Intercountry feedback and spillover effects within the international supply and use framework: A Bayesian perspective∗ Umed Temurshoev† August 26, 2012

Abstract We propose a new framework for estimating product-level global and interregional feedback and spillover factor effects directly from interregional supply and use tables (SUTs). The framework allows for SUTs to be rectangular (which is usually the case in practice) and gives a possibility of taking into account the inherent data uncertainty problems. We apply a Bayesian approach to the framework using a unique international SUTs dataset of the World Input-Output Database project, and estimate and present for the first time, to our knowledge, the global and intercountry feedback-spillover output effects at the world, country and product levels for the period of 1995-2009. Keywords: Global factor effects, interregional feedback and spillover factor effects, supply and use tables, Bayesian techniques JEL Classification Codes: R11, R15, C11

∗

I am grateful to Professor Ronald Miller for his comments. I thank Bob Dr¨oge for his assistance in working with the high performance computing facility of Millipede cluster offered by the Center for High Performance Computing and Visualisation of the University of Groningen. The views expressed in this paper are those of the author and should not be attributed to the European Commission or its services. † European Commission, Joint Research Centre, Institute for Prospective Technological Studies, 41092 Seville, Spain. E-mail: [email protected]

1

Introduction

Due to globalization countries have become highly dependent on each other in many respects. Production fragmentation is undoubtedly one the most important factors that contributes significantly to this process. High degree of interdependencies of countries is often considered to benefit these countries. For example, international economists would argue that open trade is welfare-enhancing for all participating countries since then each country, for example, will specialize in producing products that give them the lowest opportunity costs of production. However, it is also easy to realize that a high level of interdependencies can be an issue of concern, in particular, in times of economic depression. That is, if an economic crisis hits one country, then all other countries that have strong production and trade linkages with the depressed economy will suffer as well, which in their turn have further adverse effects on countries not directly related to the distressed economy. Given the continuing process of globalization, it is therefore important to quantify the degree of intercountry effects over time and get more insights from these effects. In particular, in this paper we focus on interregional effects at product level that stem from shocks in final demand categories (including consumption, investments, government expenditures and exports).1 To clarify, consider an increase in final demand for some product in region 1. In order to satisfy these needs, in general, producers of that particular good do not only increase their demand for required intermediate inputs from their region, but also from outside the region. Thus, the original stimulus in region 1 results in generation of new outputs in other regions, and these effects in the input-output (IO) literature are termed interregional spillover effects (see e.g., Miller and Blair 2009). On the other hand, these other regions in order to satisfy the subsequent intermediate demand of region 1 will require more inputs from within and outside regions, including region 1. Hence, region 1 ultimately has to produce more to satisfy these additional intermediate demands for its outputs coming from other regions. These extra effects from the outside world on the region, where the initial final demand shock originated, are called interregional feedback effects.2 Although the mentioned interregional effects 1

Throughout the paper the term “interregional” is used for “intercountry” whenever the focus is on inter-country effects. However, it is also more general since various effects among different regions within a single country (or province) are also termed interregional effects. 2 The interregional spillover and feedback effects in the literature are also called open loop and closed loop effects, respectively. Open loop because the corresponding impact goes from one region into another region, and closed loop because the corresponding effect originates and via other regions ends (or closes its loop of impact) in the same region.

2

are given in terms of gross outputs, our focus in the theoretical part of this paper is on the global and interregional (feedback and spillover) factor effects, where factor represents any economic, social, environmental or resource factor other than gross output, such as income generation, emission of greenhouse gases, creating jobs, or water consumption. The idea of understanding interregional transmission mechanisms of expansionary or contractionary shocks is an old topic and goes back to, at least, the work of Machlup (1943), Metzler (1950) and Chipman (1950). It is, however, widely recognized that Miller (1966, 1969) are the pioneering papers on the study of interregional spillovers as defined above. These studies were followed by a large number of closely related literature on interregional IO and social accounting matrix (SAM) analyses, including, among others, Yamada and Ihara (1969), Gillen and Guccione (1980), Oosterhaven (1981), Round (1985), Guccione et al. (1988), Round (2001), Sonis and Hewings (2001) and Dietzenbacher (2002).3 The main contribution of this paper is threefold. First, we provide an analytical framework for deriving product-level interregional effects directly from interregional supply and use tables (SUTs). The crucial advantage of the proposed framework is that it allows one to take into account the data uncertainty problems, which are inherent to SUTs and IO data. Further, without using the Leontief inverse, the required interregional effects are estimated from the original SUTs that always underly all the Leontief-inverse-based computation procedures. In this sense our paper motivation is entirely in line with that of ten Raa and Rueda-Cantuche (2007) who first proposed a regression framework for IO multipliers estimation. Our paper, however, differs from the mentioned study in that we: (a) consider an international SUTs setting, (b) propose a framework that allows for simultaneous estimation of various interregional effects (see Section 2), and (c) use a different estimation philosophy. There is another important advantage of using SUTs rather than symmetric IO tables that are traditionally used for computing interregional effects. It is generally now recognized that SUTs provide more detailed and perhaps more useful information due to the fact that SUTs explicitly distinguish between commodities and industries that allows appropriately considering secondary products besides the main products of industries. Also many IO analyses require the linking of an IO table to additional data sets such as international trade, employment and environmental statistics which are typically collected at an industry base. Linking these 3

A related earlier contribution cited in Miller (1966) (which we could not find) is Yamada (1961).

3

to symmetric IO tables that are either from the product-by-product or industry-byindustry type is problematic. Instead, SUTs being industry-by-product provide a natural link to the additional data sources. Second, we suggest applying Bayesian approach for estimation of product-level interregional effects. If one wants to use all the information in the published SUTs with more products than industries, then the number of unknown parameters in our interregional SUTs framework becomes larger than that of equations (observations).4 Unlike the standard econometric approaches, Bayesian methods are flexible enough to deal with these sorts of issues. However, Bayesian econometric techniques in comparison to the frequentist econometrics still tend to require more computing efforts, but are in fact becoming very popular in recent years due to the rapid development of computer technology. The last allows one to easily run, for example, various complex Bayesian posterior simulators nowadays. Bayesian estimation is based on a sound probability theory and has many advantages. For example, results are presented in terms of intuitively meaningful posterior densities. Any non-sample information can be effectively used via priors’ densities specification. Marginal posterior densities reflect all the parameter uncertainty in a model and do not condition on point estimates of parameters of no primary interest (i.e., nuisance parameters). Dealing with nuisance parameters in a general setting is, in fact, one of the major problems frequentist researchers face. Finally, using a unique dataset of international SUTs constructed by the World Input-Output Database (WIOD) project (for details, see Timmer 2012), we empirically analyze the development of global and intercountry feedback-spillover output effects over the period of 1995-2009 for 40 countries and 59 products. Possibly one of the main reasons why SUTs framework has not been used so far for estimating interregional effects was due to the lack of such dataset. To the best of our knowledge, it is the WIOD project that first constructed an international SUTs database harmonized across countries and time. Also for the first time to our knowledge, we quantify and present from a time-series perspective the intercountry output effects at the ’world’ (the 40 included countries include major economies in the world that cover around 90% of world GDP), country and product levels. The rest of this paper is organized as follows. In Section 2 we present our SUTs framework for estimating interregional feedback and spillover effects. Section 3 4

In fact, the same issue arises in ten Raa and Rueda-Cantuche (2007) where products in SUTs are first disaggregated and only then OLS is used to estimate IO multipliers. This approach has a number of drawbacks that are discussed in detail in Temurshoev (2012).

4

discusses an appropriate Bayesian technique that could be used in the empirical applications of the model. The empirical results of intercountry output effects for forty major countries of the world are derived and analyzed in Section 4. The main conclusions are summarized in the last section.

2

Interregional effects within SUTs framework

We first derive a system based on interregional input-output (IO) matrices that allows simultaneously computing the so-called global and interregional factor effects. Then we provide the corresponding supply and use tables (SUTs) framework for derivation of these effects. Without loss of generality, assume that the world consists of two regions (r, s = 1, 2). The closed form solution of the well-known interregional IO model is given by (see e.g., Miller and Blair 2009, Chapter 3) "

x1 x2

#

" =

L11 L12

#"

L21 L22

f1 f2

# ,

where " L=

L11 L12 L21 L22

#

" =

I − A11

−A12

−A21

I − A22

(1)

#−1

is the Leontief inverse in interregional setting, Arr is the (intra)regional input coefficients matrix for region r (= 1, 2), Ars is the matrix of interregional input (trade) coefficients with deliveries from region r to region s (r 6= s), f r and xr are, respectively, the vectors of (changes in) final demand and gross output for region r, and I is the identity matrix with appropriate dimension.5 Miller (1966, 1969) was first to ask a question of how a change in final demand for region, say, 1 (i.e., f 1 > 0 and f 2 = 0) would affect the outputs in that region and what would be the bias if instead of the interregional framework (1) only a single-region IO framework of x1s = (I − A11 )−1 f 1 would have been used. That is, how big would be the bias x1 − x1s if the so-called interregional feedback effects were totally ignored. The term “feedback” as we have already mentioned in Section 1 refers to the fact that economic stimulus in region 1 increases demand also for intermediate inputs delivered from region 2. However, region 2’s production in turn is, in general, dependent on the inputs from region 1 as well. Thus, region 2 will also 5

Matrices are given in bold capital letters, vectors in bold lower case letters, and scalars in italicized lower case letters. Vectors are columns by definition, thus row vectors are obtained by transposition indicated by a prime. 0 is a null vector of appropriate dimension.

