Omar Joya
email: ojoya@auaf.edu.af

Eric Rougier
email: eric.rougier@u-bordeaux.fr

Patrick Asea

Ha Nguyen

Luis Servén

Jean Imbs

Isabelle Méjean

Jean-Louis Combes

Aart Kraay

Do (all) sectoral shocks lead to aggregate volatility? Empirics from a production network perspective

Keywords: Volatility, diversification, production network, input-output structure, sectoral shock, 2008 global crisis JEL Classification: C67, D85, E32, L16

Productive diversification has long been acknowledged as a volatility-reducing strategy. Yet, recent theoretical contributions have shown that, in strongly diversified economies, idiosyncratic shocks could translate into aggregate volatility via the network of inter-industry linkages. By exploiting exogenous cross-country-sector variations in demand shocks during the 2008 Great Recession, we provide empirical evidence that the network properties of a sector affected by an individual shock determine its propensity to transmit volatility to the rest of the economy. More precisely, shocks to sectors that are located in denser parts of a production network fade out over a large number of alternative paths of propagation due to substitution effects, whereas shocks to sectors that are more influential within the network generate aggregate fluctuations through contagion effects. We also find that the impact of sectoral shocks on aggregate volatility (1) is not conditional on sector-level differences in trade intensity, and (2) is larger for developing countries because they tend to have more isolated influential sectors and larger structural holes in their production network. Our results thus help consolidate the two opposite views in the literature on the impact of productive diversification on aggregate volatility.

Introduction

Do shocks to individual sectors lead to aggregate volatility in diversified economies? This is an important question because, in general, output volatility -as it leads to economic uncertainty -brings about substantial costs to the economy, by reducing long-run growth (Ramey and Ramey, 1995), generating significant welfare loss (Aizenman and Pinto, 2005), or increasing asset risk premia. The myriad ways in which output volatility impacts an economy places it high on the priority list of both academic economists and policymakers.

The early answer to the question of whether idiosyncratic shocks translate into aggregate volatility in diversified economies was in the negative. The answer relied on the argument that, in diversified economies, only aggregate shocks -shocks that affect many economic sectors in the same way -are important. Shocks to individual sectors were considered as being unimportant because, according to the law of large numbers, independent and identically distributed shocks become inconsequential in a diversified economy as they are averaged out over the entire production network (Lucas, 1977).

Recently, however, a radically different answer to the question has been provided by a series of analytical works providing microeconomic foundations to aggregate volatility. Basically, they show that independent firm-level or sector-level shocks can have aggregate volatility effects in diversified economies due to the asymmetric distribution of inter-sectoral linkages in production networks (Gabaix, 2011, Acemoglu et al., 2012, 2017, Baqaee and Farhi, 2018). The main implication of these analyses is that greater productive diversification, characterized by greater number of different industries or sectors, does not always immunize economies from aggregate volatility when shocks hit highly influential sectors or firms in an asymmetric production network.

Undoubtedly, this novel theoretical knowledge on economic diversification and volatility risks is important and insightful. Still, a deeper knowledge of the relationship between inter-industry network structure and aggregate volatility requires the new theory to be taken to the data. This paper does so and contributes to our understanding of how sectoral shocks cumulate to aggregate volatility through interindustrial linkages in two ways.

First, unlike other studies which have relied on simulations of theoretical models calibrated usually on the US economy, 1 we use an econometric model and cross-country-sector data to study how intersectoral linkages determine the impact of idiosyncratic shocks on aggregate volatility, and derive empirical results from a real-world network of a multi-country global economy. More specifically, we look whether regularities can be found in cross-sectoral-country data as to the way (and the extent to which) the topological properties of any industry in the productive network condition the transmission of a local shock to the aggregate economy.

Second, we are the first to identify the causal impact of various sector-level network features on aggregate output volatility. Establishing causality from observational data is extremely challenging. We overcome this challenge by limiting our empirical test to a period of an exogenous global shock, i.e., the Great Recession of 2007-2009. Similar to various recent papers (Bems et al., 2011, 2012; Garbellini et al.,

(C) (D)

Figure 1. Network illustrations of asymmetry, density and centrality Graph (A) represents a symmetric network where the links are equally distributed, meaning that every sector relies on all other sectors in the economy. It is also a densely connected network. Graph (B) shows a perfectly asymmetric network where one sector (f) is highly central as it is the input supplier and purchaser for all other sectors in the economy. It is also a sparse network. Graph (C) illustrates a network with a dense sub-graph (the neighborhood of b, c, d and f), while there are 'structural holes' (missing links) between a and b, and between e and d. In graph (D), sector f has a higher first-order and second-order centrality because it is closer to or reachable by all other sectors, and it mediates the flow of goods between the subgraph comprising a, b and e, and the subgraph comprising c and d.

To the best of our knowledge, our paper is the first to empirically identify the impact of structural properties of production networks on output volatility in a broad panel of 40 economies consisting of 35 sectors each. First, we provide empirical support to the assumption that shocks to the sectors that are influential in a production network -i.e., those with the highest degree of second-order centralitygenerate aggregate fluctuations through contagion effects via the full network of inter-sectoral linkages. Our empirical findings therefore contribute directly to the recent literature on the 'granular' hypothesis about aggregate fluctuations, first put forward by Gabaix (2011), and translated into a network model of inter-sectoral input-output linkages by Acemoglu et al. (2012). Second, our findings support the assumption that sectors located in denser parts of the network, where shocks fade out over a large number of alternative paths of propagation, have a mitigating effect on aggregate volatility, which we call substitution effect. This second result is in-line with the traditional diversification argument (Lucas, 1977). Our full sample results are essentially driven by service sectors and by higher-income countries, as we find evidence of contagion effects, and no evidence of substitution effects in our sub-sample of emerging economies. This suggests that developing economies are more vulnerable to external shocks than more developed ones because their productive system features more structural holes.

Our findings actually provide empirical support for the simultaneous existence of both the contagion and substitution effects in any productive system: on the one hand, shocks to sectors with high second order centrality are more prone to trigger aggregate volatility through the network of inter-industrial linkages while, on the other hand, shocks to sectors with a high local density around them are more likely to fade out across the network of inter-sectoral linkages. A closer look at the centrality and local density characteristics of various sectors in our sample helps illustrating our results. 2 The automobile industry, as it is located at the intersection of many sectors like metal, chemistry or service industries, shows a high degree of local density but low centrality. This means that the automobile industry might show higher propensity for substitution effects and, therefore, lower potential for shock transmission. On the contrary, the construction sector, as it is simultaneously associated with potentially low substitution effects (low local density) but very high contagion effects (high centrality), is likely to be more conducive to shock propagation and aggregate volatility. Service sectors such as transportation, health, public administration and financial intermediation also appear to have high second-order centrality since they are suppliers to a large number of sectors in the economy.

This paper also contributes, more or less directly, to other important streams of literature. First, this paper is connected to the traditional literature on input-output (I-O) analysis, dating back to Leontief (1936, 1941) or Hirschman (1958), which uses various multipliers to estimate the effect of a demand or supply shock on the output. 3 The present paper, however, uses the I-O data in an alternative and innovative fashion, consisting of reconstituting a global production network from this data, and then computing various indicators that capture the network characteristics of inter-sectoral linkages. The network approach we adopt enables us to measure a sector's second-order centrality which is central for testing the contagion effect of shocks to influential sectors. Nonetheless, the way we use the I-O framework and demand-side analysis is fairly similar to that of a few recent papers mobilizing global I-O data to quantify the impact of final demand shock on trade collapse and other outcomes during the 2008 global crisis (Levchenko et al., 2010; Bems et al., 2012). However, these papers provide no identification of the impact of sectoral diversification in the process of shock transmission. 4 Second, our finding that the presence of more diversified links in the neighborhood of a sector tends to dilute the shock transmission due to substitution possibilities, helps clarify the traditional diversification argument in the economic literature. A sizeable literature has supported the assumption that sectoral diversification (i.e., expansion in the number of sectors) reduces aggregate economic volatility (di Giovanni and Levchenko, 2009; Koren and Tenreyro, 2007, 2013; Cuberes and Jerzmanowski, 2009; Malik and Temple, 2009; Haddad et al., 2010; Joya, 2015). Some findings in our paper are closer to Koren and Tenreyro's (2013) technological diversification argument which explains that the adoption of increased number of input varieties by firms provides diversification benefits against variety-specific shocks and reduces aggregate volatility.

Third, our paper is connected to the literature on contagion in financial networks whose attention has turned, since the financial crisis of 2007-08, to the growing interconnectedness of the global financial system in order to better understand the endogenous factors which contributed to the global crisis (Glasserman and Young, 2016; Belke and Dubova, 2018). Several studies have also shown how systematic risks spread into a financial network, and which network structures are more vulnerable to contagion (Allen and Gale, 2000; and Gai et al., 2011). However, we are not aware of any paper that would show in which network settings the stabilizing effects of financial diversification might arise. Our findings on the substitution effect of local density could, for example, be approximated for the stabilizing effects of portfolio diversification where each node (financial organization) becomes insensitive to other nodes' failures because they have "many connections that they are well-insured against the failure of any counterparty" (Elliott et al., 2014). Some findings in this paper also marginally relate to the rapidly-growing literature which shows that demand and supply shocks are increasingly synchronized across countries as a consequence of production-sharing and vertical specialization (Di Giovanni and Levchenko, 2010; Grossman and Meissner, 2010) and that the impact of shocks to individual firms can be considerably amplified through input-output linkages between firms (Di Giovanni et al., 2014). Our estimations notably suggest that emerging market economies might be especially vulnerable to external shocks to specific exporting sectors or firms connected to global value chains (GVCs) if their productive network are insufficiently diversified in the neighborhood of these sectors or firms, as was pointed out by Srholec (2007) or Lectard and Rougier (2018).

Lastly, although our paper deals with the process through which sectoral shocks create aggregate instability, it does not fully address uncertainty and bands of inaction issues that may explain why empirical studies find only weak evidence of the impact of sectoral shocks on aggregate volatility (Belke and Göcke, 2005). In the set-up of a short-term demand shock and of a short-term adjustment (capital and labor constant), the sunk costs of investing and of hiring, which ensure that the successive reactions to shocks are asymmetric, may be limited and may not condition the results. More generally, we cannot give an operational value function to uncertainty in our framework of analysis which fundamentally aims at identifying reduced-forms relations between observed (not random) sectoral shocks and aggregate output instability, and how it is conditioned by the characteristics of the sector in the whole production network (which are fixed).

In the next section, we develop our theoretical set-up, before section 3 explains how network indicators can address contagion and substitution effects. Our econometric identification is discussed in section 4, and the estimation results are presented in section 5. Section 6 develops policy implications our findings before section 7 concludes.

The production network perspective: Theoretical set-up

How do structural network properties transmit volatility?

In this subsection, we provide a formal theoretical framework to show how the structural properties of a production network might affect the transmission of an idiosyncratic demand shock to the aggregate level. Our aim is not to develop a full-fledged equilibrium model, but rather to formalize our argument that the topological properties of a network play an important role in the aggregation of sectoral shocks.

We consider a closed economy with n output sectors which all trade with each other. Following Bems et al. (2011), we assume that all changes in output and in final demand are in real terms, and that the quantity shares of our variables are equal to their value shares. All these sets of assumptions are consistent with the type of data that we are using for our empirical exercise in the next section.

