0.84 )0.25

(0.20, 0.53) (0.10, 0.46) ()0.10, 0.46) (0.16, 0.63)

0.27 0.91 0.37 0.16

0.17 0.49 0.21 0.13

0.41 0.93 0.54 0.45

0.13 0.44 0.29 0.10

0.39 0.97 0.48 0.17

0.31 0.49 0.23 0.32

0.84 0.52 0.69 0.34

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Data

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to be the incomplete markets, no productive spillover, version of BaxterÕs (1995) onegood model, where common parameters are set to the values previously described. In most respects, this model does a very good job matching business cycle moments. Looking first at the volatility results in Table 5, one observes that most of the modelÕs predictions concerning the standard deviation of both aggregate and disaggregated output fall within empirical ranges. One observes a similar pattern with consumption, although the model slightly overpredicts the volatility of non-traded consumption. This miss, however, is not an egregious one. The model is similarly able to match the standard deviation of investment at both the aggregate and sector levels. This is not the case with employment, however, where the modelÕs estimated labor volatilies are below those found in the data. The model also underpredicts the volatility of the current account, although in fairness this is a well-documented problem found with this class of models (Backus et al., 1994). With the exception of labor input, the standard deviations of the modelÕs other NIPA variables and employment measures relative to (aggregate or sectoral) output tend to be quite close to those observed in the data. In addition, the model is able to reproduce one key feature from the data: traded variables tend to be much more volatile than their non-traded counterparts. This is of special significance because the volatility of traded and non-traded productivity shocks is approximately equal within countries, that is, this result is generated structurally. This result is in sharp contrast to Stockman and Tesar (1995), who achieve a similar result by using traded-sector productivity shocks whose variance is three and a half times that of non-traded shocks. Moreover, since movements in investment, output, and employment in this class of models are driven primarily by capital movements, these results provide strong support for the capital use structure I have imposed. 2 Tables 6 and 7 are devoted to intra- and international correlations. The withincountry correlations found in Table 6 are fairly standard. Aggregate consumption are investment are highly correlated with aggregate output and within the ranges suggested by data, while at +0.34, the aggregate employment correlation is a bit low. The )0.53 correlation shared by aggregate output and net exports is only slightly stronger than observed empirically, but this is not surprising since the model economy features only a single trading partner. The disaggregated versions of these correlations are reasonably good, although the modelÕs predictions of a +0.12 output/investment correlation in the traded sector and a +0.14 output/employment correlation in the non-traded sector are too weak. Turning to cross-sector correlations, one observes that all four correlations have the correct (positive) sign and magnitude, a welcome achievement in the context of existing multisector RBC models (see Christiano and Fisher (1998) for more information).

2

Baxter (1996) finds a similar result using a closed-economy model producing both durable and nondurable goods, which, as previously stated, are analogous here to traded and non-traded goods. She observes that the sector producing durables exhibits more variability than the non-durable sector and shows that approximately half of this additional variability comes from larger shocks hitting that sector, the other half being generated internally.

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The modelÕs performance regarding the relative price of non-traded goods and the ratios of non-traded to traded consumption and output is reasonable. The model delivers a negative correlation between the relative prices and relative quantities of consumption, accurately capturing what may be presumed to be a dominant demand-side relationship between these two ratios. In contrast, the correlation between relative prices and relative outputs is positive; this may be again capturing a dominant demand-side relationship since both traded and non-traded goods are normal. Finally, the model predicts a much stronger correlation between the terms of trade and net exports than is observed empirically. This, however, is again a likely result of the limited number of trading partners afforded by the model economy. Table 7 contains international correlations. These are undoubtedly the modelÕs strongest selling point. The cross-country correlations for both aggregate and sectoral outputs are all positive and within empirical ranges. In addition, aggregate and traded consumption correlations are near their empirical upper bounds. An outlier is observed with regard to non-traded consumption, with at +0.91, is entirely too strong. Another minor failing is the fact that the modelÕs international consumption correlations exceed international output correlations, even though this model features incomplete asset markets. (Note, however, that the standard IRBC model with incomplete markets generates the same result.) This notwithstanding, the most promising results this model delivers are its predictions concerning the international comovement of aggregate investment and labor input. There is no comovement problem here: at +0.52 and +0.39 respectively, the model correctly predicts both the direction and magnitude of international aggregate investment and labor correlations.This latter result merits additional discussion. Indeed, one will observe that a traditional IRBC model also generates a strongly positive international investment correlation. These results, however, are not analogous. In particular, Baxter and Crucini (1993) note that single good IRBC models can generate positive international investment comovement if the persistence of productivity shocks is sufficiently low. The +0.76 and +0.69 AR(1) coefficients of the estimated productivity processes fall into this category. So generating positive international investment comovement in the one good model is achieved at the expense of realistic persistence. The first order output autocorrelation is +0.68 (not reported) in the one good model whereas this moment is well in excess of +0.90 for each of the 10 countries in my sample. Such a trade-off is not made here, as the non-traded goods model predicts a +0.97 first order autocorrelation for aggregate output. Returning to Table 7, the results are even stronger at a disaggregated level, where both the direction and magnitude of international investment and employment correlations are correctly predicted. The lone exception is traded employment, where there is still a negative correlation. Overall, these findings are unambiguously superior to the bulk of existing IRBC research. 6.2. Sensitivity The two parameters about which there is the most debate are the elasticity of substitution between own-sector and imported goods, 1=ð1 þ lÞ, and the elasticity of