5

demand more intermediate products from region 1 that results in further increase of sectoral outputs of region 1. Namely, these feedback effects are ignored by the single-region IO framework. Following Miller and Blair (2009, pp. 261-263) we consider backward factor multipliers in interregional setting as a way of quantifying interregional effects, and thus consider the effect of unitary changes in the final demand vector on any economic, social and/or environmental factor production, including gross outputs.6 The total backward factor multipliers within the two-region and single-region IO frameworks are defined, respectively, as h

h

θ10 θ20

i

θe10 θe20

i

=

h

=

h

µ01 µ02

i

µ01 µ02

i

"

L11 L12

#

L21 L22 "

e 11 L O

O e 22 L

,

(2)

,

(3)

#

e rr = (I − Arr )−1 is where µr is the vector of direct factor coefficients of region r, L the single-region Leontief inverse of region r and O is the null matrix of appropriate dimension. The jth element of θr indicates the increase of total amount of factor used/generated directly and indirectly in both regions 1 and 2 per unit increase of final demand for product j from region r. Hence, θr represents global factor effects associated with a unit increase of final demand for region r’s products.7 The jth element of θer , on the other hand, indicates the increase of total amount of factor generated in region r per unit increase of final demand for product j from region r ignoring interregional linkages. Hence, θer defines the single-region factor effects due to unitary increase in final demands. The row vector µ0r Lrr defines the intraregional factor multipliers of region r and represents the intraregional factor effects of exogenously given unitary changes in final demand for region r goods. Hence, the interregional feedback factor effects of e rr ). The unitary changes in final demand for region r products are given by µ0 (Lrr −L r

row vector

µ0r Lrs

with r 6= s, on the other hand, defines the interregional spillover

factor effects from region s to region r and represents the factor impacts that are transmitted across regional borders. That is, these are new factor production in 6

A unitary increase in final demand for region r’s product j in our two-region framework is equivalent to setting all the elements of the final demand vector to zeros except its jth element for region r which is set to one. 7 When the focus are regions within one country, θr indicates the national factor effects. Note that the change in final demand may also include a unitary change of exports of final goods from region r to the other region.

6

region r due to a unit increase of final demand for region s goods. e rr ) + µ0 Lsr where r 6= s, From (2) and (3) it follows that θr0 − θer0 = µ0r (Lrr − L s hence θr − θer gives the sum of interregional feedback and spillover factor effects due to unitary changes in region r’s final demand. Thus, we term the difference θr − θer as the vector of interregional feedback-spillover factor effects (or multipliers) associated with a unit increase of final demand for region r products.8 These effects can be considered as a measure of the impact of globalization on any factor of interest. The changes of these effects over time are caused due to two factors: changes in the corresponding input matrices and changes in the direct factor coefficients. In what follows, let us define µ0 = [µ01 , µ02 ], θ 0 = [θ10 , θ20 ], θe0 = [θe10 , θe20 ] and " A=

A11 A12 A21 A22

#

" e = , A

A11

O

O

A22

#

" e= and L

e 11 L O

O e 22 L

#

e and subsequent Postmultiplying (2) and (3), respectively, by I − A and I − A, transposition yields µ = (I − A0 )θ,

(4)

e e 0 )θ. µ = (I − A

(5)

e Add e 0 )θ. Thus, the difference between (4) and (5) is equal to 0 = (I − A0 )θ − (I − A e 0 )θ and simple to and subtract from the right-hand side of the last expression (I − A algebra gives e e 0 − A0 )θ + (I − A e 0 )(θ − θ). 0 = (A

(6)

That is, (6) can be used to find both the global factor effects, θ, and the intere This identity is true for any factor regional feedback-spillover factor effects, θ − θ. including gross output. To make the application of (6) functional, we must add another system of equations that defines the factor of our interest, namely (4). Hence, the regression-type system of equation that allows simultaneously computing θ, θe and θ − θe has the form9 8

Note that by construction this vector is non-negative. If we would have added ±(I − A0 )θe to the right-hand side of the difference between (4) and e This together with e 0 − A0 )θe + (I − A0 )(θ − θ). (5), instead of (6) we would have obtained 0 = (A (5) defines the alternative to (7) regression-type system as #" #   " e0 µ I−A O θe = . e 0 − A0 I − A0 0 A θ − θe 9

7

"

µ

#

0

" =

I − A0 O e 0 − A0 I − A e0 A

#"

θ θ − θe

# .

(7)

Therefore, premultiplication of the inverse of the first matrix on the right-hand side of (7) by its left-hand side vector [µ0 , 00 ]0 gives the values of both global and interregional feedback-spillover factor effects. The results, if needed, can be used to derive the single-region factor multipliers.10 Next we need to find the corresponding system within SUTs framework. Since we are interested in quantifying interregional effects at the product level, the socalled product technology assumption is used which states that each product is produced in its own specific way, irrespective of the industry where it is produced. This assumption is considered to be a preferred technology assumption on theoretical grounds and is advocated by Eurostat for deriving IO tables of product-by-product dimension (Eurostat 2008, Chapter 11). Under the product technology assumption, our two-region input matrices in terms of SUTs should be defined as A = UV0−1 e = UV e 0−1 , where the required international SUTs take the following forms and A " U=

U11 U12 U21 U22

#

" e = , U

U11

O

O

U22

#

" e = and V = V

V1

O

O

V2

# .

(8)

The ijth element of Urs indicates the amount of intermediate input of product i from region r used by industry j in region s, and Vr is the industry-by-product make matrix of region r. Note that for the single-region framework we simply nullify e i.e., the domestic the interregional flows of intermediate inputs in the use table U, uses of products by sectors are taken into account, but similar to the single-region IO setting the corresponding interregional flows are ignored. Generalization of the international SUTs for more than two-region framework is straightforward.11 e 0 − U0 )θ + (I − Equation (6) in terms of SUTs can be written as 0 = V−1 (U e which if premultiplied by V gives e 0 )(θ − θ), V−1 U 10

Using the theory of partitioned matrices, it is easy to show that the inverse of interest has the following form:   −1  I − A0 O L0 O = e0 . e 0 − A0 I − A e0 e 0 (A e 0 − A0 )L0 L A −L 11

Besides the use matrix regionalized system (8), an alternative make matrix regionalized SUTs framework is also discussed in Jackson and Schwarm (2011). However, the authors rightly mention that the preference for the use-regionalized SUTs framework “is based on the foundation of production behavior consistent with the demand-driven IO model rather than market share behavior, which appears to be more consistent with a supply-driven IO model” (p. 195).

8

e e 0 − U0 )θ + (V − U e 0 )(θ − θ). 0 = (U

(9)

Under the product technology assumption, direct factor coefficients vector is defined as µ0 = e0 V0−1 , where e0 = [e01 , e02 ] and er denotes sectoral factor use/production in region r (e.g., sectoral pollutant emissions or employment figures). Hence, (4) in terms of SUTs can be easily shown to be equivalent to (see ten Raa and RuedaCantuche 2007) e = (V − U0 )θ.

(10)

This equation together with (9) give the SUTs equivalent of the system (7) under the product technology assumption as12 "

e 0

#

" =

V − U0 O e 0 − U0 V − U e0 U

#"

θ θ − θe

# .

(11)

If we want θ and θ− θe to represent global and interregional feedback-spillover output multipliers, then e in (11) should be defined as a vector of sectoral gross outputs. In comparison to (7), using (11) for estimation of global and interregional feedback-spillover factor effects has one crucial advantage. While (7) requires the number of products and industries in SUTs to be equal in order to obtain the corresponding input matrices, this is not the case for system (11).13 That is, the SUTs framework of interregional factor effects allows SUTs to be non-square. Further, by adding an error term to the right-hand side of (11) and using an appropriate statistical method we have a stochastic SUTs framework that takes into account the inherent SUTs/IO data uncertainty problem. In published SUTs it is often the case that the number of products is much bigger than that of industries, implying that in system (11) the number of unknown parameters is larger than the number of equations.14 Therefore, if one does not want to aggregate a large number of 12

Similar transformations show that the alternative system given in footnote 9 in terms of SUTs under product technology assumption has the form #" #   " e0 e V−U O θe = . e 0 − U0 V − U0 0 U θ − θe 13

Notice that both (7) and (11) allow for different number of products (and industries) across regions, i.e., one region can have more or less products (industries) than the other. 14 To be more precise, assume that all regions have n industries and p products, where p > n. In the two-region world then the number of parameters and equations in (11) will be 4 × p and 4 × n, respectively.

9

products (and for good reasons), traditional econometric approaches such as OLS e in the resulting cannot be used to estimate the parameters of interest, θ and θ − θ, underdetermined or ill-posed system. A method that we advocate to use for this purpose is discussed in the next section. The final question that we address is whether one is able to estimate the interregional feedback and spillover factor effects separately from each other? In our two-region world let us redefine the direct factor coefficients vector as µ0 = [µ01 , 00 ]. Plugging this in the standard Leontief system (2) yields θ 0 = [µ01 L11 , µ01 L12 ], where the first term gives the intraregional factor effects for region 1 and the second term represents the interregional spillover factor effects from region 2 to region 1. In terms of SUTs, system (2) with such redefined µ under the product technology assumption is equivalent to (10) with e0 = [e01 , 00 ]. This is true in a general case of more than two regions, i.e., if e is defined such that all its factor use/production figures are nullified except those for region r, then the vector θ estimated from (10) has the following interpretation: the estimates corresponding to region r are the intraregional factor effects for region r and the estimates corresponding to region s (6= r) represent the interregional spillover factor effects from region s into region r. That is, the last quantify region r’s factor production due to a unit increase in final demand for region s (6= r) products. Hence, by repeatedly estimating (10) such that the factor uses of each region er appear once in the redefined vector e, we are able to quantify all region-specific spillover factor effects. This allows one to find which region is more (or less) responsive to spillover effects from any other region of interest. Finally, the difference between the interregional feedback-spillover factor e estimated from (11) and the derived spillover factor effects gives us effects, θ − θ, the value of the interregional feedback factor effects.