We define total gross output (Q) in the economy as the sum of all sectoral outputs: = ∑ . In terms of percentage changes, aggregate growth in year t will be the weighted sum of sectoral output growth rates, as following:

= , , (1)
where the accent ~ shows the percentage change in a variable, and , is the output share of sector i in the aggregate output at the beginning of the period. Each sector produces differentiated goods that are either used as an intermediate input by other sectors or are used to satisfy final demand. Let the intermediate goods from sector i used in production of output in sector j be and the final goods produced to satisfy final demand be . The sectoral output is given by: = ∑ + . The percentage change in sectoral output will therefore be:

= + (2)
The quantity of intermediate goods can be expressed as: = where = is a technical coefficient measuring the share of intermediate goods from sector i used in the production of final goods by sector j. Similar to Leontief's assumption for the production function, we assume that flows of intermediate goods from sector i to j depend entirely on changes in the total output of sector j , which leads us to suggest that: = . Equation (2) can thus be re-written as:

= 1 + (3)
For all sectors, Equation 3 can be expressed in the following matrix form:

!"# $( )% & = '!"# $( )%& + !"# $(")% ( ) (4)
where !"# $( )% is an (+ × +) diagonal matrix with elements on the diagonal, & is an (+ × 1) vector of output changes in each sector i, A is a matrix of technical coefficients with elements , !"# $(")% is a diagonal matrix with elements on the diagonal, and ( ) is a vector of final demand changes. With some matrix operations on Equation 4, we get:

& = -( ) (5)
with -= !"# $( )% /0 !1 -'% /0 !"# $(")%

The matrix !1 -'% /0 is the Leontief inverse matrix, also called total requirements matrix, which captures both direct and indirect transactions in the economy. Direct transactions refer to the units of intermediate goods that are required for production of a final good, while indirect transactions are the units of additional intermediates, primary goods or commodities that were required to produce the intermediate goods in the first place.

Equation 5 states that changes in output directly relate to changes in final demand, with the impact of final demand variability on output being conditional on the structure of the (+ × +) matrix M. As it captures both direct and indirect inter-industry flows in the economy, as well as the shares of sectoral output and sectoral final demand, matrix M thus captures the interconnectedness and linkages across sectors in the economy.

Per equation 5, the output growth for a given sector i would be: = ∑ 3 where 3 is an element of matrix M. Replacing this in equation 1, we obtain the expression for aggregate output growth :

= , 3 , (6)
or, in the matrix form, as following:

= 5 -( ) ( 7
)
where W is the (1 × +) vector of sectoral shares , /0 . We can now easily derive the aggregate output volatility. The variance for aggregate output growth 7 would therefore be:

8 9 : = (5-) Ω < ) < ) (5-) = (8)
with Ω < ) < ) being the variance-covariance matrix of sectoral demand changes. 5 Consistently with the real business cycle theory (Long and Plosser, 1983; Horvath, 1998; Malysheva and Sarte, 2011) as well as with the most recent literature based on network properties (Acemoglu et al., 2012), Equation 8decomposes the relationship between the underlying variance of fundamental shocks to sectoral final demands and the volatility of aggregate growth in the economy into direct and indirect effects. The direct effect of sectoral demand shocks on aggregate volatility depends on the distribution of sectoral shares, as captured by vector W. If sectoral demand volatility is symmetric across sectors, contributions to aggregate output volatility will be larger for those sectors that have higher weights in aggregate output, and smaller for smaller sectors. 6 This goes in the same spirit as Gabaix (2011), except that sectors' demand are used in the place of firms' sales. The indirect contribution to aggregate output volatility depends on the topology of inter-industry linkages in the productive economy, that is on the structure of the IO network. The indirect effect of sectoral shocks is captured by matrix M, which encapsulates the interconnectedness and linkages across sectors in the economy and can be described as an adjacency matrix depicting a weighted and directed input-output network of the economy. M does not only capture the existence of linkages across sectors, but also their direction and strength. Each element which would respectively show the direct contributions of individual sector volatilities into aggregate output volatility, and co-movements across sectors. In Shea (2002), for example, the bulk of aggregate volatility is explained by co-movements, notably because of input-output linkages and inter-industry complementarities. 6 Since we rely on Leontief's accounting methods, one restrictive assumption in our model is that the structure of the economy does not change after being affected by a shock, meaning that the proportions of all inputs into any productive process remain fixed. The short time period we use and the fast recovery after the 2008 global demand shock both plead for the fixity assumption. Nonetheless, empirical studies have shown that the input-output technical coefficients are relatively stable over shorter periods of time, especially when the level of sectoral aggregation is higher and more so in the case of demand-side Leontief model rather than supply-side Ghosh model (Sevaldson, 1969; Dietzenbacher and Hoen, 2006; Wood, 2011). Further, the 2008 financial shock and the consecutive demand shock are two symmetrical shocks applying equally to all productive sectors. One implication of the fixity of technical coefficient is that there could be no substitution effect between inputs during this period. However, this restriction may not be prejudicial to our empirical strategy because we do not include the network measures, calculated from the IO data, as a time variant variable in our econometric model. See section 6.

What's into the matrix M? A discussion of the substitution and contagion effects

Predicting whether an idiosyncratic shock will prompt macroeconomic volatility is not straightforward. It depends on the number of active sectors in the production network and, more chiefly, on the distribution of inter-industrial linkages and of the size of the sectors. 7 All these elements are actually included in the matrix M. Two contrasting patterns of volatility transmission through the production network can be found in the literature, which we will call, for convenience, substitution and contagion effects in the rest of the paper.

In the standard literature on sectoral and technological diversification, an increase in the number of products or inputs on which the economy relies will reduce the average risk of aggregate volatility, as individual and independent shocks to one sector fade out over the entire set of cross-sector supply and demand linkages (Lucas, 1977; Koren and Tenreyro, 2007). Koren and Tenreyro (2013) have for example established that aggregate output becomes less sensitive to individual technological shocks because, as the number of alternative input varieties increases, each individual input matters less in the production process due to firms adjusting their mix of inputs in order to absorb the shocks. In this paper, the fadingout effect of sectoral diversification is called substitution effect. In our words, substitution does not mean firm-level technological substitution between inputs, as in Koren and Tenreyro (2013), but rather that in diversified economies with balanced production networks, where upstream inputs and downstream outputs are well diversified, the existence of alternative supplying or demanding sectors enables risk diversification against sectoral shocks (Xu et al., 2011). 8 At the sub-network level, this pattern is well characterized by high densities of linkages in the neighborhood of the sector.

In the real world, however, economies tend to be strongly specialized and production networks tend to be strongly asymmetric, with few sectors or firms being predominant input suppliers to the rest of the economy. In this context, idiosyncratic sectoral shocks propagate to the aggregate economy through contagion effects. The conditions under which inter-firm or inter-sectoral linkages might prompt the transmission of idiosyncratic shocks to aggregate volatility in asymmetric production networks have been formally established by two path-breaking papers of Gabaix (2011) and Acemoglu et al. (2012). The 'granular' hypothesis about aggregate fluctuations was first put forward by Gabaix (2011), which states that shocks to individual firms or sectors can fail to average out when the distribution of firm shares of sales is sufficiently leptokurtic. By translating the granular hypothesis into a network model of intersectoral input-output linkages, Acemoglu et al. (2012) could then establish that sizable aggregate volatility can be generated by idiosyncratic shocks affecting highly influential upstream sectors, i.e., sectors that are input suppliers to a large number of other downstream sectors. They identify higher-order interconnections as the main driver of the propagation of productivity shocks to the economy through cascade effects. Acemoglu et al. (2012) therefore take into account the second-order degree, that is the influence of a sector over the whole network through its linkages with other influential sectors, to properly identify the cascade -or contagion -effects. 7 The debate over whether inter-sectoral linkages magnify aggregate volatility is not recent. It can be traced back to the real business cycle theory, notably the multisector model à la Long and Plosser (1983). Using a similar business cycle model, Horvath (1998) has for example demonstrated that the rate at which the law of large numbers applies is controlled by the rate of increase in the number of full rows in the input-output matrix (i.e. number of input-output relations or inter-industry linkages) rather than by the rate of increases in the number of rows (i.e., number of sectors). 8 Diversity of IO connections also provide alternative sources of finance or export demand (Gould, 2018).

In this paper, our empirical analysis seeks to identify both the contagion and substitution effects in a country-sector pseudo-panel. Put differently, we check whether (i) shocks to sectors with higher secondorder centrality have a higher propensity to trigger aggregate volatility through the network of interindustrial linkages, and (ii) shocks to sectors with a higher local density around them are more likely to fade out across the network of inter-sectoral linkages.

In short, the impact of an individual supply-side or demand-side shock on aggregate output volatility is uneasy to predict, since it depends on the network properties of the sector that is affected by a shock. Identifying whether the local production network structure is conducive for volatility transmission requires assessing which of the substitution or contagion effects dominates. As explained in this section, the topological characteristic of the sector within the whole network structure of inter-industry linkages, as captured in the matrix M, or in other words whether this sector is central and influential in the network, will determine the relative magnitudes of the substitution and contagion effect.

Identifying substitution and contagion effects through production network characteristics

Consistently with the theoretical literature discussed in section 2, we consider two classes of network measures which correspond to the two network characteristics that we discussed so far: (1) centrality indicators, such as degree centrality, Random Walk centrality, and PageRank centrality, which measure first-order and second-order degrees of centrality and will be used to identify contagion effects; and (2) local density indicators, such as local clustering coefficient, and average degree of a node's neighbors, which measure linkage diversification around the node/sector and are used to identify the substitution effects.

Identifying contagion effects through first-order and second-order centrality indicators

The first class of network indicators measures the centrality of a sector in terms of its direct or indirect influence on other sectors in the network. A node is central if it is (1) close to all other nodes, meaning that a shock will arrive more quickly and frequently to it, or (2) located in a central position among other nodes for which it plays a mediating role in the propagation of flows.

In this category, a very naive measure of centrality is the 'first-order degree', that is the number of adjacencies for a node/sector (Freeman, 1979). For weighted, directed graphs like input-output networks, the in-degree (? ) and out-degree (? @ ) centralities are defined as the weighted sum of, respectively, incoming and outgoing links for a given node:

? = ( , ) |( , )∈C ; ? @ = ( , ) |( , )∈C (9)
where ( , ) is the weight of the link coming from j to I, ( , ) is the weight of the link going from I to j, and E is the set of directed edges/links in the network. Degree centrality is usually labeled as a node's strength. 9 Figure 2 provides a graphical illustration of in-degree centrality. 2012) claim that second-order centrality is a more relevant measure of a sector's influence in the production network.10 Blochl et al. ( 2011) have proposed an indicator of second-order centrality, based on random walk process,11 which measures how quickly or how frequently a node is visited during the process of propagation of shocks in the economy. By defining second-order centrality as the frequency and the speed with which it is visited during a random walk process, RW centrality is particularly fitted to quantify the response of sectors to an economic shock elsewhere in the network. For sector i, Random Walk Centrality (RWC) is computed as:

F5? = + ∑ G(H, #) (10)
where G(H, #) is the mean first passage time (MFPT), i.e. the expected number of steps a random walker which starts at node j takes to reach i for the first time. Figure 3 gives a graphical illustration of the RWC. PageRank centrality is another second-order centrality measure which results from a random walk of the network (Brin and Page, 1998). It is of particular interest to us, because, according to Carvalho (2012), it coincides more strictly with Acemoglu et al (2012)'s influence vector capturing higher-order interconnections.12 PageRank centrality computes the importance of a node based on the structure of the incoming links, and considers a node to be important if it is connected with other important nodes in the network. Weighted PageRank centrality, which takes into account the weight of the links, is defined as:

JF(#) = (1 -") + " JF(H) K @L ∈M( ) ( , ) (11)
where JF(#) and JF(H) are rank scores of nodes i and j, respectively, d is a dampening factor usually set to 0.85, K @L is the number outgoing links of node j, N(#) is the set of in-neighbors of i, and ( , ) is the weight of the link between nodes i and j. A higher PageRank score indicates higher influence for the node. Figure 4 gives a graphical illustration of PageRank centrality.