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substitution in utility between traded and non-traded goods, 1=ð1 þ wÞ. While in the baseline case these elasticities have been set as to be consistent with prior empirical studies, considerable uncertainty on their values are nonetheless exists. As such, it is of some importance to assess how robust the modelÕs results are to varying values of these two parameters. This section addresses this issue in some depth. Although the model is fairly robust to small perturbations in one or both of these elasticities, ‘‘extreme’’ values of 1=ð1 þ lÞ and 1=ð1 þ wÞ have an impact on the modelÕs performance. Consider first a ‘‘low’’ elasticity experiment, with 1=ð1 þ lÞ is set to near unity and in a ‘‘high’’ elasticity experiment with 1=ð1 þ lÞ is set to 3, twice its baseline value. These two values are sensible bounds for this elasticity as most empirical studies place this elasticity somewhere between unity and two (Backus et al., 1994). The results for this exercise are summarized in the columns labeled ‘‘Sensitivity Analysis: Own sector/imported Elasticity’’ in Tables 5–7. Decreasing this parameter has the affect of slightly decreasing the volatility of most of the modelÕs non-employment variables. For example, the standard deviation of aggregate consumption falls to 1.06% per year from its baseline value of 1.28%, and the standard deviation of traded consumption is cut by over 15%. One also observes a moderate decline in traded sector investment. These results have a straightforward economic interpretation: as it becomes increasingly difficult to substitute imported capital goods, the flow of capital both into and out of traded goods sectors will diminish, lowering sectoral volatility. On net, most non-traded volatilities mirror the behavior of the traded sector and decline slightly or remain largely unchanged. One observes the opposite tendencies when 1=ð1 þ lÞ is doubled from its baseline value. Domestic and international correlations are mildly affected by perturbing this elasticity. The most notable change is a slight strengthening in output/employment correlations when 1=ð1 þ lÞ is decreased and a slight weakening when it is increased. Although the changes are mild, this is nonetheless an interesting result given this elasticityÕs impact on wages. That is, one might expect that depressed wage effects resulting from weaker foreign capital flows should lower output/employment correlations as the elasticity of substitution decreases. But what is occurring is that weaker international capital flows are making labor a relatively more important input to production, thereby strengthening the output/employment relationship in spite of opposing wage effects. Lastly, changes in international correlations are quite mild, but merit some discussion. Namely, lowering the elasticity of substitution decreases international investment correlations; intra- and international capital flows reinforce investment comovement to a much lesser degree. This in turn results is slight decreases in international employment correlations. As before, one observes the opposite behavior when this elasticity is increased. The modelÕs results are generally less susceptible to changes in the elasticity of substitution between traded and non-traded consumption goods. Decreasing this elasticity makes import substitution relatively more attractive, and the resulting capital flows increase volatility at both the traded sector and aggregate levels, leaving non-traded sectoral volatility essentially unchanged, a situation basically analogous to that when the elasticity of substitution between own-sector goods and imports was