3

Bayesian approach

If we had wanted to run OLS on (11) by adding an error term to its right-hand side, we would have needed to aggregate the product dimension for the purpose of obtaining sufficient degrees of freedom for a sensible OLS implementation. However, this would lead, in our view, to a significant loss of information on industry-product links due to aggregation when published SUTs are used. We believe that huge human, time and financial efforts of national statistical offices that are put into the construction of SUTs with more products than industries must be used effectively in the practical applications of these tables. We choose Bayesian approach as our 10

estimation philosophy, because Bayesian methods generally allow for the number of unknowns to be larger than the number of observations and are based on a sound probability theory. We are confident that by using Bayesian approach in applications of the SUTs framework presented in Section 2 both the inherent uncertainty of SUTs and the related data, and the individual heterogeneities of specific product-industry interrelationships will be adequately taken into account. Note that (10) and (11) are already given in the linear regression model form of y = Xβ + ε,

(12)

where we have added the vector of regression errors ε. To compute β in (12), we make the following assumptions:15 1. For all observations i, εi ∼ N (0, σ 2 ωi ), where the error variance consists of a constant component σ 2 and a component ωi that varies over observations. 2. All elements in X are either fixed (which is not valid in our case), or they are random variables that are independent of all elements of ε. That is, the parameters η of the probability density function of the explanatory variables, p(X|η), do not include β, σ 2 and ωi ’s. In Bayesian literature it is convenient to work with error precisions rather than variances. Hence, in what follows we work with the constant and varying components of the error precision of h = 1/σ 2 and λi = 1/ωi . Thus, the covariance matrix is h−1 Λ−1 , where Λ is a diagonal matrix with λi ’s along its diagonal and zeros otherwise. Given our assumptions and using the properties of the multivariate Normal distribution, the likelihood function can be written as16  p(y|β, h, λ) =

h 2π

n/2

1/2

|Λ|

  h 0 exp − (y − Xβ) Λ(y − Xβ) , 2

(13)

where n is the number of observations. Next, we need to define the prior density p(β, h, λ). We use the widely used independent Normal-Gamma prior for β and h, i.e., the prior density is p(β, h, λ) = p(β)p(h)p(λ), 15

(14)

For detailed discussion of the approach used in this paper, see Koop (2003, Chapter 6). To be more precise, the likelihood function is p(y, X|β, h, λ, η). However, the second mentioned assumption implies that the likelihood can written as p(y, X|β, h, λ, η) = p(X|η)p(y|X, β, h, λ), hence without loss of information we can simply work with the likelihood function conditional on X, p(y|X, β, h, λ). For notational convenience, we suppress the dependence on X throughout the paper. 16

11

with p(β) = fN (β|β, V),

(15)

p(h) = fG (h|s−2 , v),

(16)

where fN (β|β, V) indicates that β has multivariate Normal distribution with mean β and covariance matrix V, and fG (h|s−2 , v) defines h having Gamma distribution with mean s−2 > 0 and degrees of freedom v > 0. Further, we consider heteroscedasticity of an unknown form, thus assume that the λi s are independent and identically distributed (i.i.d.) draws from the Gamma distribution with mean 1 and degrees of freedom vλ , p(λ|vλ ) =

n Y

fG (λi |1, vλ ).

(17)

i=1

This implies that error variances are different from each other, but they are taken from the same distribution. “Thus, we can have a very flexible model, but enough structure is still imposed to allow for statistical inference” (Koop 2003, p. 125). Following the literature, the prior distribution for the degrees of freedom vλ is chosen to be the Gamma density with two degrees of freedom, p(vλ ) = fG (vλ |v λ , 2),

(18)

which is the exponential density. Note that the prior for λ is specified in two steps, (17) and (18). In the literature this is called hierarchical prior. Alternatively, using probability rules the prior for λ can be simply written as p(λ|vλ )p(vλ ). At this point it is worth mentioning that such a treatment of heteroscedasticity is equivalent to the so-called scale mixture of Normals models. That is, the assumption that εi are independent N (0, h−1 λ−1 i ) with prior for λi given in (17) is equivalent to the assumption that the distribution of εi is a mixture (or weighted average) of different Normal distributions with different variances (i.e., different scales) but the same means (i.e., zero means). A crucial result due to Geweke (1993) is that when such mixing is performed using fG (λi |1, vλ ) densities, the linear regression model with the mixture of Normals errors is exactly equivalent to a linear regression model with i.i.d. Student-t errors with mean zero and vλ degrees of freedom. Hence, our model allows for more flexible error distribution, because the Normal distribution is a special case of the Student-t distribution when vλ → ∞. Therefore, the above 12

two-step error prior specification allows us to free up the assumption of Normal errors. Given the data, what and how do we learn about the parameters of interest? The core of Bayesian analysis in answering this crucial question states that “the posterior is proportional to the likelihood times the prior”, i.e., p(β, h, λ|y) ∝ p(y|β, h, λ)p(β, h, λ). If we perform this multiplication, the joint posterior turns out not to take the form of any well-known and understood density, therefore it cannot be directly used for simple posterior inference. Thus, we need to use posterior simulation methods. If it turns out that draws can be taken from the so-called full conditional posterior densities of the parameters of interest, then an appropriate Markov Chain Monte Carlo (MCMC) algorithm can be used such that these draws will be the valid draws from the joint posterior distribution (see e.g., Gilks et al. 1996). Without going into the details, the posterior conditional densities of interest to us can be shown to have the following forms: p(β|y, h, λ) = fN (β|β, V), p(h|y, β, λ) = fG (h|s−2 , v),  v +1  λ p(λi |y, β, h, vλ ) = fG λi 2 , vλ + 1 , hεi + vλ  v nvλ /2  v  λ λ Γ exp(−ηvλ ), p(vλ |y, β, h, λ) ∝ 2 2 where Γ(a) ≡

R∞ 0

(19) (20) (21) (22)

ta−1 exp(−t)dt is the Gamma function (see Poirier 1995, pp. 98-99)

and V = (V−1 + hX0 ΛX)−1 , β = V(V−1 β + hX0 Λy), v = n + v,   s2 = (y − Xβ)0 Λ(y − Xβ) + vs2 /v, n
 1 1 X ln λ−1 + λ . η = + i i v λ 2 i=1 We will not delve into the interpretations of the above results, since the interested reader can find these in any book on Bayesian econometric methods (see e.g., Koop 2003). We only mention that Bayesian theory makes it possible to combine the prior and data information in an intuitively appealing and sensible way, which is importantly based on a sound probability theory. The densities (19)-(21) have 13

well-known forms, hence empirically it is easy to take draws from them. In such cases, Bayesians use a popular posterior simulator called Gibbs sampler, which strategy is taking draws from the full conditional posterior distributions of parameters conditional on the previous draws of all the remaining parameters. After discarding initial replications of all parameters draws, the so-called burn-in replications, it can be shown that under mild conditions the remaining draws are valid draws from the corresponding joint posterior distribution (see e.g., Geweke 1999). However, we cannot use only Gibbs sampler in our case because the density (22) is a non-standard density. We will use a posterior simulator called random walk chain Metropolis-Hastings algorithm to take draws from (22). We will not give the details of this simulator due to space limitation, and refer the interested reader to Chib and Greenberg (1995) and Geweke (2005, Chapter 4). So we use Gibbs sampler as posterior simulator for (19)-(21), and the Metropolis-Hastings algorithm as posterior simulator for the conditional density (22). Such mixture of posterior simulators is perfectly acceptable, and in the literature is referred to as Metropolis-within-Gibbs algorithm.

Finally, we note that for our SUTs framework we need to impose linear constraints on the coefficients of the model, β. This is due to the underlying inputoutput theory (behind the presented SUTs framework) which states that the global factor effects cannot be less than the corresponding direct factor coefficients (i.e., in terms of (2) it must be true that θ ≥ µ) and that the interregional feedback-spillover factor multipliers are non-negative (i.e., θ − θe ≥ 0). Imposing linear inequality constraints of any kind is quite simple within the Bayesian analysis, since they can be imposed through the prior. In our empirical study we consider output effects, which is equivalent to the case when µ = ı, where ı is a vector of ones of appropriate dimension. Hence, instead of (15) we use the prior given by p(β) = fN (β|β, V)1(β1 ≥ ı, β2 ≥ 0), e and 1(β1 ≥ ı, β2 ≥ 0) is the indicator function which where β1 ≡ θ, β2 ≡ θ − θ, equals one if global output effects are at least unity and the feedback-spillover output effects are nonzero, and zero otherwise. Using this prior, the conditional posterior of β can be derived as p(β|y, h, λ) = fN (β|β, V)1(β1 ≥ ı, β2 ≥ 0), 14

(23)

which is used in our empirical application instead of (19). Thus, the conditional posterior of β used in our Metropolis-within-Gibbs algorithm is the truncated multivariate Normal distribution. Various efficient techniques for simulation from such truncated distributions are well known by now, but we use the strategy proposed by Geweke (1991).