Identifying substitution effects through local density indicators

The second class of network measures deals with the position of a sector in a neighborhood of connected sectors. The average degree of neighboring nodes will measure how dense the connections around a sector are. It indicates the extent to which a sector deals with other sectors that are themselves wellconnected with other sectors in the economy, either as suppliers or as purchasers. When a sector is surround be other well-connected sectors, there will be alternatives paths for shock propagation in that neighborhood of sectors. Average degree of neighboring nodes is formally defined as:

'OP = 1 |P(#)| K ∈Q( ) ( 12
)
where P(#) are the neighbors of node i, and K is the degree of node j which belongs to P(#).

Another interesting metric in this category is the "local clustering coefficient" which measures the likelihood of a node being part of a circle of connected nodes. The idea is based on the concept of transitivity, in a sense that if node A is connected to node B, and node B to node C, then there is a heightened probability that node A will also be connected to node C. Technically, the three nodes are said to form a closed triad. The local clustering coefficient for a weighted, directed network is defined as (Fagiolo, 2007):

?? = (5 0 R ) R " " @L -" ↔ (13)
where 5

T U is a weight matrix in which each element is raised by a factor of 1/3, the subscript ii notes the ith element of the main diagonal of (5 T U ) R , " and " @L are respectively the in-degree and out-degree of node i, and " ↔ is the number of bilateral links between node i and its neighbors. (2008). In (a), the nodes around i are fully connected, and thus the local clustering coefficient for i is 1. In (c), node i acts like a hub but has a clustering coefficient equal to 0 due to existence of structural holes between its neighbors.

Local clustering is also used as an indicator of so-called "structural holes" in a network -a concept that is highly relevant for our empirical test. Missing links between neighbors in a network are considered as structural holes, which are particularly important if we are interested in studying the efficient spread of information (or shock) throughout the network because they tend to reduce the number of alternative routes of transmission (Newman, 2010, p. 202). Hence, lower values of the local clustering coefficient indicate prevalence of more structural holes around node i.

The distributions of the average number of nodes' neighbors and of the PageRank centrality indicators for our sample of observations are reported in appendix D.

Identification issues

In this section, we expose various points which are critical for the proper identification of the impact of network characteristics for the transmission of volatility.

The dependent variable: Direct and indirect contributions of sectors to aggregate volatility

One essential aspect of our empirical approach is the way we intend to identify the direct and indirect contributions of a sector to aggregate volatility, which is formally defined by Equation 8 in section 2. The expression of a sector's direct contribution to aggregate volatility can be derived from Eq. 1, using the marginal risk contribution measure employed in portfolio risk budgeting (Litterman, 1996; Davis and Menchero, 2010). From Equation 1, we can define aggregate volatility as 13 :

8 9 V : = W ?XOY W , W Z [0 (14)
As, by definition,

?X\\Y W , W Z = ]@^( V ,9 V ) _ à V _ b ) V
, Eq. ( 14) can be rewritten as:

8 9 V = W ?X\\Y W , W Z 8 V [0 8 9 V = W \ W _ [0 (15)
where 8 V is the standard deviation of output growth W in sector i in country c between 2007 and 2009, and cX\\Y W , W Z is the correlation coefficient between sectoral output growth ( W ) and aggregate output growth ( W ) in country c. \ W _ is a sector's direct marginal contribution to aggregate volatility, also called direct risk contribution. 14

13 Appendix I provides a detailed demonstration of how the definition of risk contribution is derived from Eq (1).

14 Although such measure of risk contribution is basically an approximation of the true underlying volatility, it serves our purpose as it constitutes an empirical proxy of an unobserved risk that can be used in a statistical regression. As the eminent statistician, George Box, famously noted: "…the statistician knows…that in nature there never was a normal distribution, there never was a straight line, yet with normal and linear assumptions, known to be false, he can often derive results which match, to a useful approximation, those found in the real world" (Box, 1976).

In order to identify the indirect impact of a shock on aggregate volatility which percolates through all other (non-i) sectors, the cumulative contribution of all non-ic sectors to aggregate volatility, denoted d @ / W , is computed as following15 :

d @ / W = eW \ eW _ ef = eW 8 gV cX\\Y eW , W Z ef (16)
If we accept that in a N-sector economy, the volatility contribution of the N-1 non-i sectors is a good proxy of the economy's aggregate volatility, then we can safely suggest that the impact of a shock to sector i,c on all N-1 sectors' contributions to output volatility, as done in Equation 16, is a convenient proxy for the impact of this shock on aggregate volatility. This identification restriction is not binding if N is reasonably large, as it is the case in our data where N=35. Moreover, this assumption is supported ex post by our empirical analysis.16

Identification assumptions: The 2008 global crisis and the Bartik instrument

A second crucial aspect of our empirical strategy pertains to the identification of a causal impact of network characteristics on aggregate volatility. In order to respond to the central question of our paper, that is how the structural characteristics of the production network condition the transmission of sectoral volatility to the whole productive system, the contribution of all non-i sectors to aggregate volatility has been regressed on the interaction of the shock intensity with network characteristics for sector ic, as well as other determinants, as in Equation 17:

d @ / W =∝ +∝ 0 ( W +∝ : -W +∝ R ( W -W + i j @ / W ∝ k + l W + m + n W (17)
where d @ / ,W is the sum of the contributions of all non-i,c sectors in the aggregate volatility between 2007 and 2009 as defined in Eq. 16, ( W is the Bartik indicator of final demand shock for sector i in country c between 2007 and 2009 defined in Equation 18 below, -W is a measure of network properties for sector i,c in the base year (i.e., 2007), i j @ / ,W is a vector of average observed characteristics for noni,c sectors, including changes in capital stock and changes in employment, l W and m are country and sector fixed effects, and n ,r is the error term. We use panel data Fixed Effect estimator to estimate Equation ( 17). Data is stratified by country c and then by sector i. Country and sector fixed effects are systematically included in order to account for unobservable country-and sector-specific factors explaining volatility, like technology or supply chains.17 There is no time dimension since the dependent variable and ( W account for variations between 2007 and 2009. 18 Two controls for non-i sectors are also included: labor and capital growth over the same period. They ensure that the fundamental drivers of the dynamics of the rest of the economy, i.e. the non-i sectors, is adequately controlled for.

The estimated direct impact of an exogenous demand shock in sector i on all non-ic sectors' contribution to the aggregate volatility is identified by the term ∝ 0 in Equation 17. However, we are more interested in identifying the indirect impact of a shock, that is how this shock interacts with the network characteristics of a sector to generate aggregate volatility through its interactions with all other sectors. In eq. 17, the sum of estimated coefficients ∝ 0 +∝ R measures the average impact of a shock in the global final demand for each sector's output or volatility risk, conditional on the average population value of the network characteristic of the sector. Put differently, the sum of estimated coefficients ∝ 0 + ∝ R identifies whether a sector's sensitivity to global demand shock is magnified or smoothed by various features describing the pattern of its linkages to the whole production network.

Assessing the causal impact of sectoral shocks on aggregate volatility raises two potential concerns. First, the level of final demand in a given sector that is captured by national account data may reflect the equilibrium level of demand in that sector rather than the actual level of demand. In case of supply shortage in the short run, for example, the actual demand in a sector could well be higher than what was effectively supplied and is measured at equilibrium, biasing the measure of shocks and volatility. Thus, it can be tricky to capture empirically the actual demand irrespective of the supply conditions, essentially because what the national statistical agencies collect a posteriori or what we observe empirically is the result of market clearing.

Second, along a crisis episode, demand shock to some sectors can be endogenous to aggregate volatility. The credit crisis in 2008 rapidly transformed into a trade-induced demand crisis, all sectors being eventually affected. Because of huge credit constraints and exchange rate uncertainty, global trade collapsed faster than world incomes, this decline being highly synchronized across countries, albeit with different intensities across sectors (Grossman and Meissner, 2010). Hence, there can be a two-way effect, with aggregate volatility prompted by a limited set of sectors initially hit by shock, like finance or trade, driving significant fluctuations of demand to other sectors at the end of the day.

With these two issues in mind, we define our variable for final demand shock as following:

( W = W, & , & , & , -1 = W, ∆( , ( 18
)
where W, is the share of sector i in country c in the global production of goods for final demand in the base year (i.e. 2007), and ∆( is the change in the global final demand for sector i between 2007 and 2009. The main idea behind this shift-share indicator is to isolate the exogenous component of the final demand shock, making the variable ( W exogenous to the dependent variable (non-i sectors' contribution to aggregate volatility). 19 The intuition behind Eq. 18 is that if final demand for a particular industry rises or drops at the global level, the main effects from that change will be observed most in the countries in which the relevant local industry has a higher share in the global sector output. In summary, this shock indicator fulfills the condition that shocks have heterogeneous intensities across sectors and are exogenous to the dependent variable.

It is worth being emphasized that the present article does not explicitly address how sectoral comovements, i.e. correlated shocks across sectors, impact aggregate volatility, chiefly because our empirical design based on sectors does not allow us to do so. 20 Still, sectoral co-movements are included as a component of the dependent variable (sector contribution to volatility) in our model, and the influence of sectoral co-movements within the same country is accounted for by the simultaneous inclusion of country fixed effects and by clustering errors by country in the robustness check's estimations reported in section 6. The potential influence of co-movements across countries for specific sectors is also systematically controlled for by sector fixed effects.

Following Acemoglu et al. (2012), we assume in our analysis that the microeconomic functions of reaction to shocks can be aggregated with no restrictions. This means that our set-up does not allow identifying hysteresis effects due to partial adjustment and band of inaction (Dixit, 1989; Pindyck, 1991). 21 Indeed, we know since the early nineties that while certain threshold values of the shock at the micro level (for one firm or sector) have to be exceeded in order to produce sector-to-sector transmission, because sunk costs of investing/hiring or disinvesting/firing can justify that firms will wait before adjusting to price or demand shocks. In the climate of high uncertainty due to the conjunction of a generalized demand crisis and a credit crunch characterizing the 2008-2009 period, however, the band of inaction of firms may have shrunken compared to the event of an isolated price shock in normal times. 22 First, because firms were suddenly and highly financially constrained, they may not have waited too long before reducing their input demand to upstream providers. Second, even though some reactive firms may have chosen to delay the adjustment of their productive capacities, the negative demand shock was nevertheless partially transmitted to equipment goods sectors. 23 From what precedes, we can be fairly confident that the magnitude of our estimated coefficients might not be significantly affected by band of inactions. Nonetheless, if we suspect that, in the particular set-up of cumulative uncertainty characterizing the 2008 crisis, the impact of the demand shock may be only weakly identified in our empirical strategy, then we can consider that the strongly significant impacts of sectoral demand shocks, that we empirically identify, provide a lower bound of the impact of sectoral shocks on the aggregate economy.

Data sources and descriptive statistics

We use world input-output tables (WIOTs) developed by Timmer et al. (2015) to build a unique global production network which consists of 35 sectors in 40 countries 24 (1,435 sectors in total). The list of sectors and countries are shown in Appendix II. The descriptive statistics of the variables are presented in 20 See Foerster et al. (2011) for a recent study accounting for these co-movements. 21 Our unit of analysis is an industry. Although aggregation issues certainly exist at that level, they have not been extensively discussed in the literature on strong hysteresis which has essentially focused on macroeconomic aggregation and seldom addressed sectoral heterogeneity issues (Cross, 1994; Göcke, 2002). 22 See for example Belke and Göcke (2005) and Belke et al. (2013) for the impact of exchange rate shocks on hiring. 23 A simple and straightforward way to acknowledge band of inactions in our analysis would be to consider that sectors with higher second order centrality tend to exhibit a tighter band of inaction than other sectors, as they react more strongly or more rapidly to swings of demand by reducing their own demand for inputs, therefore contributing more intensively to transmitting instability to the aggregate economy. On the contrary, sectors which are located in denser neighborhoods may wait more before reacting compared to other sectors. Nevertheless, confirming this would require additional evidence based on multi-period adjustment. 24 In fact, there are 39 individual countries, with the fortieth being the rest of the world (ROW) aggregated into one. World input-output tables are in chain-linked volumes, and are thus comparable across years. The data for gross output and final demand come from the WIOTs, while the data for capital stock and employment that are used are controls in estimations come from the Socio-Economic Accounts, also developed by Timmer et al. (2015) for the 2013 release of the WIOTs, expressed in constant prices. We had to estimate the capital stock changes for a number of missing countries using data from the OECD's STAN Database for Structural Analysis.