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191

increased. In a relative sense, however, this is not the case. A smaller value of 1=ð1 þ wÞ expectedly decreases relative consumption volatilies, in addition to increasing relative investment volatilities at the non-traded and aggregate levels. The pattern of domestic correlations is not altered in a noteworthy way, with one exception: making substitution of traded/non-traded consumption goods more attractive creates a negative cross-sector consumption correlation. Internationally, the value of 1=ð1 þ wÞ primarily affects consumption correlations; all other international correlations are more or less unchanged. Specifically, more substitution among consumption goods substantially decreases international consumption correlations. This result is not surprising, especially when coupled with the fact that a near-zero value of 1=ð1 þ wÞ results in lower relative consumption volatilies and a negative cross-sector consumption correlation. Further facilitating the ability of consumers to substitute between traded and nontraded goods by doubling 1=ð1 þ wÞ to 0.60 increases both absolute and relative consumption volatilies. This increase also encourages a higher volume of intersector trade at the expense of international trade, as evidenced by a decrease in the standard deviation of net exports. One also observed decreased volatility in output and investment. In this experiment, one observes the standard deviation of aggregate output move from 1.74 in the baseline case to 1.31, a 25% decrease. Increasing the value of 1=ð1 þ wÞ has significant, and sometimes undesirable implications for domestic correlations. Stronger capital flows across sectors weaken the relationship between own-sector output and investment. Indeed, the traded output/ investment correlation is now negative. Cross-sector correlations tend to be stronger under this elasticity. These results are mirrored at the international level, where stronger comovement is witnessed. Given the results of this experiment, it is clear that more research is needed to better pin down this parameter. 6.3. Complete markets Another important issue is how much of the modelÕs ability to solve to comovement problem is attributable to its structural restrictions on capital use and mobility and how much is due to its asset market structure. Recall that incomplete asset markets severely curtail agentsÕ ability to hedge against idiosyncratic risk, which in turn limits the international employment divergence in response to wealth changing shocks that are unique to one location. To investigate this issue, I recalculate moments for a complete markets variant of the model. Results of this experiment are located in Tables 5–7 in the columns marked ‘‘Complete Markets.’’ The modelÕs volatility predictions are not surprising. A richer menu of financial assets results in a higher volume of trade and hence generally higher volatility in the modelÕs variables. Complete asset markets also increases the relative (to output) volatility of investment, exports, and particularly consumption. These results are consistent with prior work (see, for example, Baxter and Crucini (1995)). Along most lines, the volatility results for the complete markets economy are inferior to the baseline case, although this difficulty could be easily overcome by increasing the parameters of the investment and employment adjustment cost functions.

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Within country correlations similarly yield few surprises. The ability to engage in perfect risk pooling lowers the correlation between consumption and output for both aggregate and sectoral data. This decrease is most striking in the non-traded sector, where the output–consumption correlation is reduced from +0.72 under incomplete markets to +0.24 here. Output–investment correlations are not systematically altered; the aggregate and traded sector correlations, for example, are strengthened while the non-traded correlation is weakened. With the exception of labor input, cross-sector correlations are considerably weakened. The correlations between traded and non-traded output and consumption fall to +0.12 and +0.13 respectively, and the cross-sector investment correlation is a strongly negative )0.90. The relationship between relative prices and relative quantities is considerably different. There has been a sign change on the relative price/relative consumption correlation––its sign is now positive and it is near perfect––and the correlation between relative prices and relative outputs is considerably weaker. International correlations (see Table 7) change in expected ways. First, since agents are now able to hedge against all manner of risk, aggregate and traded consumption are nearly perfectly correlated internationally. This finding, often called the ‘‘quantity anomaly’’ (Stockman and Tesar, 1995), is a common one in IRBC models featuring complete asset markets. Second, international output correlations are unchanged. This differs from what is observed in typical IRBC models, where instituting a complete asset markets structure results in counterfactually low international output comovement, all else being equal. In this context, however, international output correlations are unchanged because the complete markets economy is still able to generate positive international investment, and hence capital stock, comovement. Third, the international investment correlations are generally much stronger relative to the baseline case, and are consequently higher than is observed empirically. On the upside, this does not raise undue concern as the ‘‘typical’’ IRBC model also generates this result; again, it is a result of relatively low shock persistence. Finally, the complete markets economy also generates negative international employment comovement at the traded and aggregate levels, suggesting that industry structure alone is insufficient to overcome the divergent wealth effects on labor supply arising from perfect risk-pooling. 6.4. Sector-specific capital The final alteration imposes a capital use structure similer to that found in the model developed by Stockman and Tesar. While the use and accumulation of physical capital is not eliminated, capital stocks are now sector specific. Implementing this feature involves explicitly differentiating between domestically- and foreign-proTR duced traded consumption goods (cTR h and cf respectively). Aggregate consumption is thus: h   i1=l l l cTR ¼ x1 cTR : þ x2 ðcTR t ht ft Þ

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The use of the Armington aggregator and associated variables is also eliminated and the economyÕs four resource constraints assume a much simpler form: TR þ iTR ytTR ¼ cTR ht þ cht t ;