4

An empirical application

We now present an application of the method discussed in Section 3 to our SUTs framework for interregional effects computation using the international supply and use dataset of the World Input-Output Database (WIOD) project. This database includes time series of national and international supply and use tables, world inputoutput (IO) tables, various socio-economic and environmental accounts for 40 major economies of the world covering about 90% of world GDP at the level of 35 industries and 59 products (for details, see Timmer 2012). It provides harmonized data for 15 years, from 1995 to 2009. Since we are mainly interested in the development of the level of interdependencies of production structures of countries over the period of 1995-2009, we choose gross output as the factor of our interest. We start with the elicitation of the prior hyperparameters β, V, s−2 , v and v λ . It is highly desirable to choose theory-based priors for global and interregional feedback-spillover output effects, i.e., for θ and θ − θe in (11) in a forty-country setting. The prior multipliers are computed on the base of the industry technology assumption, which assumes that each industry has its own specific way of production, irrespective of its product mix. This is an alternative technology assumption that can be used as an analytical device to transform SUTs into product-by-product IO matrices. Mathematically, the priors are derived from θ 0 = ı0 (I − A)−1 and θe0 = e −1 , where A = Uˆ e = Uˆ e x−1 Vˆ ˆ and q ˆ being diagonal ı0 (I−A) x−1 Vˆ q−1 and A q−1 with x e and V are defined matrices of, respectively, industry and product outputs, and U, U similar to (8) but for forty-country setting. That is, the prior vector for parameters β in (12) is chosen as β = [θ 0 , θ 0 − θe0 ]0 . Note that computation of the Leontiefinverse-based factor multipliers under the industry technology assumption is always feasible irrespective of whether the underlying SUTs are square or rectangular.17 Apparently, the multipliers under the two different technology assumptions are different: while it will be the case that under the industry technology model all 17

For SUTs framework of the basic transformation models, including that under the industry technology assumption, see Temurshoev (2012).

15

products representing one industry will have (almost) identical output multipliers, that should not definitely be the case with the product technology model. Hence, we define the prior variance V such that 95% of the probability in the prior density is located within the interval that allows the value of the prior coefficient to be a ≥ 2 times larger or smaller than β j s computed under the industry technology assumption. Using the useful rule-of-thumb, which states that approximately 95% of the outcomes of a random variable βj will fall within two standard deviations of its mean β j , if we want to have the corresponding upper “bound” to be as large as a times its mean, then from β j + 2σβj = aβ j we derive the prior standard deviation of βj as σβj = 0.5(a − 1)β j . Thus, the prior variance of βj is chosen to be var(βj ) =

(a − 1)2 2 βj 4

(24)

for all j. The prior covariance matrix V is then defined as a diagonal matrix with jj-th element equal to var(βj ) and zero otherwise. That is, following the common practice, we set all the prior covariances to zero because it is usually hard to make reasonable guesses about the covariance values. In our empirical application we set a = 2.5 in (24) being confident that such choice of prior information does not miss any reasonable value of βj under the product technology assumption. In the overwhelming majority of cases (if at all) IO multipliers under the product technology model cannot be larger or smaller than the corresponding industry technology model multipliers by more than 250%, implying that, in fact, our prior for β is relatively non-informative. In the setting of this model the prior can be interpreted as arising from a fictitious data set, where, for example, the prior degrees of freedom of the constant error precision h, v, can be interpreted as the prior sample size. Given that our prior for β is somewhat non-informative, we set v = 0.01n = 28, where the number of observations is n = 2800 (= 2 × 35 × 40, see (11)). Strictly speaking, we are assuming that our prior information about h has 1% of the weight as the data information. This means that we want our results to be driven mainly by the data information rather than the priors. Further, given that s−2 is the prior mean of h, we take the variance of y − Xβ as a reasonable prior guess for s2 . Finally, the degrees of freedom hyperparameter for the prior of varying error precisions is set to v λ = 25, “a value which allocates substantial prior weight both to very fat-tailed distributions (e.g., v λ < 10), as well as error distributions which are roughly Normal (e.g., v λ > 40)” (Koop 2003, p. 129). We do not give here the details of the random walk chain Metropolis-Hastings algorithm with Normal increment random 16

variable used for simulations from distribution (22) in our Metropolis-within-Gibbs simulator, and refer the interested reader to Koop (2003, p. 129) whose presented steps we closely follow here.18 We discard the initial 200 burn-in replications and retain the subsequent 1000 replications for deriving the estimates of the parameters of our model for each year separately. The derived Markov Chain Monte Carlo (MCMC) diagnostics of the parameters (such as numerical standard errors and Geweke’s (1992) convergence diagnostic) confirmed the convergence of our MCMC algorithms. Due to space constraints, we leave out the details of the MCMC diagnostics. To give a flavor of the Bayesian analysis, in Figure 1 we illustrate the priors and derived posteriors of the interregional feedback-spillover and global output effects for the US product “Other transport equipment” in 2009. Figure 1: Prior and posterior distributions: Other transport equipment, US, 2009 8

Prior Posterior

7

Prior Posterior

1.2

6 Probability density

1.4

0.12

Posterior

0.1

1 0.08

5 0.8 4

0.06 0.6

3 0.04 0.4

2

0

0.02

0.2

1

0

0.3 0.6 0.9 1.2 Feedback−spillover effect

0

1

2

3 4 5 6 Global output effect

7

0

0

10 20 30 40 50 60 Fs−to−global effects ratio

The standard Leontief IO approach gives the value of 0.4965 as the interregional feedback-spillover output multiplier under the industry technology assumption, which is chosen as the mean of the (truncated) Normal prior for this parameter. The first graph in Figure 1 shows that this prior has rather large variance. However, the corresponding posterior (derived from the retained 1000 replications) is much 18

We use MATLAB software in performing the Bayesian analysis for this study and adopt for our purposes the relevant MATLAB programs of Gary Koop’s Bayesian Econometrics (Koop 2003) and James LeSage’s Econometrics Toolbox (LeSage 1999). The large scale of our dataset requires heavy computing performance, hence we made use of the advanced high performance computing facility of Millipede cluster offered by the Center for High Performance Computing and Visualisation of the University of Groningen. We used one node in our computations that has 24 GB memory.

17

more informative, i.e., it has much lower variance. Our estimate of the feedbackspillover output multiplier of the US product Other transport equipment in 2009 is the mean of this posterior which equals 0.9593. The corresponding 95% highest posterior density interval (HPDI) is [0.8527, 1.0624]. Hence, we observe that the derived estimate is 93.2% larger than the corresponding estimate based on the industry technology assumption, and, moreover, the last is not included in the 95% HPDI of our feedback-spillover estimate that is based on the product technology assumption. Similar results are also obtained for the global output effects of the same product, whose prior and posterior are graphed in the middle part of Figure 1. The corresponding estimates are given in Table 1, which shows that the Leontiefinverse-based prior is 2.5214, while the corresponding posterior and its 95% HPDI obtained from the Bayesian analysis are, respectively, 3.1702 and [2.6686, 3.8785]. Hence, for the mentioned product the Leontief-inverse-based values underestimate both the global and interregional feedback-spillover output effects. Or put it differently, in light of the data information our priors via the Bayes rule are updated such that they become quite different from our original “belief”. The important question is why we find such big differences? Table 1: Global multipliers and the number of production ties, US, 2009 Products making industry ”Transport equipment” Motor vehicles, trailers and semitrailers Other transport equipment

Industry technology

Product technology Estimate

95% HPDI

2.5295

2.0513

[1.5031, 2.4221]

2.5214

3.1702

[2.6686, 3.8785]

Net output shares

Number of linkages within/ outside the US economy* > 0.1%

> 0.01%

> 0.001%

0.6145

21/6

29/54

31/163

0.3855

9/22

16/120

21/278

Note: *The number of production ties in the SUTs system of the two considered products are equal to the number of positive entries in the corresponding column of |V − U0 |. The expression “> 0.1%” means that we count such positive entries only when the absolute values of the net outputs are larger than 0.1% of the overall sum of the absolute values of the net outputs for each product.

In terms of the WIOD’s product and industry classifications, we find that industry “Transport equipment” includes two types of products which are “Motor vehicles, trailers and semi-trailers” and “Other transport equipment”. The estimates of the 2009 global effects of the first product are also shown in Table 1. We observe that the Leontief-inverse-based global multipliers of the two products are almost the same. This is entirely expectable because these estimates are based on the industry technology assumption, which in this case states that the industry Transport equipment has its own specific way of production irrespective of its 18

product mix, i.e., irrespective of weather it produces Motor vehicles, trailers and semi-trailers or Other transport equipment. However, the Bayesian estimates based on the product technology assumption turn out to be quite different also for the mentioned product. The global output multiplier of 2.0513 is lower than the corresponding Leontief-inverse-based multiplier of 2.5295, and, moreover, the last is not contained in the derived 95% HPDI. Our Bayesian results are based on the product technology assumption, which treats each product in a separate way irrespective of the industry where it is produced. The last three columns of Table 1 explain (to a large extent) the differences of the outcomes of the two technology assumptions. For the two products we count the number of significant production linkages both within and outside the US production structure. For example, if we count all the linkages with absolute values of net outputs greater than 0.01% of the overall sum of the absolute values of the net outputs in our 40 country framework, we find that the net output vector of the product Motor vehicles, trailers and semi-trailers (i.e., the corresponding column of V − U0 ) has links to 83 sectors (out of which to 29 industries domestically and to 54 internationally). The corresponding number for the second product Other transport equipment is 136 (out of which 16 are domestic and 120 are international ties). That is, what we see is that Other transport equipment has rather much more extensive linkages within the forty-country SUTs system than Motor vehicles, trailers and semi-trailers does, especially across the US borders. Therefore, the product specific global and feedback-spillover output effects must be larger (resp. lower) for the product with more (resp. less) extensive production-usage linkages, and that is exactly what we arrive at.19 The last graph in Figure 1 shows the posterior distribution of the ratios of the feedback-spillover to global output multipliers in percentage terms. These ratios are computed at each replication, hence the 1000 retained replications allow us to infer everything about the degree of the intercountry feedback-spillover relative to the global output effects. The mean and 95% HPDI of this posterior are, respectively, 19

The following interesting observation (conjecture) can be made from Table 1: the industry technology estimate of the global output multiplier of roughly 2.52 is a weighted average of the corresponding product technology estimates of 2.05 and 3.17, where the weights are shares of products’ contribution to the total of net outputs produced within the industry of interest. These last shares are reported in Table 1 as well. In our case this figure is 0.6145 × 2.0513 + 0.3855 × 3.1702 ≈ 2.5 which is quite close to the corresponding reported multipliers. The Leontief-inversebased estimate of the feedback-spillover output effect for Motor vehicles, trailers and semi-trailers is 0.4988, which is practically identical to 0.4965 that we reported for Other transport equipment. The corresponding Bayesian estimate for the first product is 0.1463 (which reflects the existence of fewer international linkages of Motor vehicles product). Hence, the industry technology estimate of the feedback-spillover effect maybe approximated as 0.6145 × 0.1463 + 0.3855 × 0.9593 ≈ 0.46.