The WIOT includes the rest of the world (ROW) as a single consolidated region, which captures all residual transactions with the rest of the 39 individual countries. While the node-level network measures, defined in Equations 9-13, have been computed over the entire world input-output network (including the ROW), the econometric model only uses the data for 39 countries and excludes the observations for the ROW because it is a group of heterogeneous countries and may bias our estimates due to the large weights they carry. Nonetheless, the connections with and within the ROW are included in the computation of the network measures, because it is important that they are measured over a full global network and that we capture all existing inter-industry linkages. Likewise, the rest of the world is accounted for in the shock variable. We produce the network of inter-sectoral flows using the WIOT in 2007, and compute the node-level network measures using MATLAB.

Estimation results

Baseline estimation results

Results from the fixed effect estimation of the baseline equation ( 17) are reported in Table 2. Country and sector fixed effects are included. Under our identification assumptions, the direct effect of a sectoral shock on aggregate volatility is captured by the estimated coefficient of the Shock variable, while the indirect effect, conditional on the various network characteristics of the sector, is captured by the interaction of the Shock and the Ntwrk variables.

Unsurprisingly, a shock to sector i has no direct effect on the contribution of all other sectors to aggregate volatility, as suggested by the statistically insignificant coefficient for Shock i . The indirect impacts of a sectoral shock on aggregate volatility that goes through inter-industry linkages are reported in columns 2 to 7 for the network characteristics of centrality and local density of the sector hit by the shock presented in section 3.

In what concerns first-order centrality, we see that only shocks to sectors featuring high out-degree centrality, that is large input suppliers, had a significant and positive impact on aggregate volatility during the period investigated (Column 3). This result is perfectly in line with the idea that in asymmetric production networks, shocks to sectors or firms with a large weight in the sales vectors will prompt macroeconomic volatility (Gabaix, 2011; Acemoglu et al., 2012). . The Network variable is specified at the head of columns 2-7. For example, in column 2, the Network coefficient gives the estimated main impact of the number of incoming flows to sector i on the aggregate volatility in the absence of any shock, while the coefficient of the interaction Shock*Network gives the average impact of the number of incoming degrees in the case of a sectoral shock.

Second-order centrality seems to be having a similar impact on shock transmission as shown by the positive coefficient of the interaction term Shock*PageRank reported in column 5. Recall that, by measuring the intensity of a sector's connections to other influential sectors, PageRank centrality is the most consistent proxy of Acemoglu et al. (2012)'s influence vector (Carvahlo, 2012). The positive coefficient taken by the interaction means that a shock to a more influential sector does increase aggregate volatility. Unsurprisingly, the coefficient of the interaction Shock*Random walk centrality is not significant (column 4), as Random walk centrality measures the vulnerability of a sector to shock(s) originating elsewhere in the economy. This type of second-order centrality might not drive volatility transmission to the rest of the economy, and indeed, it is supported by our data. Taken together, these findings therefore provide empirical support for Acemoglu et al (2012, 2017)'s assumption that shocks to more central sectors matter for explaining aggregate volatility, with second-order interconnections prompting aggregate volatility through 'cascade' effects, that is through the sequence of links between upstream (in the case of demand shocks) influential sectors.

Interestingly, our estimations also provide evidence of a substitution effect. The negative coefficients of the interaction terms in columns 6 and 7 suggest that the contagion effect is lower when the sector hit by the shock is surrounded by other sectors having themselves more diversified linkages to the rest of the economy (Average degree of a node's neighbor) or stronger connections with their neighbors (Local clustering coefficient). The estimated impact on aggregate volatility of the local density around the sector affected by a shock (as reported in columns 6 and 7) arises from the fact that the shock fades out across the different routes that exist around the sector. Our results therefore show that a shock to a denser and better-connected region within the production network will be more easily absorbed throughout a larger number of alternatives routes of volatility transmission than shocks to less dense regions of the network, which is fairly consistent with the assumption of a substitution effect. Note that fixed effects estimations with errors clustered by country do not significantly modify these results (See table C1 in Appendix C). 25 Computing predictive margins might help characterizing the impact of a shock over the entire distribution of network characteristics. Predicted margins at various levels of network indicators show that while a one-unit shock has no impact on aggregate volatility at the mean levels of the network indicators, the impact becomes significant for higher values of the indicators of local density (Average degree of neighboring nodes) and second-order centrality (PageRank centrality). The predicted marginal effects of a one-unit increase in the intensity of demand shock on non-i sectors' contribution to aggregate volatility for various levels of the two indicators are reported in the upper panel of Figure 6. The histogram and cumulative distribution graphs of PageRank centrality and of Average degree of neighboring nodes are reported in the intermediate and lower panels of Figure 6.

The magnitude of marginal effects suggests that, everything else equal, aggregate volatility will be 4 to 7 percentage point higher after a one-unit increase in the intensity of shock to sectors with very high second-order centrality. Figure 6 shows that the PageRank centrality distribution is strongly positively skewed, with only a few sectors -the top 1% of the variable distribution -featuring values above the .008 threshold beyond which a one-point increase of the shock variable increases aggregate volatility. Note that this pattern is fairly consistent with Gabaix (2011) and Acemoglu et al. (2012) which both insist, albeit from different units of observation, on the fat-tailed distribution of influence within the productive network. At the top 1% of the distribution of the PageRank centrality are such sectors as Finance and banking in the USA, health and social work in the USA, Italy, UK and Germany, construction in Spain, France, UK and the USA, transport equipment in Germany, USA, Japan and China, textile in China and Turkey, and electrical and optical equipment, basic metals, and machinery in China. This suggests that while both services and manufacturing sectors are conducive to aggregate volatility in our sample. As for local density, although our computations show that the Average degree of neighboring nodes needs to be very high (around 2500) to have a significant smoothing effect on aggregate volatility, the cumulative distribution graph reported in the intermediate panel of figure 6 (right-hand side) reveals that this area corresponds to the four highest deciles of the distribution of country-sectors for this variable. More precisely, aggregate volatility is 5 to 10 percent point lower after a one-unit increase in the intensity of shock for sectors with high local density, that is the top 40% of the Average degree of neighboring nodes distribution).

In other words, both second-order centrality and local density have significant average impacts on aggregate volatility. Still, marginal effects suggest that while only few sectors might turn idiosyncratic shocks into aggregate volatility, due to their large influence over the whole productive network, there might be numerous sectors around which the local density of linkages might absorb idiosyncratic shocks.

Heterogeneous effects across sectors and levels of income

Two sources of heterogeneous effects of a sectoral shock in our sample might be further investigated as they shed light on interesting patterns of our baseline results. A first source of heterogeneity might be related to country income levels. As productive systems get more diversified when national income grows (Imbs and Wacziarg, 2003, Koren and Tenreyro, 2013), the impact of network characteristics on aggregate volatility, which is conditional on the degree of economic diversification, is likely to vary. A second source of heterogeneity pertains to different patterns of volatility transmission across sectors. Demand shocks to the service sectors, whose output cannot be stocked, might be more prone to contaminate the whole economy. Moreover, service industries are generally located in dense parts of the production network as they provide support activities to other sectors. Sectors such as finance and banking services might be particularly prone to transmit volatility and could partially drive the fullsample results. Table 3 shows the coefficients of the interaction term when the baseline model (Equation 17) is reestimated on various sub-samples, with the results of the full sample baseline estimations being reported in the first row for the sake of comparison. We can see in the second row that the coefficient estimates of the interaction term for the sub-sample of higher income countries are highly consistent with full sample estimates, both for the second-order centrality and the local density. This is more so as higher income countries observations are restricted to the services sectors. By contrast, estimations for the manufacturing sector sub-sample does not show statistically significant coefficient, suggesting that full sample results are mainly driven by the services industries. Nonetheless, estimation results for the samples excluding the banking and finance sector show that the full sample or the subsample results are not driven by the banking and finance sector which ignited the 2007 crisis.

As for middle-income countries, various interesting issues arise. First, coefficients reported in the third row of Table 3 show that shocks to sectors with higher second-order centrality increase aggregate volatility in the developing countries sub-sample, albeit with a weaker significance than for developed economies. By contrast, localization in a dense neighborhood of the production network does not mitigate volatility propagation. The absence of substitution effects in the sub-sample of middle-income economies suggests that they are more vulnerable to output volatility through contagion effects than higher-income countries. In the productive systems of emerging countries, structural holes are more frequent and larger, which makes these economies more vulnerable to external demand shocks. It is now well documented that FDI in global value chains (GVC) prompts the expansion of a few exporting sectors featuring only limited forward and backward linkages to the rest of the economy (Srholec, 2007; Baldwin, 2011). 26 Lastly, the fact that services do not drive the results for the middle-income sample, as can be seen in the seventh row of Table 3, suggests that manufacturing sectors probably have a larger influence on volatility in middle-income than in higher-income economies.

Sensibility and robustness checks

In this section, we conduct various sensibility and robustness tests in support of the validity of our main findings shown in section 5. Table 6 reports the estimated coefficient of different shock*network interactions for various sensitivity and robustness checks of this section. Full estimation tables are reported in Appendix, as indicated in the last column of Table 6. Likewise, results of the baseline estimation are reported in the first row of Table 6.

First, we ensure that the definition of the dependent variable, which is based on the second moment (i.e. standard deviations) of GDP growth, does not bias our estimations because of measurement issues. Indeed, output volatility is computed using two data points, namely 2008 and 2009 growth rates, which may either underestimate the true volatility, because of the limited number of observations, or overestimate it because the 2008-2009 period corresponds to a phase of extreme volatility -it covers the succession of bust and recovery prompted by the financial crisis. Moreover, an inherent flaw in the measurement of standard deviation on a short time period is that it may underestimate the true extent of volatility and output losses in the case of homogenous successive negative growth performances. For instance, if the output growth of a sector is constantly minus two percent in both years, the standard deviation would give a value of zero which shows no indication of volatility. In one sense, this may not be a flaw, because a constant minus two percent growth every year is not a fluctuation per se. However, for the purpose of our study, we are equally interested in knowing the output losses during the Great Recession. A priori, we expect that these features not to raise much concern about the robustness of our results, because, in our sample, no sector has recorded constant growth rates over 2008 and 2009, and for only 6 percent of the sectors, the absolute difference in growth rates between the two successive years is less than 0.5 percentage point.