ytNT ¼ cNT þ iNT t t ; TR ytTR ¼ cTR þ iTR ; ft þ cft t

ytNT ¼ cNT þ iNT : t t The results of this exercise are reported in the columns labeled ‘‘Sector-specific Capital’’ in Tables 5–7. This alteration decreases volatility on both the aggregate and sectoral levels are less variable because capital can now only come from one source, its own sector, and adjustment costs are still in place. This result is consistent with closed-economy research incorporating adjustment costs or time-to-build; essentially the world economy consists of four ‘‘closed economies’’ with regard to capital flows. Finally, relative consumption and investment volatility are now lower while relative employment volatility is higher. Within-country and international correlations deliver a variety of interesting results. First, output/investment correlations are considerably higher when capital trade is eliminated since all of a given sectorÕs capital goods must be generated within that sector. This result has a strong parallel with closed-economy RBC models, where output/investment correlations in excess of +0.90 are the rule, not the exception. This in turn generates stronger output/labor input correlations at the aggregate and nontraded levels. In contrast, the traded output/employment correlation is slightly weakened but is still well within empirical ranges. This model variantÕs is able to accurately reproduce the direction and magnitude of cross-sector output and employment correlations. In contrast, traded and non-traded investment are negatively correlated and the cross-sector consumption correlation is near perfect. At first glance, international correlations are quite favorable. With the twin exceptions of a )0.28 traded investment correlation and a )0.10 traded employment correlation, there is no comovement problem to speak of. An initially odd result, both disaggregated and aggregate consumption are highly correlated across countries, even in the presence of restricted trade in financial assets. Recall again, however, that these results are coming from two national economies linked only be trade in consumption goods. Thus, comovement at both the sectoral and national levels springs almost exclusively from the fact that the shock hitting each sector is highly correlated with the other three sector-specific shocks. Moreover, it is conceivable that consumption smoothing in the presence of a symmetric shock structure may result in more highly correlated consumption spending.

7. Conclusion One of the most conspicuous flaws in IRBC research is that the models employed generally predict negative international comovement of investment and employment.

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One proposed method to deal with this comovement problem has been to model disaggregated economies in the hope that the sectoral linkages which would exist both within countries and internationally might serve to eliminate or at least mitigate this difficulty. This paper has investigated this notion by developing a four-sector, twocountry model of the international economy. Following the lead of Stockman and Tesar (1995), a multilateral non-traded goods sector was introduced into a openeconomy RBC model. Unlike Stockman and TesarÕ s work, however, trade in capital goods was permitted between both countries and sectors, correcting what could be called a serious omission, given the importance of capital movements to international business cycles. The results obtained from this study were on the whole quite positive. In most cases, the model was able to replicate the successes of prior IRBC research by matching many of the basic empirical regularities found both within and across countries. More importantly, the model generated two unique successes. First, it was able to internally generate the observed result that variables associated with traded goods sectors exhibit much more volatility than those in non-traded sectors. Second and perhaps most promising, it is able to (largely) solve the comovement problem by correctly predicting positive international investment and labor input correlations. Additional experiments and modifications to the basic model were considered, but none of these alterations produced a systematic improvement over the baseline results. Allowing for trade in a complete set of contingent claims changed model performance in comparatively minor ways that have been previously documented. Elimination of capital trade permitted investigation of the role of asset market structure. The results obtained from these two experiments suggests that it is industry, not asset market structure that is most important in successfully overcoming the comovement problem. Finally, these results give additional support to the notion that models with multisector economies provide the best opportunity for solving some of the traditional difficulties experienced in the IRBC research program without resorting to complicated alterations with regards to production, consumption, and/or market structure.

Acknowledgements This paper is based on Chapter 1 of my Ph.D. dissertation at the University of Virginia. I would like to thank Marianne Baxter, Jane Ihrig, and two anonymous referees for helpful comments and suggestions. All errors are mine.

Appendix A. Data appendix The data used in this paper were obtained from the 1996 International Sectoral Data Base (ISDB) and National Accounts complied by the OECD. This database and others are found on the OECDs International Statistical Compendium available on CD-ROM. Brief descriptions are provided below. The date runs from 1970 to

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1992 at annual frequencies for the following 10 country sample: United States, Germany, France, Canada, United Kingdom, Australia, Belgium, Denmark, Norway, and Sweden. All data were rendered stationary by applying the Hodrick–Prescott filter. Sectoral output, employment and capital stocks are defined using 1- and 2-digit international standard industrial classification (ISIC) codes. Traded sectors are: agriculture, mining & quarrying, manufacturing, retail and wholesale trade, transportation. The non-traded sectors are: electricity/gas/water, construction, FIRE, government services, and social, community, and private services. This industrial breakdown is was chosen to be consistent with Stockman and Tesar (1995). It should also be noted that minor alterations of sectoral definitions (e.g. including retail trade in the non-traded aggregate) do not fundamentally alter the business cycle properties of the traded/non-traded aggregates. Sectoral output is measured as value added and sectoral investment is estimated using gross fixed capital formation data. Consumption and price data were taken from OECDs Quarterly National Accounts. Private final consumption measures aggregate household spending. Traded consumption is measured by consumption of durables; not-traded consumption is proxied using consumption of services less rent. Wholesale Price Indices for either manufactures or durables measure traded prices; Consumer Price Indices for either services less rent or non-durables measure non-traded prices. With the exception of net exports, which are summed, annual data is constructed by averaging quarterly data.

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