19

30.65 and [25.3, 35.4], which indicate that the feedback-spillover output effects make almost one-third of the global output effects in case of the American product Other transport equipment in 2009. This is, in fact, a significant number, which quantifies the extent of globalization effect of a unit change of final demand for the product under consideration.20 Next, we want to analyze the development of the intercountry feedback-spillover and the global output effects over the period of 1995-2009. First, we derive the overall results for all countries and all products on an annual basis. There are, for example, 2360 (= 59 × 40) estimates of the global output effects for each year, thus we take their weighted average as an overall indicator of the global effects, where the weights are the shares of product outputs in our forty-country setting. Using the corresponding posterior distributions, such commodity-weighted results for the feedback-spillover and global output effects, and their ratios with the corresponding 90% HPDIs were derived, which are graphed in Figure 2. Figure 2: Product output-weighted aggregate results (with 90% HPDIs), 1995-2009 2.1

13

2.05

12

2 Global output effects

Feedback−spillover−to−global output effects ratios, %

14

11

1.95

10

1.85

0.3

1.8

0.25 0.2 0.15

1996

1998

2000

2002 Year

2004

2006

2008

0.1

Feeback−spillover output effects

1.9

9 8 7 6 5 4

1996 1998 2000 2002 2004 2006 2008 Year

The top part of the first graph in Figure 2 illustrates the development of the 20

We should note that simply using the means of the feedback-spillover and global output effects in finding the mentioned ratio is, in general, a wrong procedure, which in our example gives 0.9593/3.1702 × 100 = 30.26. The reason is that the mean of the ratio of two random variables is, in general, not equal to the ratio of the means of the two random variables and should take into account the dependence of the two variables. One could, of course, derive the means of such ratios using the corresponding covariance matrix by the well-known Delta method, but we do not need to do it here as the Bayesian simulation framework automatically accounts for this.

20

average global output effects, while its bottom part shows the average intecountry feedback-spillover output effects over the period under study. We observe that the mean average global output effect within our forty-country system was 1.90 in 1995, stayed more or less stable at this level until 2002, and consequently increased up to 2.02 in years 2007-2008 and somewhat declined to 2.01 in 2009. The corresponding 90% HPDIs are roughly 0.05 of magnitude far away from the means. On the other hand, the mean average intercountry feedback-spillover output effect was 0.164 in 1995 and we observe a steady increase of these multipliers until 2008, where it reaches the value of 0.255, and then decreases to 0.216 in 2009. The corresponding 90% HPDIs are roughly 0.03 of magnitude far away from the reported means. This trend is more clear in the second graph of Figure 2, which shows the development of the feedback-spillover-to-global (FS/G) output effects ratios. The reported means imply that the intercountry feedback-spillover output effects contributed, on average, 7.9% to the global output effects in 1995 and steadily increased until the year of 2008, where the corresponding figure becomes 11.5%, and then we see a sharp decline of the ratio to 9.8% in 2009. The corresponding 90% HPDIs are 1.4%-1.6% of magnitude far away from the means. Hence, we can conclude that the average across-the-border production interdependency of countries increased dramatically over the considered 15 years. In the IO parlance, a unit increase in average final demand within our forty-country system caused, on average, an increase of 1.9 units of total output in all forty countries in 1995, and, on average, 7.9% of this increase was due to the international production interdependencies of countries. In 2008, on average, 2.02 units increase of total output were required per unit of average final demand, and a large fraction of 11.5% of this increase was due to the existence of cross-border production linkages among countries. The decline of such interdependencies in 2009 can be explained by the unprecedented 2008-2009 global financial crisis that severely hit many economies around the world. Nevertheless, its degree in 2009 is still much higher than that in 1995-1999. From the overall average figures discussed above we cannot say anything about the country-specific interregional output effects. Hence, next we compute commodity output-weighted intercountry effects for each country separately. The derived means and corresponding 90% HPDIs (represented by bars) of the FS/G output effects ratios are given in Figure 3. To make the plots readable, we graph these ratios for five countries within one subplot and include countries according to the size of their 1995-2009 average of product output-weighted FS/G multipliers ratios in descending order in the subplots from the top to the bottom of Figure 3. The 21

list of WIOD country acronyms and the description of products and industries are given in Appendix 1. Figure 3: Country-level feedback-spillover-to-global effects ratios (%), 1995-2009 60

50

lux mlt 40 irl hun 20 est

40

svk bgr ltu cze svn

30 20 10 1996

1998

2000

2002

2004

2006

2008

1996

40 bel lva 30 cyp nld 20 rou 10

1998

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25

twn aut fin dnk swe

20 15 10 1996

1998

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25 20

pol prt 20 can 15 kor mex 10

grc esp deu gbr fra

15 10

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20

5

1996

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12

idn ita 15 chn tur 10 aus

rus usa ind jpn bra

10 8 6 4

5 1996

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2002 Year

2004

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2

1996

1998

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2002 Year

2004

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2008

Countries with the largest average FS/G output effects ratios for the entire period of 1995-2009 are (the ratios are given in parentheses): Luxembourg (36.1%), Malta (29.4%), Ireland (28.2%), Hungary (27.0%), Estonia (27.0%), Slovak Republic (26.9%), Bulgaria (25.0%), Lithuania (24.5%), Czech Republic (23.9%) and Slovenia (23.7%). On the other hand, countries with the smallest average FS/G output effects ratios include Indonesia (10%), Italy (9.8%), China (9.8%), Turkey (9.3%), Australia (7.9%), Russia (7.7%), United States (6.0%), India (5.4%), Japan (4.9%) and Brazil (4.8%). Hence, we find that small countries (in terms of their economic power) tend to have larger FS/G output multipliers ratios than large countries. Indeed, with 600 (= 40 × 15) observations we find a highly significant correlation coefficient of -0.73 between these ratios and the logarithm of the country-level total commodity outputs (as a measure of countries’ size). This finding is not surprising, because it implies that in comparison to large economic powers, small countries are generally more 22

dependent on the external world production. That is, smaller economies are more prone to negative external shocks, and at the same time may reap large economic benefits from the globalization processes in normal times. This relationship also explains why the ranges of the overall results of the FS/G effects ratios given in Figure 2 are smaller/narrower than what we observe from the corresponding countryspecific findings. Note also from Figure 3 that the 90% HPDIs are wider for smaller countries, hence their corresponding reported point estimates (i.e., posterior means) of both the intercountry feedback-spillover and the global output effects have less precision than those of the large countries. To see more clear patterns of the development of the FS/G output effects ratios, we compute the percentage changes of their posterior means and the 90% HPDIs’ lower and upper intervals for the year of 2009 relative to the beginning year of 1995. These results are presented in Figure 4. Figure 4: Changes in the FS/G output effects ratios (%), 2009 vs. 1995 pol tur bgr ind rou hun lux jpn bra svk irl deu cze ltu kor chn dnk grc fin aut rus svn lva swe mex esp usa cyp nld twn ita prt fra gbr bel est aus can idn mlt −30−15 0 15 30 45 60 75 90 105120 Percentage changes in the FS/G output effects ratios: 90% HPDIs lower intervals

pol tur jpn deu ind kor hun bra rou chn dnk bgr lux aut fin swe grc irl esp twn usa cze nld mex svn fra ita prt rus ltu gbr svk bel cyp lva mlt can aus est idn

jpn deu tur pol kor ind dnk bra swe aut chn hun fin rou grc bgr twn lux nld fra esp usa ita prt irl svn gbr mex bel cyp mlt ltu cze rus svk can aus lva est idn

−30 −20 −10 0 10 20 30 40 50 60 Percentage changes in the FS/G output effects ratios: posterior means

−30 −20 −10 0 10 20 30 40 50 60 Percentage changes in the FS/G output effects ratios: 90% HPDIs upper intervals

Figure 4 shows that for Indonesia, Estonia, Australia, Canada and Malta the changes in the estimates and 90% HPDIs intervals of their FS/G output effects ratios are negative. The corresponding percentage changes of the posterior means for these countries ranges from -11.8% to -26.5%, which essentially indicate the decline of the 23

degree of participation of these countries in international production processes in 2009 compared to 1995. For the majority of other countries the reverse is true. For example, countries for which the means of the FS/G output effects ratios increased by more than 25% include Poland, Turkey, Japan, Germany, India, Korea, Hungary, Brazil, Romania, China and Denmark. For countries like Czech Republic, Mexico, Slovenia, Russia and Lithuania both the posterior means and 90% HPDIs’ lower bounds of the ratios of interest increase, while the corresponding HPDIs’ upper bounds go down. For these cases one can also infer that the size of the feedbackspillover effects within the corresponding global output effects increased, although the sizes of these changes are much more moderate. For Cyprus and Latvia the HPDIs’ lower bounds increase, while the corresponding means and HPDIs’ upper intervals decrease. The FS/G ratios of the United Kingdom (GBR) practically do not change at all. All and all, Figure 4 clearly shows that, in general, the world production system is becoming more and more fragmented in the sense that national economies are becoming much more dependent on external production and supplies of inputs and outputs. The all idea of using SUTs framework was estimating interregional multipliers at product level, thus in what follows we discuss our results for products. Table 2 gives the mean of the average global and intercountry feedback-spillover output effects and FS/G output ratios (including their 90% HPDIs) over the period of 1995-2009 (in descending order of the reported effects). The underlying corresponding annual estimates were derived as weighted averages of the posterior means and 90% HPDIs, where we have used country-level total commodity output shares (which change from year to year) as the corresponding weights. The average estimates of the global output effects show the magnitudes of the average changes in total output produced by all forty countries as a result of a unit change in average final demand in these countries for particular products. Table 2 shows that demand for product Other transport equipment (code: 29) generates the largest global and feedback-spillover output effects across the world (the corresponding multipliers are 2.91 and 0.65, respectively). This commodity includes such products as ships and boats, railway locomotives and rolling stock, air and spacecraft and related machinery, military fighting vehicles, and other transport equipment (e.g., motorcycles, bicycles and invalid carriages). It turns out that the second commodity in this list also has to do with transport equipment, i.e., product Motor vehicles, trailers and semitrailers (28) has the second largest global and feedback-spillover output effects. 24