Still, in order to ensure that our results are not biased by such measurement flaws of our dependent variable, we replace the second moment (i.e., standard deviation) with the first moment (i.e., average) of economic growth, i.e., non-i sectors' contribution to GDP growth, averaged over 2008-2009, in equation 17. Indeed, at country level, output growth and output volatility tend to be inversely correlated over the long-term (Ramey and Ramey, 1995). We observe a similar pattern in our cross-sectoral data as well, as illustrated in Figure 7 which plots sectoral growth contributions over 2008-2009 against their long-term pre-crisis volatility (i.e., for 1998-2007), suggesting that the sectors which were inherently more volatile did experience lower output growth. Given the inverse relation between growth and volatility, we should get opposite results as compared to the baseline estimation of our model, that is the coefficient of our main variable of interest (i.e., Shock*Ntwrk interactions) should now take opposite signs to those in Table 2. 4. They show that the signs of the interactive terms between shock and respectively PageRank centrality, Average degree of neighboring nodes, and Local clustering coefficient are now the opposite to those estimated in Table 2. 27 Overall, using the output growth contribution of all non-ic sectors as the dependent variable therefore corroborates the baseline results from the estimation of Equation 17. 28 Thus, it is unlikely that the estimation results from the baseline model are driven by dependent variable definition and measurement issues. . The Network variable is specified at the head of columns 2-7. For example, in column 2, the Network coefficient gives the estimated main impact of the number of incoming flows to sector i on the aggregate output growth in the absence of any shock, while the coefficient of the interaction Shock*Network gives the average impact of the number of incoming degrees in the case of a sectoral shock.

Second, we test whether Table 2's estimation results are not biased by misspecification issues related to unknown forms of correlation between countries or sectors. Given that unknown patterns of crosssector and cross-country co-movements might have been prompted by the intensity and the global nature of the 2008-2009 crisis episode, through inter-country and inter-sector financial and trade relations, various unknown patterns of cross-sector or cross-country dependence might bias FE estimates. 29 We therefore re-estimate Eq. 17 by using the Generalized Estimating Equations (GEE) estimator that was first developed by Liang and Zeger (1986). By producing estimates for "population-averaged" effects of a change in one or more covariates, rather than "individual-specific" effects which are traditionally estimated by the fixed effects (FE) models, GEE estimator controls for correlations across individuals within the same cluster, when these groups are not known a priori, therefore leading to improved standard errors and more efficient parameter estimators (Liang and Zeger, 1986; Burton et al., 1998). 30 Table 6 (Table A2 in Appendix) show that the coefficients of our variables of interest remain fairly unchanged when unknown sources of country-and sector-level clustering are accounted for.

Third, we test the sensibility of our baseline results to the inclusion of country-level observable policy variables: trade openness (proxied by the sum of export and import in percent of GDP), financial development (proxied by domestic credit in percent to GDP) and distance to technological frontier (measured by distance in income per capita with the U.S). In order to protect ourselves against this risk of 29 See Gould (2018) for a recent analysis of linkages between financial and trade flows and their impact on economic growth in Europe and Central Asia. See also di Giovani and Levchenko (2010) on the cumulative impact of trade and investment on aggregate volatility. 30 Eq. 17 is re-estimated with the GEE estimator using a Gaussian distribution (as the distributions of our respective dependent variables are close to normal distribution), an identity link function (i.e. the dependent variable has not been transformed), and an exchangeable (symmetric) or independent working relation for the covariance matrix as indicated in table C2. Note that these estimation parameters are the most general ones.

reverse causality, we took the initial value (i.e. 2007) of these policy variables rather than their mean value over the period. 31 Table 6 shows that the results of the baseline estimations are unaffected by the inclusion of these policy controls. In addition, Appendix Table C3 shows that, whereas country-level average trade openness has no impact on aggregate volatility, higher financial development does increase aggregate volatility, assuming other things constant. This finding is not surprising given the financial nature of the crisis. Likewise, countries standing closer to the technological frontier also experienced higher aggregate volatility, all other factors being set equal, than those featuring greater distance, which is consistent with the fact that the crisis originated in developed countries. Values in parentheses are standard errors; *** for p < 0.01, ** for p < 0.05, and * for p < 0.1. All regressions include country and sector fixed effects. The dependent variable is the contribution of non-i sectors to aggregate volatility between 2007 and 2009. The Network variable is specified at the head of columns 2-7. For example, in column 1, the coefficient reported for the interaction Shock*Network gives the average impact of the number of incoming degrees in the case of a sectoral shock.

Fourth, we test whether not including the degree to which each sector is exposed to external shocks, accounted for by the sector's trade intensity (measured by its sales to foreign sectors as a share of its output) biases our results. Indeed, if certain network characteristics of a given sector are correlated with its degree of trade exposure, then estimated coefficient of shock*network could partially include the impact of the sector's exposure to external demand shocks. We therefore tested whether the coefficient of shock*network interaction remained significant after the inclusion of the interaction term between shock and the sector trade openness to Eq. 17. Tables 6 andC4 show that our main results are left unchanged when sectoral trade intensity is included as an additional control. This implies that the extent to which sectoral shocks transform into aggregate volatility relies fundamentally on a sector's characteristics in the production network, and not on the sector-level degree of exposition to external trade shocks.

Fifth, we test against various potential concerns that may arise with respect to the shock variable. We verify in the first place that the impact of a shock to sector i in country c is properly identified and is not driven by a possible co-movement between this shock and the shocks to all other non-i sectors. We therefore controlled for the intensity of shocks to non-i sectors in Equation 17 by using the average value of the Bartik instrument for all non-i sectors as a control variable. The estimation results, reported in tables 6 and C5 (in the appendix), remain fully consistent with our core estimation in Table 2, enabling us to conclude that the results are not driven by co-movements in sectoral shocks. 32 Another potential is raised by the risk that in countries where the local sector has a large share in the global production, our specification of the Bartik instrument may not remain entirely exogenous. In the event where the local industry is dominant in the global supply of the industry and is possibly a price-maker at the global level, the final demand shock as captured by the shift-share instrument could be influenced by the dependent variable. To rule out the risk that such potential endogeneity may be a concern, we excluded the dominant sectors from our sample and checked whether our results are unchanged. We exclude national sectors weighing more than 10 percent in the global gross output of that industry: many industries in the US, China and Japan, which is not surprising given the size of these economies, as well as German machinery and transport equipment sectors, and Italian leather and footwear industries are consecutively excluded. Estimation results for the restricted sample reported in tables 6 and C6 (in the appendix) show that the results remain unchanged compared to the full sample results of Table 2.

Finally, we exclude the United States from the sample as it shows the most extreme values of the shock variable. Estimation results reported in tables 6 and C7 (in the appendix) show that some of the results change after excluding the US. 33 In particular, the shock*network interactions for local density measures are no more statistically significant and the estimated coefficient for the demand shock turns negative and statistically significant. This deviation from our baseline results indicates that US industries feature network properties which strongly influence the transmission of sectoral shocks. This composition issue is particularly concerning as all other empirical studies on production networks have largely relied on US industrial data to validate their theoretical results. Accordingly, and in contrast with our findings in this paper, their result might not be automatically valid for other productive systems.

Extensions and policy implications

Our estimations in this paper show that because different sectors have different topological characteristics in their production network from one country to another, a sizable common shock can have asymmetric effects on aggregate volatility, country-wise and sector-wise. Our empirical framework allows us to identify those countries and sectors which are more prone to volatility contamination after they are hit by a shock. Our approach based on the construction of a global production network may also prove helpful to analyze a large variety of complex policy issues. As an illustration, we can show which countries and sectors are more exposed to stabilization losses within a common economic or currency area, which may have interesting implications for the cost-benefit analyses of the current Euro-outsiders such as Polish and the Czech governments when thinking about future Euro area membership.

Using equation 7 in our model, an adverse shock of a 10 percent drop in the final demand 34 for each sector in 12 Euro area countries were simulated, and the resulting aggregate volatility in the relevant countries was observed. Expectedly, the simulation results are in conformity with our empirical results, i.e., shocks to more influential sectors lead to higher aggregate volatility (Figure 8). Moreover, our simulation suggests cumulative effects of multiscale centrality in production networks as we could build the global production network for the 12 Euro area countries (Figure 9). Indeed, Figure 8 shows that a shock to an influential sector (i.e., a sector with high PageRank centrality), which might happen to be in a Euro area country that is also central in the network, will lead to larger aggregate output changes. Importantly, the simulation results also show that Euro area countries located in the periphery of the I-O network -those with lower average PageRank centrality -have to face larger aggregate output volatility in response to shocks to other sectors and countries in the Euro area. Figure 10, which plots the country's average PageRank centrality against its aggregate output volatility in response to a 10 percent drop in the final demand of each sector in the Euro area, shows that such countries as Portugal, Greece, Ireland, or Luxembourg -those featuring fewer influential sectors and more structural holes -seem actually more vulnerable to idiosyncratic shocks happening elsewhere in the Euro area than countries that are more central in the Euro area production network.

These simple simulations based on our model may help explain why economies of Greece, Portugal and Ireland were more deeply affected in the aftermath of the 2008 global financial crisis than other Euro area economies. One possible implication of this result is that economic integration treaties should provide additional insurance mechanisms to the member countries that are likely to be in the periphery of the regional production network, because these countries will be structurally more vulnerable to macroeconomic volatility that might originate elsewhere in the union. 35 This macroeconomic risk could be an important decision element for Euro area membership for such current outsiders as Poland and the Czech Republic. Note: Weak links with less than 2 percent weight in countries' exports are removed, to enhance visualization of the network.

Our simulations thus show that the topological characteristics of a sector in the production network and of a country's position in the global production network should be considered more seriously for any type of economic integration policy. A few other studies have also found similar results. In a recent study mobilizing network analysis to map trade and FDI connections, Gould (2018) could show that countries with higher centrality in a multidimensional connectivity network enjoy both higher economic growth and higher resilience to shocks while economies that are strongly dependent on a few connections are more vulnerable to shocks in the global network.

By extension, network characteristics not only matter for economic integration policies, but also for any type of domestic or common industrial policy. As an illustration, when industrial policy planners choose the sectors targeted for investment promotion and investment subsidies, they should carefully consider the national and global structure of the production network. This is not to suggest that merely targeting the sectors with the highest centrality would be the most effective approach. By carefully and systematically analyzing industrial policies in a production network set-up, Liu (2018) develops a 'distortion centrality' capturing both the sector's influence and the cost of promoting that sector, and proposes that the sectors with the highest distortion centrality should be targeted for industrial policies. Liu shows that market imperfections tend to accumulate through backward demand linkages, leading to large distortions in upstream sectors, thus creating a strong "incentive for a well-meaning government to subsidize upstream sectors." Liu's (2018) results support and complement our findings, i.e., that any targeted industrial policy or investment promotion strategy should carefully consider both the position of a sector in dense parts of the production network and the influence of this sector over the whole production network. For example, sectors in the upstream of the network, as they are a crucial vector of aggregate volatility, play a strategic role as input providers to downstream distorted sectors (Liu, 2018), and notably service sectors, could be the ones most appropriate to be targeted for an active public support policy, both in industrialized and emerging market economies. Likewise, our approach and results could also have relevant implications as for how countries should go about diversifying their economies. Our results suggest that diversification strategies must not only be based on the comparative advantage and fundamentals of potential sectors to be developed but they should also consider their idiosyncratic characteristics (Hausmann et al, 2007; Lederman and Xu, 2007; Joya, 2018) which include their topological properties in the production network and their potential for transmitting volatility.

Conclusion

By measuring sector-level network indicators in a multi-country production network comprising 40 highand middle-income countries, the present paper provides original empirical evidence for the causal effects of different input-output structures on the transmission of idiosyncratic shocks to aggregate volatility. By clearly identifying how the network features of a sector transmit shocks to aggregate level, our results provide robust empirical evidence for both the substitution and contagion effects of shock propagation as put forward in the literature.

Our empirical findings provide a nuanced perspective on the relation between diversification and volatility. The structure of the production network and inter-industry linkages play an important role in how diversification conditions the impact of idiosyncratic shocks on aggregate volatility. In fact, the structural characteristics of any single production network may convey simultaneously both substitution and contagion effects: shocks to sectors situated in dense sub-networks dissipate across the network of inter-sectoral linkages due to possibility of substitution between alternative input-output routes, whereas shocks to more influential sectors translate into aggregate volatility through contagion effects.