Table 2: Product-level average intercountry output effects, 1995-2009 Product code 29 28 10 24 27 13 12 22 9 19 14 16 18 23 11 25 15 21 40 30 34 26 20 41 2 7 3 4 1 17 38 33 39 42 5 32 57 35 8 31 48 44 43 56 54 50 49 58 51 52 36 46 37 55 45 53 47 59 6

Global output effects Estimate 2.9069 2.5652 2.5187 2.4463 2.4268 2.4231 2.4053 2.3874 2.3816 2.3798 2.3666 2.3628 2.3471 2.3361 2.2957 2.2952 2.2900 2.2654 2.2465 2.2397 2.1472 2.1426 2.1325 2.1140 2.0656 2.0329 2.0172 1.9755 1.9582 1.9294 1.9267 1.8723 1.8627 1.8513 1.8417 1.8409 1.8322 1.8313 1.7957 1.7883 1.7844 1.7713 1.7628 1.7554 1.7515 1.7353 1.7148 1.6810 1.6667 1.6661 1.6457 1.6328 1.6058 1.5978 1.5803 1.4800 1.4191 1.3039 1.0476

90% HPDI [2.6200, [2.4546, [2.0921, [2.2215, [2.1999, [1.9985, [2.2250, [2.3066, [2.3572, [2.3170, [2.2541, [2.2527, [2.3172, [2.2926, [2.1694, [2.1870, [2.1802, [2.1882, [2.0563, [2.1561, [2.1349, [1.9908, [2.0768, [1.9905, [1.7245, [1.4882, [1.5993, [1.5821, [1.9290, [1.8828, [1.8966, [1.6387, [1.8308, [1.7875, [1.5994, [1.8068, [1.7472, [1.7547, [1.5962, [1.5025, [1.6100, [1.7136, [1.7246, [1.5969, [1.7268, [1.5740, [1.5982, [1.5494, [1.6130, [1.6496, [1.6269, [1.4500, [1.5771, [1.4602, [1.4336, [1.4545, [1.3974, [1.2353, [1.0101,

3.2105] 2.6691] 2.9698] 2.6827] 2.6639] 2.8708] 2.5927] 2.4678] 2.4051] 2.4425] 2.4806] 2.4722] 2.3772] 2.3793] 2.4237] 2.4022] 2.4001] 2.3432] 2.4456] 2.3237] 2.1594] 2.2994] 2.1883] 2.2412] 2.4381] 2.6573] 2.4675] 2.4062] 1.9874] 1.9767] 1.9569] 2.1200] 1.8947] 1.9154] 2.0982] 1.8750] 1.9182] 1.9121] 2.0064] 2.0935] 1.9676] 1.8304] 1.8035] 1.9200] 1.7765] 1.9056] 1.8386] 1.8197] 1.7197] 1.6827] 1.6652] 1.8292] 1.6363] 1.7447] 1.7315] 1.5058] 1.4436] 1.3722] 1.0910]

Product code 29 28 26 24 25 27 12 13 23 19 11 22 21 18 30 15 16 14 40 17 10 41 9 34 20 31 3 35 2 7 1 4 8 5 33 32 39 54 38 43 42 50 56 52 48 58 51 49 57 36 55 37 45 44 46 53 59 47 6

FS output effects Estimate 0.6537 0.5085 0.4535 0.4467 0.4465 0.4453 0.4092 0.4013 0.3957 0.3761 0.3744 0.3597 0.3594 0.3564 0.3190 0.2882 0.2827 0.2814 0.2728 0.2648 0.2480 0.2474 0.2385 0.2352 0.2251 0.2002 0.1938 0.1935 0.1894 0.1817 0.1796 0.1786 0.1761 0.1657 0.1630 0.1526 0.1460 0.1448 0.1412 0.1380 0.1378 0.1374 0.1356 0.1244 0.1234 0.1155 0.1030 0.1030 0.1028 0.1010 0.0916 0.0860 0.0802 0.0796 0.0691 0.0652 0.0576 0.0488 0.0106

90% HPDI [0.5047, [0.4544, [0.3691, [0.3330, [0.3722, [0.3144, [0.2893, [0.1963, [0.3598, [0.3235, [0.2810, [0.3108, [0.3166, [0.3306, [0.2543, [0.2184, [0.2150, [0.2067, [0.1810, [0.2282, [0.1174, [0.1753, [0.2224, [0.2251, [0.1804, [0.0723, [0.0642, [0.1444, [0.0792, [0.0654, [0.1569, [0.0764, [0.0863, [0.0851, [0.0663, [0.1263, [0.1236, [0.1275, [0.1202, [0.1127, [0.1009, [0.0696, [0.0680, [0.1119, [0.0591, [0.0667, [0.0849, [0.0647, [0.0626, [0.0877, [0.0377, [0.0672, [0.0472, [0.0623, [0.0272, [0.0485, [0.0341, [0.0388, [0.0030,

0.8016] 0.5635] 0.5386] 0.5628] 0.5206] 0.5784] 0.5299] 0.6108] 0.4316] 0.4284] 0.4683] 0.4086] 0.4023] 0.3822] 0.3836] 0.3581] 0.3506] 0.3565] 0.3657] 0.3011] 0.3844] 0.3199] 0.2545] 0.2454] 0.2700] 0.3322] 0.3290] 0.2424] 0.3032] 0.3033] 0.2023] 0.2843] 0.2681] 0.2496] 0.2622] 0.1789] 0.1684] 0.1621] 0.1622] 0.1634] 0.1752] 0.2070] 0.2041] 0.1370] 0.1892] 0.1653] 0.1212] 0.1419] 0.1447] 0.1145] 0.1471] 0.1056] 0.1139] 0.0969] 0.1127] 0.0820] 0.0815] 0.0591] 0.0187]

Product FS/G output ratios (%) code Estimate 90% HPDI 29 26 28 25 27 24 12 13 23 11 19 21 18 22 30 17 15 40 16 14 41 34 20 10 35 9 3 8 2 31 1 4 7 5 33 54 32 39 43 50 56 52 38 42 48 58 36 49 51 57 55 37 45 44 53 46 59 47 6

23.41 20.99 19.97 19.45 18.79 18.63 17.60 17.55 17.02 16.63 16.04 16.02 15.25 15.15 14.29 13.71 12.76 12.23 12.11 12.03 11.37 10.85 10.54 10.38 10.13 10.00 9.88 9.55 9.48 9.41 9.11 9.10 9.01 8.76 8.62 8.11 8.10 7.77 7.63 7.56 7.50 7.34 7.26 7.01 6.60 6.56 5.85 5.79 5.70 5.52 5.10 5.10 4.83 4.44 4.24 3.76 3.30 3.26 0.48

[17.24, 29.92] [16.95, 25.31] [17.63, 22.44] [15.97, 23.07] [12.88, 25.29] [13.41, 24.44] [12.01, 23.62] [ 8.01, 28.19] [15.37, 18.72] [12.24, 21.25] [13.63, 18.52] [13.96, 18.15] [14.07, 16.46] [12.93, 17.45] [11.30, 17.38] [11.78, 15.71] [9.52, 16.14] [7.98, 16.76] [9.03, 15.31] [8.65, 15.57] [7.95, 14.95] [10.38, 11.34] [8.36, 12.77] [4.55, 17.02] [7.45, 12.88] [9.31, 10.71] [3.10, 17.62] [4.51, 14.94] [3.71, 15.95] [3.21, 16.33] [7.91, 10.33] [3.70, 15.23] [2.98, 16.22] [4.45, 13.61] [3.43, 14.26] [7.09, 9.14] [6.67, 9.56] [6.55, 9.01] [6.15, 9.15] [3.70, 11.73] [3.69, 11.51] [6.57, 8.12] [6.15, 8.38] [5.02, 9.07] [3.17, 10.30] [3.71, 9.61] [5.04, 6.67] [3.54, 8.19] [4.64, 6.79] [3.29, 7.91] [2.06, 8.38] [3.97, 6.28] [2.79, 6.99] [3.40, 5.50] [3.07, 5.42] [1.41, 6.38] [1.95, 4.72] [2.58, 3.98] [0.11, 0.94]

Note: FS and FS/G denote, respectively, intercountry feedback-spillover and feedback-spillover-to-global output ratio effects. For product codes see Appendix 1.