More specifically, we find that: (1) the impact of a sectoral shock on aggregate volatility does exist; (2) it is indirect and integrally transmitted through inter-sectoral linkages across the production network;

(3) its sign and direction varies with respect to the type of network characteristics, with shocks to more influential sectors or input suppliers leading to larger aggregate volatility, while shocks to sectors that are located in denser sub-networks being absorbed throughout the network; (4) services are more conducive than other sectors in translating idiosyncratic shocks into aggregate volatility through contagion effects;

(5) middle-income countries are more exposed to the aggregate effects of idiosyncratic shocks through contagion effects, because their productive system features more structural holes and more isolated influential sectors; and (6) observable country characteristics like trade openness or technological level, and sectoral trade intensity do not condition the transmission of shocks. We also checked the robustness of our main findings to alternative samples, estimators, definition of the dependent variable, exclusion of potential outliers, and control of unobservable sector and country characteristics.

The policy implications of our paper is that the topological characteristics of a sector in the production network, meaning its position and its influence in the network, should be carefully considered while designing any type of targeted industrial policy which may include industry-specific investment subsidies or promotion. Sectors located upstream in the production network which might be playing a strategic role as input providers to downstream distorted sectors, and service sectors -as they may be a crucial vector of aggregate volatility -could be the ones more appropriate to be targeted for an active public support policy. Further, the simulation of our model to 12 Euro area countries shows that countries in the periphery of a production network tend to be most vulnerable to shocks happening elsewhere in a network of integrated economies. Therefore, providing additional insurance mechanisms to the member countries that are likely to be in the periphery could be justified and2009. The Network variable is specified at the head of columns 1-6. For example, in column 2, the Network coefficient gives the estimated main impact of the number of incoming flows to sector i on the aggregate volatility in the absence of any shock, while the coefficient of the interaction Shock*Network gives the average impact of the number of incoming degrees in the case of a sectoral shock. Values in parentheses are standard errors; *** for p < 0.01, ** for p < 0.05, and * for p < 0.1. All regressions include country and sector fixed effects. The dependent variable is the contribution of non-i sectors to aggregate volatility between 2007 and 2009. The Network variable is specified at the head of columns 1-6. For example, in column 2, the Network coefficient gives the estimated main impact of the number of incoming flows to sector i on the aggregate volatility in the absence of any shock, while the coefficient of the interaction Shock*Network gives the average impact of the number of incoming degrees in the case of a sectoral shock. .99 Values in parentheses are standard errors; *** for p < 0.01, ** for p < 0.05, and * for p < 0.1. All regressions include country and sector fixed effects. The dependent variable is the contribution of non-i sectors to aggregate volatility between 2007 and 2009. The Network variable is specified at the head of columns 2-7. For example, in column 2, the Network coefficient gives the estimated main impact of the number of incoming flows to sector i on the aggregate volatility in the absence of any shock, while the coefficient of the interaction Shock*Network gives the average impact of the number of incoming degrees in the case of a sectoral shock. p < 0.01, ** for p < 0.05, and * for p < 0.1. All regressions include country and sector fixed effects. The dependent variable is the contribution of non-i sectors to aggregate volatility between 2007 and 2009. The Network variable is specified at the head of columns 1-6. For example, in column 2, the Network coefficient gives the estimated main impact of the number of incoming flows to sector i on the aggregate volatility in the absence of any shock, while the coefficient of the interaction Shock*Network gives the average impact of the number of incoming degrees in the case of a sectoral shock. Values in parentheses are standard errors; *** for p < 0.01, ** for p < 0.05, and * for p < 0.1. All regressions include country and sector fixed effects. The dependent variable is the contribution of non-i sectors to aggregate volatility between 2007 and 2009. The Network variable is specified at the head of columns 2-7. For example, in column 2, the Network coefficient gives the estimated main impact of the number of incoming flows to sector i on the aggregate volatility in the absence of any shock, while the coefficient of the interaction Shock*Network gives the average impact of the number of incoming degrees in the case of a sectoral shock.

Figure 2 .

 2 Figure 2. An illustration of a directed network. Node f has the highest in-degree centrality, while node b has the highest out-degree centrality.

Figure 3 .

 3 Figure 3. The network is taken from Blochl et al. (2011). Node b has a higher Random Walk centrality than a and c, because any shock

Figure 4 .

 4 Figure 4. The network is taken from Rieder (2012). Node size represents indegree, and color represents PageRank score via a heat scale (blue > yellow > red). For instance, although node n1 has one of the smallest in-degrees, it has

Figure 5 .

 5 Figure 5. The networks are taken from Costa et al.(2008). In (a), the nodes around i are fully connected, and thus the local clustering coefficient for i is 1. In (c), node i acts like a hub but has a clustering coefficient equal to 0 due to existence of structural holes between its neighbors.

Figure 6 :

 6 Figure 6: Predicted margins of the impact of sectoral shock for various values of network characteristics

Figure 7 :

 7 Figure 7: Scatterplot of sectoral contributions to aggregate growth (2008-2009) and to aggregate volatility (1998-2007), for approximately 1435 sectors (35 sectors in 41 countries)

Figure 8 .

 8 Figure 8. 3D scatterplot of simulated sectoral shocks and aggregate output change in 12 Euro area countries

Figure 9 .Figure 10 .

 910 Figure 9. Graph of the production network for 12 Euro area countries

Table 1 .Table 1 :

 11 Sample descriptive statistics of selected variables

		No. Obs.	Mean	Std. Dev.	Min	Max
	Contrib. to volatility non-i	1416	5.703	3.629	-0.787	16.514
	Shock i	1416	0.358	0.920	-1.052	13.344
	Cap. gr. non-i	1144	0.049	0.100	-0.980	0.241
	Lab. gr. non-i	1331	-0.005	0.050	-0.143	0.140
	In-degree i	1391	36,388	91,192	0	1,091,579
	Out-degree i	1396	36,258	109,864	0	2,207,168
	Random walk centrality i	1389	7.45e-04	0.0052	6.0.e-07	.15309
	PageRank i	1435	0.001	0.001	0.000	0.012
	Ave. degree of neighb. nodes i	1389	1,596	515	237	2,763
	Local clustering coef. i	1389	0.575	0.185	0.086	0.995

Table 2 .

 2 Regression of non-i sectors' contribution to aggregate volatility (2007-2009): Interaction of shock and network characteristics of sector i

	Dependent variable: Non-i sectors' contributions to aggregate volatility
			First-order centrality	Second-order centrality	Local density
		(1)	(2)	(3)	(4)	(5)	(6)	(7)
	Network characteristics of sector i	-	In-degree	Out-degree	Random walk centrality	PageRank centrality	Average degree of a neighbors node's	Local clustering coefficient
	Cap. gr. non-i	1.236	1.270	1.174	1.205	.955	.238	.238
		(1.36)	(1.36)	(1.36)	(1.36)	(1.34)	(1.32)	(1.32)
	Lab. gr. non-i	-7.81***	-7.30***	-7.28***	-7.96***	-6.57**	-7.10***	-7.10***
		(2.74)	(2.78)	(2.79)	(2.76)	(2.74)	(2.68)	(2.68)
	Shock i	-.024	-.062**	-.050**	-.025	-.036	.045	.045
		(.018)	(.028)	(.022)	(.018)	(.025)	(.029)	(.029)
	Network i	-	-2.7e-08	-.5.9e-	4.05**	-95.37***	2.6e-04***	.734***
			(2.9e-07)	07**	(.002)	(20.33)	(3.1e-05)	(.086)
	Shock i *Ntwrk i	-	7.0e-08	(3.0e-07)	.932	11.08***	-5.5e-05**	-.153**
			(5.3e-08)	1.4e-07**	(1.48)	(3.89)	(2.7e-05)	(.076)
	Constant	5.97***	6.00***	(6.5e-08)	5.96***	6.05***	5.63***	5.63***
		(.087)	(.089)	6.00***	(.090)	(.088)	(.09)	(.095)
				(.089)
	N	1,109	1,109	1,109	1,099	1,109	1,099	1,099
	Groups	35	35	35	35	35	35	35
	R 2 within	.18	.19	.20	.18	.20	.23	.23
	Values in parentheses are standard errors; *** for p < 0.01, ** for p < 0.05, and * for p < 0.1. All regressions
	include country and sector fixed effects. The dependent variable is the contribution of non-i sectors to aggregate
	volatility between 2007 and 2009

Table 3 .

 3 Regression of non-i sectors' contribution to aggregate volatility: Interaction between shock and network characteristics for various subsamples

	Dependent variable: Non-i sectors' contributions to aggregate volatility
		First-order centrality	Second-order	Local density
				centrality
		(2)	(3)	(4)	(5)	(6)	(7)
	Estimated coefficient of the interaction term Ntwrk*Shock	In-degree	Out-degree	Random walk centrality	PageRank centrality	Average degree of a node's neighbors	Local clustering coefficient	N
	Full sample	7.0e-08	1.4e-07**	.932	11.08***	-5.5e-05**	-.153**	1,109
	Higher income subsample	9.0e-08**	8.3e-08	-1.219	9.667***	-5.4e-05**	-.149**	661
	Middle income subsample	2.0e-06	-9.5e-07	-.365	227.68*	-1.0e-04	-.277	338
	Services subsample	4.4e-07***	1.8e-07***	1.038	19.63***	-6.8e-05**	-.188**	484
	Manufacturing subsample	3.7e-08	1.5e-08	2.022	-19.79	1.7e-04	.465	446
	Services & Higher income	3.7e-07***	1.2e-07**	.786	15.42***	-5.7e-05**	-.158**	290
	Services & Middle income	-1.4e-06	-4.0e-06	.852	-211.27	1.3e-05	.036	149
	Full sample: Banking &	5.7e-08	9.8e-08	.785	10.72***	-5.3e-05**	-.147**	1,066
	Finance excluded
	Services, B & F excluded	3.6e-07***	1.2e-07**	.805	18.39***	-5.6e-05**	-.155**	451
	Services & Higher income B	3.5e-07***	8.3e-08	.842	16.26***	-4.7e-05*	-.130*	270
	& F excluded

Values in parentheses are standard errors; *** for p < 0.01, ** for p < 0.05, and * for p < 0.1. All regressions include country and sector fixed effects. The dependent variable is the contribution of non-i sectors to aggregate volatility between 2007 and 2009. The Network variable is specified at the head of columns 2-7. For example, in column 2, the coefficient of the interaction Shock*Network gives the average impact of the number of incoming degrees in the case of a sectoral shock.

Table 4 :

 4 Regression of non-i sectors' contribution to GDP growth: Shock and network characteristics

	Dependent variable: Non-i sectors' contribution to aggregate GDP growth
		First-order centrality	Second-order centrality	Local density
		(2)	(3)	(4)	(5)	(6)	(7)
	Network i	In-degree	Out-degree	Random walk	PageRank centrality	Average degree of a node's	Local clustering coefficient
				centrality		neighbors
	Cap. gr. I	-.232**	-.228**	-.222**	-.232**	-.273**	-.273**
		(.106)	(.106)	(.107)	(.105)	(.106)	(.106)

Table 6 .