25

However, not always the generators of largest global and intercountry feedbackspillover effects coincide. For example, Tobacco products (10) has the third ranking in terms of global output effects, but shows up only as the 21st in terms of feedbackspillover effects. On the other hand, Radio, television and communication equipment and apparatus (26) has the third largest feedback-spillover output effects, but comes only 22nd in terms of global output effects. In fact, the correlation coefficient between the two product orderings is 0.62, implying that often products with the largest global output effects tend to have also (relatively) higher intercountry feedback-spillover output effects, but that is not always exactly the case. Office machinery and computers (24), Medical, precision and optical instruments, watches and clocks (27), Leather and leather products (13), Wearing apparel, furs (12), Fabricated metal products, except machinery and equipment (22), Food products and beverages (9) and Rubber and plastic products together with the mentioned products make up the top ten commodities with the largest average global output effects over the period of 1995-2009. Most of these products also have the largest intercountry feedback-spillover output multipliers. On the other hand, Education services (53), Real estate services (47), Private households with employed persons (59) and Uranium and thorium ores (6) have the lowest global and feedbackspillover output effects. It is not surprising that services generally have lower output generating power compared to other goods, because the first are non-tradable products. As far as Uranium and thorium ores is concerned, it turns out to be produced only in Czech Republic (in small amounts) and there is practically no trade of this product among the considered forty countries. The last three columns of Table 2 show the average FS/G output effects percentages for the entire period. The largest contribution of the feedback-spillover effects to the global output effects in the ranges of 18.6%-23.4% are found for Other transport equipment (29), Radio, television and communication equipment and apparatus (26), Motor vehicles, trailers and semitrailers (28), Electrical machinery and apparatus (25), Medical, precision and optical instruments, watches and clocks (27) and Office machinery and computers (24). That is, an increase in demand for products of electrical and optical equipment and transport equipment have generated the largest average intercountry output effects across the world during the period under study. As expected non-tradable products account for the smallest intercountry FS output effects. The annual development of the ratios of interest (including their 90% HPDIs) is illustrated in Figure 5. The products are again given in descending order of the mean value of the average FS/G output ratios for the entire period, 26

Figure 5: Product-level feedback-spillover-to-global effects ratios (%), 1995-2009 35 29 30 26

30

24

19

12 20

21 18

25

28 25

13

20

25 20 27 15

23

22

15

30

11

15 10 10 1995 20

2000

1995

2005 17

10 2000

2005

20

40

15

14

2005 9

20

3

20 15 10

16 10

2000

34

15 15

1995 41

10

8 2

10

35

31 5

5 1995 20

2000

2005

1995 14

2000

2005

1 12 4

15

7 10

32 10

39 43

33

6

50

6

2 1995 10 36

8

49 51

6

57

38 42 48

4 2000

2 1995

2005

58 10

56 52

5

2005

2005

10 8

4 2000

2000

12

8

5 1995 12

1995 14 54

2000

2005 46

55 8

37 45

6

6

59 47

4

6

44 4

53

2

4 2 2 1995

2000

2005 Year

1995

2000

2005

0 1995

2000

2005 Year

Year

as reported in Table 2. We observe that all the posterior means of the FS/G output effects, except for Uranium and thorium ores (6), generally show an increasing trend. Thus, the intensity of cross-border shipment of all kinds of intermediate and final goods in order to satisfy demands for an overwhelming majority of products has definitely increased over the considered 15 years. The degree of these changes is illustrated in Figure 6, which gives the percentage changes of the posterior means and the 90% HPDIs lower and upper intervals of the FS/G output effects ratios for the year of 2009 relative to the beginning year of 1995. Indeed, our Bayesian estimates of the FS/G output effects ratios are larger in 2009 than in 1995 for all products, except for Uranium and thorium ores (6). Products that show more than 40% change in the average posterior means of the ratio of interest include Collected and purified water, distribution services of water (33), Renting services of machinery and equipment without operator and of personal and household goods (48), Electrical energy, gas, steam and hot water (32), Post and telecommunication services (43) and Air transport services (41). Note that if we would have used 2008 as the ending period, then the percentage changes would 27

Products

Figure 6: Changes in the FS/G output effects ratios (%), 2009 vs. 1995

59 50 33 43 58 32 48 57 5 41 46 45 51 44 39 47 53 7 3 42 31 27 54 37 17 19 18 36 29 56 52 49 35 8 30 1 2 25 40 22 23 4 26 34 11 20 55 9 21 38 28 15 24 10 14 16 12 13 6 −30 −15 0 15 30 45 60 75 90100 100 Percentage changes in the FS/G output effects ratios: 90% HPDIs lower intervals

33 48 32 43 41 39 44 58 51 3 18 11 19 47 2 1 57 45 37 30 54 53 27 42 50 59 36 25 5 52 17 26 23 29 31 13 46 22 8 20 9 24 34 55 12 40 10 4 21 56 15 35 38 28 14 16 49 7 6 −10

13 48 33 11 12 41 3 32 1 2 39 18 43 19 24 30 44 26 25 58 37 51 47 23 27 45 54 42 20 9 52 10 53 36 57 22 31 34 8 29 17 55 5 15 14 4 46 21 40 38 16 50 56 59 28 35 49 7 6 0 10 20 30 40 50 55 Percentage changes in the FS/G output effects ratios: posterior means

−10 0 10 20 30 40 50 Percentage changes in the FS/G output effects ratios: 90% HPDIs upper intervals

Note: Product 6 is an outlier with -90% change in its FS/G output effects ratios in all three cases (subplots).

have been much larger as can be inferred from Figure 5. That is, the 2008-2009 global financial crisis sharply decreased the magnitude of the intercountry feedbackspillover output effects for (almost) all products, but nonetheless the corresponding positive changes in 2009 compared to 1995 are huge. Note that for 56 out of 59 products the average changes of the FS/G output effects ratios are over 10%. The lowest average positive change of 1.9% is observed for Metal ores (7), while the one-rank higher product in this list is Computer and related services (49) with the change in the average ratio of interest of 8.4%. All these numbers represent the rapid speed of globalization process that took place over 1995-2009 in terms of more interdependent and complex structure of the world production system. Finally, we want to find out whether it was worthwhile to use a more flexible 28

Figure 7: Posterior density for degrees of freedom, p(vλ |y) 1.4

2000 2009

1.2

Probability density

1 0.8 0.6 0.4 0.2 0

3

4

5 6 Degrees of freedom

7

8

(non-Normal) distributional assumption on regression errors. Recall that in our specification of the errors hierarchical prior we had a crucial parameter vλ indicating the degrees of freedom for the distribution of the regression errors. Since this parameter is univariate, we can easily plot its posterior. As an example, Figure 7 shows two posterior densities of vλ for years 2000 and 2009, while the means and 95% HPDIs of vλ for all years are given in Appendix 2. Figure 7 indicates that the posterior distributions of the degrees of freedom may be skewed. Furthermore, Figure 7 and Appendix 2 show that virtually all of the posterior probability is allocated to small values for the degrees of freedom parameter. Therefore, the errors in our SUTs framework regressions (11) for estimating interregional effects exhibit substantial deviations from Normality. Thus, it was definitely worthwhile to use a more flexible model (i.e., the scale mixture of Normals models, see Section 3). Note also from the posterior results that there is no support for extremely small values of vλ which would imply extremely fat tails of the error distribution.

5

Conclusion

In this paper we proposed a new stochastic framework for estimating product-level global and intercountry (interregional) feedback and spillover factor effects using international (interregional) supply and use tables (SUTs). The advantages of using SUTs rather than symmetric input-output (IO) tables, which are themselves 29

analytical constructs from SUTs, are well known by now. These mainly include explicit distinction between products and industries that appropriately accounts for both the main and secondary products of industries, natural linking of products to additional data sources that are collected at an industry base (e.g., international trade, employment and environmental statistics), and constructing frameworks that allow one to take data uncertainty into account (see ten Raa and Rueda-Cantuche 2007, Rueda-Cantuche 2011). In contrast to the standard Leontief-inverse-based procedures, our SUTs framework allows the underlying SUTs to be rectangular and gives a possibility of taking into account the data uncertainty problems, which are inherent to SUTs and the related data. We suggest using a Bayesian approach in the empirical applications of estimating various interregional effects. Bayesian methods are based on a sound probability theory, present the results in terms of intuitively meaningful posterior densities, and can use any non-sample information sensibly via priors specification. Bayesian econometric techniques in comparison to the frequentist econometrics still tend to require more computing efforts, but are becoming very popular over time due to the (rapid) development of computing technology. Using a unique dataset of international SUTs constructed by the World InputOutput Database project, we quantify and present the global and intercountry feedback-spillover output effects at the ’world’ (the 40 included countries are major economies in the world that cover around 90% of world GDP), country and product levels for the period of 1995-2009. Some of our findings are as follows. We find that the overall average of the global output effects (or multipliers) in our forty-country system increased over time, from 1.90 in 1995 to 2.01 in 2001 (in both cases with 90% highest posterior density intervals of roughly ±0.05). The overall intercountry feedback-spillover effects contribution to the global output effects was, on average, 7.9% in 1995, 11.5% in 2008 and decreased to 9.8% in 2009. This decrease is apparently due to the unprecedented 2008-2009 global financial crisis. These figures, however, vary widely across countries and products. For instance, we find that, in general, small countries have larger shares of the intercountry feedback-spillover effects in the global output effects than the large economic powers. Thus, small economies are more dependent on the external world production, being far more prone to negative shocks during crises than larger countries, but at the same time may reap large economic benefits in normal times due to the on-going globalization processes. In our forty-country setting, we find that it is Other transport equipment (which includes such products as ships and boats, railway locomotives and 30

rolling stock, air and spacecraft and related machinery, military fighting vehicles, and other transport equipment such as motorcycles, bicycles and invalid carriages) and Motor vehicles, trailers and semitrailers that have the largest average global and intercountry feedback-spillover output effects. Thus, an increase in final demand for the transport equipment-related products had the largest gross output generating power across the world over the period of 1995-2009. Further, we find positive average changes of the feedback-spillover-to-global output effects ratios in 2009 relative to 1995 for all products, except Uranium and thorium ores. 56 out of 59 products show the corresponding average changes of more than 10%. Products related to electricity, gas and water supply, renting services of machinery and equipment, post and telecommunications, and air transport show more than 40% change in the average feedback-spillover-to-global output effects ratios. All these findings clearly confirm that the sizes of interregional output effects significantly went up over the 15 considered years. Thus, countries today are functioning in a much more interdependent environment, where definitely the intertwined complex structure of the world production makes an important part of the on-going globalization processes.