 6 Summary of the robustness and sensitivity checks

	Dependent variable: Non-i sectors' contributions to aggregate volatility
		First-order centrality	Second-order centrality	Local density
		(1)	(2)	(3)	(4)	(5)	(6)
	Estimated coefficient of the interaction term Ntwrk*Shock	In-degree	Out-degree	Random walk centrality	PageRank centrality	Average degree of a node's neighbors	Local clustering coefficient	Table
	Baseline: FE, full sample	7.0e-08	1.4e-07**	.932	11.08***	-5.5e-05**	-.153**	2
	FE, full sample, country clusters	7.0e-08	1.4e-07	.933	11.08*	-5.5e-05**	-.153**	C1
	GEE, full sample	2.3e-06***	2.8e-06***	1.34	135.88***	-8.9e-05***	-2.49***	C2
	FE, full sample, controlling for	6.7e-08	1.3e-07**	.698	11.00***	-5.9e-05**	-.154**	C3
	country-level characteristics
	FE, full sample, controlling for	6.4e-08	1.1e-07**	.493	10.34***	-6.4e-05**	-.179**	C4
	sectoral trade openness*shock
	FE, full sample, controlling for	7.0e-08	1.4e-07**	.933	11.08***	-5.5e-05**	-.153**	C5
	shocks to non-i sectors
	FE, dominant sectors excluded	7.6e-07	1.3e-06*	2.34	144.9***	-5.1e-05	-.144	C6
	FE, high intensity shock (US)	1.9e-07	5.9e-07	2.97	72.74***	-9.8e-05	-.272	C7
	excluded

Table B2 : List of countries

 B2

		High-income		Middle-income
		countries*		countries
	1	Australia	30	Brazil
	2	Austria	31	Bulgaria
	3	Belgium	32	China
	4	Cyprus	33	India
	5	Canada	34	Indonesia
	6	Czech Republic	35	Latvia
	7	Denmark	36	Lithuania
	8	Estonia	37	Mexico
	9	Finland	38	Romania
	10	France	39	Russia
	11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29	. Sale, maintenance and repair of motor vehicles and motorcycles; retail sale of fuel Germany 40 Turkey Other non-metallic mineral Greece Basic metals and fabricated metal Hungary Machinery Ireland Electrical and optical equipment Italy Transport equipment Japan Manufacturing; recycling Korea, Republic of Electricity, gas and water supply Luxembourg Construction Malta Netherlands Wholesale trade and commission trade, except of motor vehicles and motorcycles Poland Retail trade, except of motor vehicles and motorcycles; repair of household goods Portugal Hotels and restaurants Slovak Republic Other Inland transport Slovenia Other Water transport Spain Other Air transport Sweden Other Supporting and auxiliary transport activities; activities of travel agencies Taiwan Post and telecommunications United Kingdom Financial intermediation Real estate activities United States
	30	Renting of machinery & equipment and other business activities
	31	Public administration and defense; compulsory social security
	32	Education
	33	Health and social work
	34	Other community, social and personal services
	35	Private households with employed persons

* countries classified as "higher-income" in or before 2007

Table C2 :

 C2 Regression of non-i sectors' contribution to aggregate volatility (2007-2009): Generalized Estimating Equations estimation

	Family distribution: Gaussian; Link function: Identity; Working correlation: Independent
	Dependent variable: Non-i sectors' contribution to aggregate volatility
		First-order centrality	Second-order centrality	Local density
		(1)	(2)	(3)	(4)	(5)	(6)
	Network i :	In-degree	Out-degree	Random	PageRank	Average	Local
				walk	centrality	degree of a	clustering
				centrality		node's	coefficient
						neighbors
	Cap. gr. non-i	4.40***	4.39***	4.66***	4.51***	4.49***	4.49***
		(.993)	(.991)	(1.01)	(1.00)	(1.00)	(1.00)
	Lab. gr. non-i	-27.1***	-27.1***	-26.0***	-26.1***	-26.1***	-26.1***
		(2.06)	(2.05)	(2.08)	(2.06)	(2.07)	(2.07)
	Trade i	.001	.002	.003	.001	.001	.001
		(.003)	(.003)	(.003)	(.003)	(.003)	(.003)
	Shock i	-1.32***	-1.28***	-1.21***	-1.47***	-.249	-.249
		(.213)	(.154)	(.131)	(.185)	(.291)	(.291)
	Network i	-1.3e-05***	-1.4e-05***	.033*	-553.1***	.0005**	1.44**
		(2.1e-06)	(2.1e-06)	(.018)	(158.9)	(.0002)	(.615)
	Shock*Ntwk	2.3e-06***	2.8e-06***	1.34	135.9***	-.0009***	-2.49***
		(4.1e-07)	(5.0e-07)	(7.10)	(33.95)	(.0002)	(.712)
	Constant	6.43***	6.41***	6.02***	6.47***	5.32	5.32
		(.164)	(.164)	(.163)	(.183)	(.375)	(.375)
	N	1,101	1,100	1,099	1,109	1,099	1,099
	Groups	35	35	35	35	35	35
	Values in parentheses are standard errors; *** for p < 0.01, ** for p < 0.05, and * for p < 0.1. The dependent
	variable is the contribution of non-i sectors to aggregate volatility between 2007

Table C3 .

 C3 Regression of non-i sectors' contribution to aggregate volatility(2007-2009): Country-level controls included All regressions include country and sector fixed effects. The dependent variable is the contribution of non-i sectors to aggregate volatility between 2007 and 2009. The Network variable is specified at the head of columns 2-7. For example, in column 2, the Network coefficient gives the estimated main impact of the number of incoming flows to sector i on the aggregate volatility in the absence of any shock, while the coefficient of the interaction Shock*Network gives the average impact of the number of incoming degrees in the case of a sectoral shock.

	Dependent variable: Non-i sectors' contributions to aggregate volatility
			First-order centrality	Second-order centrality	Local density
		(1)	(2)	(3)	(4) Random	(5)	(6)	(7)
	Network i :	-	In-degree	Out-degree	walk centrality	PageRank centrality	Average degree of a	Local clustering
							node's	coefficient
							neighbors
	Cap. gr. non-i	1.082	1.133	1.041	1.098	.833	.163	.163
		(1.25)	(1.25)	(1.25)	(1.26)	(1.24)	(1.22)	(1.22)
	Lab. gr. non-i	-8.06***	-7.64***	-7.74***	-7.99***	-6.83**	-7.46***	-7.46***
		(2.53)	(2.57)	(2.58)	(2.56)	(2.54)	(2.47)	(2.47)
	Shock i	-.029*	-.071***	-.052**	-.028	-.045**	.042	.042
		(.017)	(.026)	(.021)	(.017)	(.023)	(.027)	(.027)
	Network i	-	1.01e-07	-4.6e-07*	.003	-86.59***	2.5e-04***	.700***
			(2.7e-07)	(2.8e-07)	(.002)	(18.85)	(2.9e-05)	(.081)
	Shock*Ntwrk	-	6.4e-08	1.1e-07*	-.493	11.00***	-5.9e-05**	-.164**
			(4.8e-08)	(5.9e-08)	(1.41)	(3.59)	(2.5e-05)	(.070)
	Openness	-.0004	-.0003	-.0003	-.0005	-.0002	-.001	-.001
		(.001)	(.001)	(.001)	(.001)	(.001)	(.001)	(.001)
	Financial dev.	.040***	.039***	.039***	.039***	.039***	.040***	.040***
		(.001)	(.002)	(.002)	(.001)	(.002)	(.001)	(.001)
	Dist. to GDP US	-.874***	-.902***	-.884***	-.853***	-.914***	-.825***	-.825***
		(.202)	(.204)	(.204)	(.205)	(.201)	(.197)	(.197)
	Constant	2.57***	2.56***	2.57***	2.58***	2.55***	2.16***	2.16***
		(.174)	(.176)	(.177)	(.176)	(.173)	(.177)	(.177)
	N	1,074	1,067	1,066	1,065	1,074	1,065	1,065
	Groups	35	35	35	35	35	35	35
	R 2 within	.99	.99	.99	.99	.99	.99	.99
	Values in parentheses are standard errors; *** for p < 0.01, ** for p < 0.05, and * for p < 0.1.

Table C4 :

 C4 Estimation of the sectors non-i's contribution to aggregate volatility (2007-2009): Shock*sectoral trade openness included Dependent variable: Non-i sectors' contribution to aggregate volatility

		First-order centrality	Second-order centrality	Local density
		(1)	(2)	(3)	(4)	(5)	(6)
	Network i :	In-degree	Out-degree	Random walk	PageRank	Average	Local
				centrality	centrality	degree of a	clustering
						node's	coefficient
						neighbors
	Cap. gr. non-i	1.30	1.20	1.24	.969	.271	.271
		(1.36)	(1.36)	(1.36)	(1.34)	(1.32)	(1.32)
	Lab. gr. non-i	-7.32***	-7.28***	-7.91***	-6.63***	-7.08***	-7.07***
		(2.78)	(2.79)	(2.76)	(2.75)	(2.67)	(2.67)
	Shock i	-.057*	-.044*	-.020	-.025	.050*	.050*
		(.030)	(.023)	(.019)	(.026)	(.029)	(.030)
	Network i	-2.3e-08	-5.7e-07*	.004**	-95.53***	.2.7e-04***	.759***
		(2.9e-07)	(3.0e-07)	(.002)	(20.33)	(3.2e-05)	(.088)
	Sect. Trade i	-.001*	-.001*	-.001*	-9.6e-04*	-.001**	-.001**
		(5.9e-04)	(5.9e-04)	(.5.9e-04)	(5.7e-04)	(5.7e-04)	(5.7e-04)
	Shock*Ntwrk i	6.7e-08	1.4e-07**	.658	10.34***	-6.4e-05**	-.179**
		(5.3e-08)	(6.5e-08)	(1.49)	(3.96)	(2.8e-05)	(.079)
	Shock*Trade i	-1.9e-04	-6.2e-04	-5.2e-04	-8.9e-04	.001	.001
		(.001)	(.001)	(.001)	(.001)	(.001)	(.001)
	Constant	6.02***	6.02***	5.98***	6.06***	5.63***	5.62***
		(.090)	(.090)	(.091)	(.089)	(.096)	(.096)
	N	1,101	1,100	1,099	1,109	1,099	1,099
	Groups	35	35	35	35	35	35
	R2 within	.19	.19	.19	.20	.25	.24
	Sector FE	Yes	Yes	Yes	Yes	Yes	Yes

Table C5 :

 C5 Fixed effect regression of non-i sectors' contribution to aggregate volatility (2007-2009): Controlling for shock to non-i sectors Dependent variable: Non-i sectors' contributions to aggregate volatility

			First-order centrality	Second-order centrality	Local density
		(1)	(2)	(3)	(4)	(5)	(6)	(7)
	Network i :	-	In-degree	Out-degree	Random walk	PageRank centrality	Average degree of a	Local clustering
					centrality		node's	coefficient
							neighbors
	Cap. gr. non-i	1.236	1.271	1.174	1.205	.955	.238	.238
		(1.36)	(1.36)	(1.36)	(1.36)	(1.34)	(1.32)	(1.32)
	Lab. gr. non-i	-7.81***	-7.30***	-7.28***	-7.96***	-6.57**	-7.10***	-7.10***
		(2.74)	(2.79)	(2.79)	(2.76)	(2.74)	(2.68)	(2.68)
	Shock i	-.082***	-.119***	-.106***	-.083***	-.091***	-.011	.012
		(.018)	(.028)	(.022)	(.019)	(.025)	(.030)	(.030)
	Network i	-	-2.7e-08	-5.9e-07**	.004**	-95.37***	2.6e-04***	.735***
			(2.9e-07)	(2.9e-07)	(.001)	(20.33)	(3.1e-05)	(.086)
	Shock*Ntwrk	-	7.0e-08	1.4e-07**	.933	11.08***	-5.5e-05**	-.153**
			(5.3e-08)	(6.5e-08)	(1.48)	(3.89)	(2.7e-05)	(.076)
	Shock Non-i	-1.95***	-1.91***	-1.90***	-1.96***	-1.86***	-1.93***	-1.93***
		(.180)	(.185)	(.185)	(.182)	(.181)	(.177)	(.177)
	Constant	7.07***	6.99***	7.01***	7.09***	6.99***	6.71***	6.71***
		(.478)	(.483)	(.484)	(.482)	(.477)	(.469)	(.469)
	N	1,109	1,101	1,100	1,099	1,109	1,099	1,099
	Groups	35	35	35	35	35	35	35
	R 2 within	.99	.99	.99	.99	.99	.99