31

References Chib, S. and E. Greenberg: 1995, ‘Understanding the Metropolis-Hastings algorithm’. American Statistician 49, 327–335. Chipman, J. S.: 1950, ‘The multi-sector multiplier’. Econometrica 18, 355–374. Dietzenbacher, E.: 2002, ‘Interregional multipliers: Looking backward, looking forward’. Regional Studies 36, 125–136. Eurostat: 2008, European Manual of Supply, Use and Input-Output Tables. Methodologies and Working Papers. Luxembourg: Office for Official Publications of the European Communities. Geweke, J.: 1991, ‘Efficient simulation from the multivariate Normal and Student-t distributions subject to linear constraints’. In: E. Keramidas (ed.): Computer Science and Statistics: Proceedings of the Twenty-Third Symposium of the Interface. Fairfax: Interface Foundation of North America, Inc., pp. 571–578. Geweke, J.: 1992, ‘Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments’. In: J. M. Bernando, J. O. Berger, A. P. Dawid, and A. F. M. Smith (eds.): Bayesian Statistics 4. Oxford: Clarendon Press, pp. 641–649. Geweke, J.: 1993, ‘Treatment of the independent Student-t linear model’. Journal of Applied Econometrics 8, S19–S40. Geweke, J.: 1999, ‘Using simulation methods for Bayesian econometric models: inference, development, and communication (with discussion and rejoinder)’. Econometric Reviews 18, 1–126. Geweke, J.: 2005, Contemporary Bayesian Econometrics and Statistics. New Jersey: John Wiley & Sons. Gilks, W. R., S. Richardson, and D. Spiegelhalter: 1996, Markov Chain Monte Carlo in Practice. New York: Chapman & Hall. Gillen, W. J. and A. Guccione: 1980, ‘Interregional feedbacks in input-output models: some formal results’. Journal of Regional Science 20, 477–482. Guccione, A., W. J. Gillen, P. D. Blair, and R. E. Miller: 1988, ‘Interregional feedbacks in input-output models: the least upper bound’. Journal of Regional Science 28, 397–404. Jackson, R. W. and W. R. Schwarm: 2011, ‘Accounting foundations for interregional commodity-by-industry input-output models’. Letters in Spatial and Resource Sciences 4, 187–196. Koop, G.: 2003, Bayesian Econometrics. Chichester: John Wiley & Sons. LeSage, J. P.: 1999, Applied Econometrics using MATLAB. Available at http://www. spatial-econometrics.com/. Machlup, F.: 1943, International Trade and National Income Multiplier. Philadelphia: The Blakiston Company.

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Metzler, L. A.: 1950, ‘A multiple-region theory of income and trade’. Econometrica 18, 329–354. Miller, R. E.: 1966, ‘Interregional feedbacks in input-output models: some preliminary results’. Journal of the Regional Science Association 17, 105–125. Miller, R. E.: 1969, ‘Interregional feedbacks in input-output models: some experimental results’. Western Economic Journal 7, 41–50. Miller, R. E. and P. D. Blair: 2009, Input-Output Analysis: Foundations and Extensions. Cambridge: Cambridge University Press, 2nd edition. Oosterhaven, J.: 1981, Interregional Input-Output Analysis and Dutch Regional Policy Problems. Aldershot: Gower. Poirier, D. J.: 1995, Intermediate Statistics and Econometrics: A Comparative Approach. Cambridge: The MIT Press. Round, J. I.: 1985, ‘Decomposing multipliers for economic systems involving regional and world trade’. Economic Journal 95, 383–399. Round, J. I.: 2001, ‘Feedback effects in interregional input-output models: What have we learned?’. In: M. L. Lahr and E. Dietzenbacher (eds.): Input-Output Analysis: Frontiers and Extensions. New-York: Palgrave, pp. 54–70. Rueda-Cantuche, J. M.: 2011, ‘Econometric analysis of European carbon dioxide emissions based on rectangular supply-use tables’. Economic Systems Research 23, 261–280. Sonis, M. and G. J. Hewings: 2001, ‘Feedbacks in input-output systems: Impacts, loops and hierarchies’. In: M. L. Lahr and E. Dietzenbacher (eds.): Input-Output Analysis: Frontiers and Extensions. New-York: Palgrave, pp. 71–99. Temurshoev, U.: 2012, ‘Bayesain analysis of product-level global CO2 emission multipliers from 1995 to 2009’. Unpublished manuscript. ten Raa, T. and J. M. Rueda-Cantuche: 2007, ‘Stochastic analysis of input-output multipliers on the basis of use and make tables’. Review of Income and Wealth 53, 318–334. Timmer, M. P. (ed.): 2012, The World Input-Output Database (WIOD): Contents, Sources and Methods. Available at http://www.wiod.org/publications/source_docs/WIOD_ sources.pdf. Yamada, H. and T. Ihara: 1969, ‘Input-output analysis of interregional repercussion’. Papers and Proceedings of the Third Far East Conference of the Regional Science Association 3, 3–29. Yamada, I.: 1961, Theory and Application of Interindustry Analysis. Tokyo: Kinokuniya Bookstore Co. Ltd.

33

Appendix 1: Country acronyms, product and industry descriptions Acr.

Country

Code

AUS

Australia

1

AUT

Austria

2

BEL BGR BRA CAN

Belgium Bulgaria Brazil Canada

CHN CYP CZE DNK ESP EST FIN FRA

Czech Republic Denmark Spain Estionia Finland France

9 10 11 12 13 14

GBR DEU GRC

United Kingdom Germany Greece

15 16 17

HUN

Hungary

18

IDN

Indonesia

IND

Product description

Code

3 4 5 6

Products of agriculture, hunting and related services Products of forestry, logging and related services Fish and other fishing products Coal and lignite; peat Crude petroleum and natural gas Uranium and thorium ores

1

3 4 5 6

China

7

Metal ores

7

Cyprus

8

Other mining and quarrying products

8

2

Industry description Agriculture, hunting, forestry and fishing Mining and quarrying

9 10 11 12 13 14 15 16 17

Transport equipment Manufacturing, nec; recycling Electricity, gas and water supply

19

Food products and beverages Tobacco products Textiles Wearing apparel; furs Leather and leather products Wood and products of wood and cork (except furniture) Pulp, paper and paper products Printed matter and recorded media Coke, refined petroleum products and nuclear fuels Chemicals, chemical products and manmade fibres Rubber and plastic products

Food, beverages and tobacco Textiles and textile products Leather, leather and footwear Wood and products of wood and cork Pulp, paper, printing and publishing Coke, refined petroleum and nuclear fuel Chemicals and chemical products Rubber and plastics Other non-metallic mineral Basic metals and fabricated metal Machinery, nec Electrical and optical equipment

India

20

Other non-metallic mineral products

20

IRL

Ireland

21

Basic metals

21

ITA

Italy

22

22

JPN KOR LTU LUX

Japan Korea Lithuania Luxembourg

23 24 25 26

18

Construction

19

Sale, maintenance and repair of motor vehicles and motorcycles Wholesale trade and commission trade, exc. of motor vehicles and motorcycles Retail trade; repair of household goods Hotels and restaurants

LVA

Latvia

27

MEX MLT NLD

Mexico Malta Netherlands

28 29 30

Fabricated metal products, exc. machinery and equipment Machinery and equipment n.e.c. Office machinery and computers Electrical machinery and apparatus n.e.c. Radio, television and communication equipment and apparatus Medical, precision and optical instruments, watches and clocks Motor vehicles, trailers and semi-trailers Other transport equipment Furniture; other manufactured goods n.e.c.

POL

Poland

31

Secondary raw materials

31

PRT ROU

Portugal Romania

32 33

32 33

RUS

Russia

34

Electrical energy, gas, steam and hot water Collected and purified water, distribution services of water Construction work

SVK

Slovak Republic

35

SVN

Slovenia

36

SWE

Sweden

37

TUR TWN

Turkey Taiwan

38 39

USA

United States

40 41 42 43 44 45 46 47 48

49 50 51 52 53 54 55 56 57 58 59

Trade, maintenance and repair services of motor vehicles and motorcycles Wholesale trade and commission trade services Retail trade services, except of motor vehicles and motorcycless Hotel and restaurant services Land transport; transport via pipeline services Water transport services Air transport services Supporting and auxiliary transport services; travel agency services Post and telecommunication services Financial intermediation services, exc. insurance and pension funding services Insurance and pension funding services, exc. compulsory social security services Services auxiliary to financial intermediation Real estate services Renting services of machinery and equipment without operator and of personal and household goods Computer and related services Research and development services Other business services Public administration and defence services; compulsory social security services Education services Health and social work services Sewage and refuse disposal services, sanitation and similar services Membership organisation services n.e.c. Recreational, cultural and sporting services Other services Private households with employed persons

34

23 24 25 26 27 28 29 30

34 35

Inland transport Water transport Air transport Other supporting and auxiliary transport activities Post and telecommunications Financial intermediation Real estate activities Renting of M&Eq and other business activities Public admin and defence; compulsory social security Education Health and social work Other community, social and personal services Private households with employed persons

Appendix 2: Posterior results for degrees of freedom, vλ Year

Mean

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

4.58 4.25 4.36 4.61 4.57 5.36 5.59 5.16 5.08 4.80 4.77 4.72 4.85 4.58 4.52

35

95% HPDI [3.99, [3.79, [3.79, [4.12, [4.05, [4.74, [4.93, [4.41, [4.32, [4.24, [4.19, [4.23, [4.13, [4.04, [3.96,

5.23] 4.90] 5.22] 5.18] 5.11] 6.22] 6.42] 6.25] 5.71] 5.35] 5.38] 5.24] 5.52] 5.16] 5.02]