Table C6 :

 C6 Estimation of the sectors non-i's contribution to aggregate volatility (2007-2009): Dominant sectors excluded Dependent variable: Non-i sectors' contribution to aggregate volatility

		First-order centrality	Second-order centrality	Local density
		(1)	(2)	(3)	(4)	(5)	(6)
	Network i :	In-degree	Out-degree	Random walk	PageRank	Average	Local
				centrality	centrality	degree of a	clustering
						node's	coefficient
						neighbors
	Cap. gr. non-i	1.33	1.26	1.36	.730	.357	.357
		(1.37)	(1.37)	(1.37)	(1.34)	(1.33)	(1.33)
	Lab. gr. non-i	-7.78***	-7.99***	-8.39***	-7.23***	-8.39***	-8.39***
		(2.83)	(2.88)	(2.83)	(2.76)	(2.74)	(2.74)
	Shock i	-.138***	-.174***	-.129***	-.170***	.023	.023
		(.052)	(.052)	(.039)	(.045)	(.088)	(.088)
	Network i	-1.2e-06*	-1.6e-06***	.004**	-256.1***	.0003***	.768***
		(7.1e-07)	(6.0e-07)	(.002)	(40.6)	(3.4e-05)	(.094)
	Shock*Ntwrk	7.6e-07	1.3e-06*	2.34	144.9***	-5.1e-05	-.144
		(6.3e-07)	(7.0e-07)	(1.55)	(32.5)	(5.8e-05)	(.162)
	Constant	6.21***	6.22***	6.15***	6.33***	5.77***	5.77***
		(.093)	(.092)	(.092)	(.093)	(.101)	(.101)
	N	1058	1056	1056	1065	1056	1056
	Groups	35	35	35	35	35	35
	R2 within	.20	.20	.20	.23	.25	.25
	Sector FE	Yes	Yes	Yes	Yes	Yes	Yes
	Clustd err.	No	No	No	No	No	No
	Values in parentheses are standard errors; *** for

Table C7 .

 C7 Fixed effect regression of non-i sectors' contribution to aggregate volatility (2007-2009): Excluding extreme shock values (i.e. USA) Dependent variable: Non-i sectors' contributions to aggregate volatility

			First-order centrality	Second-order centrality	Local density
		(1)	(2)	(3)	(4)	(5)	(6)	(7)
	Network characteristics of sector i	-	In-degree	Out-degree	Random walk centrality	PageRank centrality	Average degree of a neighbors node's	Local clustering coefficient
	Cap. gr. non-i	1.353	1.326	1.257	1.291	.919	.328	.328
		(1.37)	(1.37)	(1.37)	(1.37)	(1.35)	(1.34)	(1.34)
	Lab. gr. non-i	-7.26**	-6.99**	-6.836**	-7.50***	-6.25**	-7.11**	-7.11**
		(2.81)	(2.84)	(2.86)	(2.83)	(2.74)	(2.74)	(2.74)
	Shock i	-.123***	-.135***	-.159***	-.140***	-.164***	.057	.057
		(.018)	(.051)	(.049)	(.018)	(.045)	(.090)	(.090)
	Network i	-	-3.3e-07	-8.3e-07*	.004**	-152.8***	2.7e-04***	.756***
			(4.9e-07)	(4.7e-07)	(.002)	(27.99)	(3.3e-05)	(.093)
	Shock i *Ntwrk i	-	1.9e-07	5.9e-07	2.197	72.74***	-9.8e-05	-.272
			(4.7e-07)	(4.9e-07)	(1.56)	(24.6)	(6.7e-05)	(.184)
	Constant	6.19***	6.21***	6.22***	6.17***	6.29***	5.81***	5.81***
		(.091)	(.093)	(.093)	(.093)	(.092)	(.100)	(.100)
	N	1,075	1,067	1,066	1,065	1,075	1,065	1,065
	Groups	34	34	34	34	34	34	34
	R 2 within	.19	.19	.19	.20	.22	.24	.24

[START_REF] Carvalho | Aggregate fluctuations and the network structure of intersectoral trade[END_REF],[START_REF] Acemoglu | The network origins of aggregate fluctuations[END_REF]

2015),[START_REF] Contreras | Propagation of economic shocks in input-output networks: A crosscountry analysis[END_REF] and[START_REF] Roson | Input-output linkages and the propagation of domestic productivity shocks: assessing alternative theories with stochastic simulation[END_REF] and[START_REF] Baqaee | The macroeconomic impact of microeconomic shocks: Beyond Hulten's theorem[END_REF] all propose quantitative simulations of theoretical models, usually calibrated with the IO data for the United States. Although traditional input-output multipliers approach could be useful to account for complete systemic contagion effects, the network approach used in this paper allows characterizing more precisely the diversity of impacts that might be associated with one sector and its localization in the national and global production network.

Figure A1 in Appendix IV shows the average values of centrality and local density for all

sectors in our sample of 40 countries, as included in the World Input-Output Database.

See for instance the recent paper by Garbellini et al. (2014) which analyzes the impact of a final demand shock on trade in intermediate goods during the 2008-09 Great Recession.

Our theoretical framework is fairly close to[START_REF] Bems | Vertical linkages and the collapse of global trade[END_REF] which uses a Leontief, demand-driven model as the basis of their empirical test.Kireyev and Leonidov (2015) also develop a network model for international spillover of demand shocks, albeit without looking at the diversification aspect.

in the adjacency matrixrepresents the weight of the edge (link) from node (sector) i to node j. In the next subsection, we discuss the two main patterns of volatility transmission through the production network that are found in the literature.5 Note that the variance-covariance matrix Ω < ) < ) can be further decomposed into diagonal and off-diagonal elements,

Note that in the directed production network, the vector of out-degrees might be assimilated with the vector of sectoral sales which is used to define asymmetry as defined by[START_REF] Gabaix | The granular origins of aggregate fluctuations[END_REF].

As input-output networks are directed, and almost completely connected, with strong self-loops (intra-industry transactions sometimes account more than 50 percent of the sum of a sector's edges), centrality indicators based on shortest paths are in fact meaningless. For instance, "closeness centrality" defined as the mean distance from a node to all other nodes in the network would make little sense in the case of densely connected networks like input-output graphs, and they usually tend to ignore self-loops (i.e., intra-industry transactions).

[START_REF] Borgatti | Centrality and network flow[END_REF] has shown that the movement of goods between sectors is best characterized as a random walk.

It is worth mentioning that V. M. Carvalho is one of the co-authors of[START_REF] Acemoglu | The network origins of aggregate fluctuations[END_REF].[START_REF] Cerina | World input-output network[END_REF] have, for example, used the PageRank Centrality to identify the industries with the largest capacity of influence over other (influential) industries through the chain of indirect linkages.

See Appendix I for detailed demonstration.

Indeed, in the robustness section, we verify that our main findings are not driven by the fact that sector I has a large size in the economy.

We checked for modelling with individual effects through the sequential Hsiao test; we also tested separately for country FE = 0 (F=7.35, pval=.000) and sector FE = 0 (F=5.98, pval=.000); all these tests confirmed that individual fixed effects were required.

Other recent studies using similar country-sector panel settings are[START_REF] Rajan | Aid, Dutch disease, and manufacturing growth[END_REF] andChauvet and Ehrart (2015).

Our definition for ( W is inspired by the "shift-share instrument" initially proposed by[START_REF] Bartik | Who benefits from state and local economic development policies? Upjohn Institute for Employment Research[END_REF] and extensively employed in the empirical literature on labor. However, our definition is different from the predominant specification of the instrument, because the Bartik instrument is principally used to capture labor demand changes for a "region" (usually counties or municipalities) which consists of several operating local industries, while we would like to capture the demand changes for a "sector" in a given region (i.e., country). See[START_REF] Beaudry | In search of labor demand[END_REF] for a recent application of the Bartik instrument in labor economics.

Still, in our model including group fixed effects (country-groups and sector-groups), clustering by groups of countries or sectors is not necessary as our pseudo-treatment (sectoral shock*sectoral network characteristic) is heterogeneous across individuals, meaning that individual, and not group units, are assigned to treatment.

[START_REF] Koren | Technological diversification[END_REF] have documented that emerging economies exhibit lower levels of technological diversification than higher-income economies, that is they dispose of a less diversified set of inputs than developed economies.

Note that for the reasons which were previously discussed, the interaction with RW centrality is not statistically significant, similarly to in the baseline model.

As for first-order degrees, the shock interaction is now statistically significant for in-degree, while it was significant for out-degree in the Table2. It means that idiosyncratic shocks to large input purchasers have, on average, led to lower growth contributions (or possibly output loss) through inter-industry linkages during the period investigated.

Although trade openness and financial development might be affected by the level of economic development, they are probably less prone to be impacted by our dependent variable, i.e., aggregate volatility, as long as the latter does not lead to a reversal of structural policies, which is not a strong assumption given the short-term framework of our empirical analysis. Lastly, as they are measured at country level, these structural policy proxies might not be correlated to other sector-level regressors.

It should be noted that clustering errors by country (TableC1) also enabled concluding that co-movements across sectors within countries do not drive our main findings.

Needless to say that doing this does not undermine the stability of our results against changes in the sample. The results were consistent when high-and middle-income countries samples were separately tested. However, it seems that the US observations have a particular impact on shock transmission in the sample of high-income countries.

This roughly corresponds to a one unit increase in the intensity of shock which is considered in the predicted marginal effects analysis in section 5.2.

does not mean a value of -3 for the PageRank centrality, rather a normalized level.

Although in the absence of a fiscal union, the European Financial Stability Facility might be seen as a first step towards this insurance mechanism, it may, according to some observers, aggravate volatility in peripheral countries rather than relieving it[START_REF] Manasse | The problem with the European stability facility[END_REF].

Appendix A: Sector contribution to aggregate growth volatility

In section 2, we defined aggregate output growth as the weighted sum of sectoral output growth rates, as following:

where W, is the share of sector i,c in the aggregate output of country c in the base year, t0, and W, is the output growth in sector i,c in period t. The standard deviation of W will therefore be:

where 8 9 is the standard deviation of aggregate output growth in country c, 8 W or 8 W is the standard deviation of output growth in sector i or j in country c, and 8 ( W, W) is the covariance between sectors ic and jc. In a vector form, the Eq. (A2) can be written as:

where 5 is a vector of sectoral output shares and Σ is a covariance matrix. Per Euler's theorem, we can suggest that, as Eq. ( A3) is a homogenous function of degree one and continuous and differentiable in W, it can be additively decomposed into the following components: where each

is the marginal contribution to volatility for sector i,c, also called risk contribution (\ W _ ). Equation (iv) can thus be re-written as:

Eq. (A4) can also be expressed as the ratio of covariance between output growth of sector i,c and the aggregate growth of country c, to the standard deviation of country c's aggregate growth. This can be easily seen if we write the Eq. (A4) in the matrix form: Eq. (A7) which is a ratio of the covariance between W and W and the variance of W is principally a beta (slope) of sectoral output growth W versus aggregate output growth W , whose sum would equal 1:

('8)

By definition, ƒ W can also be interpreted as the marginal contribution of sector i,c to aggregate output volatility (8 † ). We can therefore define \ W _ as:

We also know that the correlation between sectoral output growth W and aggregate output growth W is:

Replacing the value of covY W , W Z in Eq. (viii), and putting equations ( A8) and (A9) together, we get:

To express this in total contribution to volatility, and not merely in marginal contribution of a sector, we can write equation (A11) per the additive function expressed in (A5) as:

Appendix B: List of sectors and countries